Showing 1–50 of 287 results for author: Regnault, N

The "Moiré Capacitor Effect" and Stabilization of Fractional Chern Insulators in Rhombohedral Graphene Superlattices

Authors: Nicolas Regnault, Heqiu Li, Yves H. Kwan, B. Andrei Bernevig, Jonah Herzog-Arbeitman

Abstract: While the necessity of a moiré potential for fractional Chern insulators (FCIs) in rhombohedral graphene-hBN superlattices, first predicted in Ref. 1, is now grounded in experiments, a theory of its origin and importance remains at large. We present a mechanism---the moiré capacitor effect---that enhances the moiré potential by electrostatically imprinting the valence charge density onto the condu… ▽ More While the necessity of a moiré potential for fractional Chern insulators (FCIs) in rhombohedral graphene-hBN superlattices, first predicted in Ref. 1, is now grounded in experiments, a theory of its origin and importance remains at large. We present a mechanism---the moiré capacitor effect---that enhances the moiré potential by electrostatically imprinting the valence charge density onto the conduction bands. We derive the analytical form of this term and reveal its crucial role in stabilizing a parent state with Chern number $C=1$ at filling $ν=1$. We propose a parent state theory which posits that stability of the Chern insulator and flatness of its hole excitations are necessary for obtaining FCIs upon doping. We then perform multi-band exact diagonalization calculations to confirm the emergence of FCIs at $ν= 2/3$ in the presence of the moiré capacitor effect. Our FCI state is stabilized by inter-band fluctuations, unlike in the moire-free case which collapses with band-mixing. We provide the first consistent theory for this state in aligned samples and explain its absence in unaligned ones. △ Less

Submitted 12 August, 2026; originally announced August 2026.

Comments: 6 + 55 pages

Composite-Fermion Study of Cavity-Modified Fractional Quantum Hall Excitation Gaps

Authors: Dalin Boriçi, Nicolas Regnault, Cristiano Ciuti

Abstract: We investigate how cavity-mediated attractive electron-electron interactions modify the excitation gaps of fractional quantum Hall states within the composite-fermion framework. We compute both the neutral magnetoroton excitation spectrum and the charged excitation gap relevant to transport experiments for the Laughlin $ν=1/3$ and $ν=1/5$ states. We consider a spin-polarized lowest-Landau-level mo… ▽ More We investigate how cavity-mediated attractive electron-electron interactions modify the excitation gaps of fractional quantum Hall states within the composite-fermion framework. We compute both the neutral magnetoroton excitation spectrum and the charged excitation gap relevant to transport experiments for the Laughlin $ν=1/3$ and $ν=1/5$ states. We consider a spin-polarized lowest-Landau-level model in which the interaction is mediated by a cavity mode with a spatially uniform vacuum-field gradient and a finite interaction range controlled by a long-distance cutoff. Finite-size scaling reveals that the transport gap is consistently enhanced by the cavity-induced interaction, with the gap enhancement scaling quadratically with the electron number and with the fourth power of the vacuum-field gradient. By contrast, the magnetoroton spectrum exhibits a richer dependence on the interaction range. The high-$k$ magnetoroton gap is enhanced for all interaction ranges considered, consistent with its close connection to the charged excitation gap, even with the long-range character of the interaction. △ Less

Submitted 7 July, 2026; originally announced July 2026.

Comments: 21 pages, 11 figures

Three-dimensional Foliated Fractional Quantum Hall Phases

Authors: Sahana Das, Navketan Batra, Andrea Kouta Dagnino, Dan Mao, Nicolas Regnault, Glenn Wagner, Titus Neupert

Abstract: Foliated topological orders in three dimensions are layered systems in which anyons are free to move within a layer but cannot hop between them. A simple model with such a phase is a stack of decoupled two-dimensional electron gases in a strong magnetic field, each in the same fractional quantum Hall state. By focusing on the case of filling $ν=1/3$ of the lowest Landau level in each layer, we sho… ▽ More Foliated topological orders in three dimensions are layered systems in which anyons are free to move within a layer but cannot hop between them. A simple model with such a phase is a stack of decoupled two-dimensional electron gases in a strong magnetic field, each in the same fractional quantum Hall state. By focusing on the case of filling $ν=1/3$ of the lowest Landau level in each layer, we show that (i) the limit of decoupled Laughlin states is stable upon introducing interlayer interactions and (ii) the system can enter a spontaneously layer-trimerized foliated non-Abelian Fibonacci phase. We support our claims by numerical exact diagonalization of up to 10 layers as well as perturbative analytical calculations. Specifically, we show that the foliated Fibonacci phase exists in the 9-layer system with pseudopotential interactions within and between neighboring layers. We identify the phase via quasihole counting and by calculating the overlap with a model wave function which we derive from the associated conformal field theory. Our numerical results suggest the possibility of realizing these phases in layered van der Waals crystals in strong magnetic fields, as well as in multilayer heterostructures. △ Less

Submitted 17 June, 2026; originally announced June 2026.

Dispersion of Anyon Bloch Bands

Authors: Kishore Iyer, Andreas Feuerpfeil, Valentin Crépel, Nicolas Regnault, Christophe Mora

Abstract: Fractional Chern insulators (FCIs) are zero magnetic field analogs of fractional quantum Hall states. While the electrons forming an FCI are not subject to an external magnetic field, their anyonic excitations experience a magnetic field with finite-flux due to a many-body Berry phase, whose lattice periodicity generically induces some dispersion. From Laughlin wavefunctions at filling 1/m, we ana… ▽ More Fractional Chern insulators (FCIs) are zero magnetic field analogs of fractional quantum Hall states. While the electrons forming an FCI are not subject to an external magnetic field, their anyonic excitations experience a magnetic field with finite-flux due to a many-body Berry phase, whose lattice periodicity generically induces some dispersion. From Laughlin wavefunctions at filling 1/m, we analytically construct single-anyon Bloch states in an ideal band, providing a basis to efficiently compute the dispersion. The anyon spectrum exhibits an $m$-fold degeneracy in the reduced magnetic Brillouin zone (BZ), which originates from the topological degeneracy of the FCI. From our wavefunctions, we derive the m^2-fold degeneracy seen in previous works, showing it to be a splicing of anyon momenta into the electronic BZ. Finally, we find that the anyon dispersion bandwidth is controlled by quantum geometry non-uniformity, growing linearly at weak modulation and saturating at strong modulation. Remarkably, higher harmonics of the quantum geometry alone strongly suppress the dispersion, which we attribute to emergent magnetic translation symmetries. When combined with the first harmonic, a positive (negative) second harmonic drives the system toward a second- (first-) harmonic-dominated regime, thereby reducing (enhancing) the bandwidth. Our results offer an analytically controlled method for evaluating anyon spectra in ideal band FCI, shedding light on how non-uniform quantum geometry and emergent symmetries shape the dispersion of anyons. △ Less

Submitted 27 April, 2026; originally announced April 2026.

Magnetic Signatures of a Putative Fractional Topological Insulator in Twisted MoTe2

Authors: Yiping Wang, Gillian E. Minarik, Weijie Li, Yves Kwan, Shuai Yuan, Eric Anderson, Chaowei Hu, Julian Ingham, Jeongheon Choe, Takashi Taniguchi, Kenji Watanabe, Xavier Roy, Jiun-Haw Chu, Raquel Queiroz, James C. Hone, N. Regnault, Xiaodong Xu, Xiaoyang Zhu

Abstract: The interplay among electronic correlation, topology, and time-reversal-symmetry (TRS) often leads to exotic quantum states of matter, as highlighted by the discoveries of fractional Chern insulators (FCIs) in twisted bilayer MoTe2 (tMoTe2). Among the FCIs in tMoTe2, the most robust is at a hole filling factor of v=-2/3 per moiré unit cell. Here, employing pump-probe circular dichroism (CD) measur… ▽ More The interplay among electronic correlation, topology, and time-reversal-symmetry (TRS) often leads to exotic quantum states of matter, as highlighted by the discoveries of fractional Chern insulators (FCIs) in twisted bilayer MoTe2 (tMoTe2). Among the FCIs in tMoTe2, the most robust is at a hole filling factor of v=-2/3 per moiré unit cell. Here, employing pump-probe circular dichroism (CD) measurement on tMoTe2 at twist angles (3.9 and 3.7 degrees), we show that a correlated state at v =-4/3 exhibits an unusual Ising antiferromagnet behavior. The v =-4/3 state with no net magnetization undergoes first order phase transitions at extremely low magnetic fields of ~ 2-6 mT to partially valley polarized (PVP) states. This behavior is notably absent for all other correlated states in tMoTe2 and also disappears for v =-4/3 at higher or lower twist angles (4.0 or 3.3 degree). The observed magnetic signature is consistent with a theoretically proposed fractional topological insulator (FTI), consisting of two copies of v =-2/3 FCIs with opposite chirality in the two K valleys. The experimental results are supported by interacting continuum model calculations that reveal the extreme closeness in energy ( < 1 meV) between the putative FTI and PVP states. Our findings present a candidate FTI with TRS and call for advanced transport and imaging measurements to establish the quantized helical edge modes. △ Less

Submitted 27 March, 2026; v1 submitted 26 January, 2026; originally announced January 2026.

Comments: 46 pages, 4 figures, and 14 SI figures

Study of the anisotropy of cosmic expansion on ZTF type Iasupernovae simulations

Authors: C. Barjou-Delayre, P. Rosnet, C. Ravoux, M. Aubert, M. Ginolin, R. Kebadian, M. Amenouche, J. Bautista, U. Burgaz, B. Carreres, J. Castaneda Jaimes, G. Dimitriadis, F. Feinstein, D. Fouchez, L. Galbany, C. Ganot, M. Graham, S. L. Groom, A. Goobar, J. Johansson, M. M. Kasliwal, Y-L. Kim, T. E. Müller-Bravo, B. Popovic, B. Racine , et al. (7 additional authors not shown)

Abstract: The cosmological principle assumes the isotropy of the Universe at large scales. It is a foundational assumption in the $Λ$CDM model, which is the current standard model of cosmology. Recent tensions give legitimacy to investigating the possibility of anisotropies in the Universe. The large sky coverage achieved by the Zwicky Transient Facility survey (ZTF) allows us to test the veracity of the co… ▽ More The cosmological principle assumes the isotropy of the Universe at large scales. It is a foundational assumption in the $Λ$CDM model, which is the current standard model of cosmology. Recent tensions give legitimacy to investigating the possibility of anisotropies in the Universe. The large sky coverage achieved by the Zwicky Transient Facility survey (ZTF) allows us to test the veracity of the cosmological principle using observations of Type Ia supernovae (SNe Ia). In this article, we develop a methodology to measure potential anisotropies in the Hubble constant $H_0$. We test our method on realistic simulations of the second data release (DR2) of ZTF SNe Ia in which we introduce a dipole. We develop an unbiased method both to introduce a dipole in the simulations and to recover it. We test a potential $H_0$ dependency of our method while varying the dipole amplitude. We analyse the impact of introducing large-scale structures in the simulations and the efficiency of using a volume-limited sample, which is an unbiased subsample of the ZTF SNe Ia sample. Finally, we build an error model applied to the recovered dipole amplitude ($ΔH_0$) and its direction ($α_0$, $δ_0$). Our analysis allows us to recover a dipole with an error on the amplitude of $0.33\,\mathrm{km\,s^{-1}\,Mpc^{-1}}$, and uncertainties of $3.4^\circ$ and $6.1^\circ$ on the right ascension and declination, respectively, for an initial dipole amplitude of $ΔH_0 = 3\,\mathrm{km\,s^{-1}\,Mpc^{-1}}$. The resulting dipole is independent of the chosen $H_0$ value and sky coverage. This paper paves the way for a future precise ZTF dipole investigation. △ Less

Submitted 16 January, 2026; originally announced January 2026.

Comments: 13 pages and 16 figures

Does Moire Matter? Critical Moire Dependence with Quantum Fluctuations in Graphene Based Integer and Fractional Chern Insulators

Authors: Zihao Huo, Wenxuan Wang, Jian Xie, Yves H. Kwan, Jonah Herzog-Arbeitman, Zaizhe Zhang, Qiu Yang, Min Wu, Kenji Watanabe, Takashi Taniguchi, Kaihui Liu, Nicolas Regnault, B. Andrei Bernevig, Xiaobo Lu

Abstract: Rhombohedral multilayer graphene has emerged as a powerful platform for investigating flat-band-driven correlated phenomena, yet most aspects remain not understood. In this work, we systematically study the moire-dependent band topology in rhombohedral hexalayer graphene. For the first time we demonstrate that the moire twist angle plays a crucial role in the formation of the moire Chern insulator… ▽ More Rhombohedral multilayer graphene has emerged as a powerful platform for investigating flat-band-driven correlated phenomena, yet most aspects remain not understood. In this work, we systematically study the moire-dependent band topology in rhombohedral hexalayer graphene. For the first time we demonstrate that the moire twist angle plays a crucial role in the formation of the moire Chern insulators in rhombohedral hexalayer graphene/hexagonal boron nitride (RHG/hBN) moire superlattices. In the moire-distant regime at filling factor v = 1, only systems with a twist angle θ < 1.1° exhibit an integer moire Chern insulator, while the fractional Chern insulator at v = 2/3 requires smaller twist angle to be stabilized. Our theoretical modelling, which includes quantum fluctuations and exact diagonalization results, suggests that mean-field theory, which has been widely adopted, does not explain the twist-angle dependence of the v = 1 phase diagram, and that correlation effects are crucial. Moreover, we realize two distinct stacking configurations ( /Xi=0 and /Xi=1) between graphene and hBN, and find that both cases can yield a Chern insulator at v = 1. Our experimental work upends the current mean-field paradigm, illuminates how quantum fluctuations and moiré effects shape the RHG/hBN phase diagram, and paves the way for future understanding and engineering of topological correlated states in rhombohedral graphene moire systems. △ Less

Submitted 17 October, 2025; originally announced October 2025.

Chern-Selective multi-valley Flat Bands in Twisted Mono-Bilayer and Mono-Trilayer MoTe$_2$

Authors: Ziyue Qi, Hanqi Pi, Yan Zhang, Jiaxuan Liu, Nicolas Regnault, Hongming Weng, B. Andrei Bernevig, Jiabin Yu, Quansheng Wu

Abstract: The interplay between moiré flat bands originating from different valleys can give rise to a variety of exotic quantum phases. In this work, we investigate the electronic properties of twisted mono-bilayer (A-AB) and mono-trilayer (A-ABA) MoTe$_2$ using first-principles calculations and continuum models. Unlike previous studies on twisted bilayer systems, in which low-energy flat bands originate s… ▽ More The interplay between moiré flat bands originating from different valleys can give rise to a variety of exotic quantum phases. In this work, we investigate the electronic properties of twisted mono-bilayer (A-AB) and mono-trilayer (A-ABA) MoTe$_2$ using first-principles calculations and continuum models. Unlike previous studies on twisted bilayer systems, in which low-energy flat bands originate solely from the $K/K'$ valleys, in A-AB and A-ABA twisted MoTe$_2$ (\tmt) the moiré bands at low energies arise from both the $Γ$ and $K/K'$ valleys, with spin Chern numbers $C_s=0$ (for $Γ$) and $C_{\uparrow/\downarrow}=\pm1$ (for $K/K'$), respectively. We show that the multi-valley moiré flat bands are governed by interlayer-hybridization effects, and that different stacking configurations and thicknesses tune the relative energy alignment between the $Γ$ and $K$ valley moiré flat bands. By constructing valley-resolved continuum models and performing Wannierization for the low-energy moiré bands, we further uncover that the Berry curvature and quantum metric distributions can be effectively tuned by the layer number and stacking configuration. Unlike other moiré systems, where only one kind of valley influenced the low energy physics, the simultaneous appearance of two distinct types of valleys, with different symmetries, establish A-AB and A-ABA \tmt\ as ideal platforms for studying layer-controlled multi-valley physics. △ Less

Submitted 14 October, 2025; originally announced October 2025.

Journal ref: Phys. Rev. B 113, 125116 (2026)

Obtaining the Spectral Function of Moiré Graphene Heavy-Fermions Using Iterative Perturbation Theory

Authors: Dumitru Călugăru, Haoyu Hu, Lorenzo Crippa, Gautam Rai, Nicolas Regnault, Tim O. Wehling, Roser Valentí, Giorgio Sangiovanni, B. Andrei Bernevig

Abstract: The spectral functions of twisted bilayer graphene (TBG) in the absence of strain have recently been investigated in both the symmetric and symmetry-broken phases using dynamical mean-field theory (DMFT). The theoretically predicted Mott-Hubbard bands and gapless semimetallic state at half-filling have since been confirmed experimentally. Here, we develop several second-order perturbation theory a… ▽ More The spectral functions of twisted bilayer graphene (TBG) in the absence of strain have recently been investigated in both the symmetric and symmetry-broken phases using dynamical mean-field theory (DMFT). The theoretically predicted Mott-Hubbard bands and gapless semimetallic state at half-filling have since been confirmed experimentally. Here, we develop several second-order perturbation theory approaches to the topological heavy-fermion (THF) model of TBG and twisted symmetric trilayer graphene (TSTG). In the symmetric phase, we adapt, implement, and benchmark an iterative perturbation theory (IPT) impurity solver within DMFT, enabling computationally efficient yet accurate spectral function calculations. We present momentum- and energy-resolved spectra over a broad range of temperatures and fillings for both symmetric and symmetry-broken states. In addition, we derive analytic expressions for the spectral function within the ``Hubbard-I'' approximation of the THF model and, as expected, find that while it provides a tractable description of Mott physics, it does not capture the low-energy Kondo peak or the finite lifetime broadening of the bands. Our methodology can be extended to include strain, lattice relaxation, and parameter variations, thereby allowing systematic predictions of TBG and TSTG spectral properties across a wide range of physical regimes. Because our perturbative approaches are far less computationally intensive than DMFT with numerically exact impurity solvers, they can be used to efficiently benchmark and scan extensive phase diagrams of the THF parameters, paving the way for full DMFT analyses of the TBG spectral function in the presence of strain and relaxation. △ Less

Submitted 22 September, 2025; originally announced September 2025.

Comments: 21+106 pages, 5+71 figures, 0+4 tables. See also arXiv:2402.14057

Critical Majorana fermion at a topological quantum Hall bilayer transition

Authors: Cristian Voinea, Wei Zhu, Nicolas Regnault, Zlatko Papić

Abstract: Quantum Hall bilayers are a uniquely tunable platform that can realize continuous transitions between distinct topological phases of matter. One prominent example is the transition between the Halperin state and the Moore--Read Pfaffian, long predicted to host a critical theory of Majorana fermions but so far not verified in unbiased microscopic simulations. Using the fuzzy sphere regularization,… ▽ More Quantum Hall bilayers are a uniquely tunable platform that can realize continuous transitions between distinct topological phases of matter. One prominent example is the transition between the Halperin state and the Moore--Read Pfaffian, long predicted to host a critical theory of Majorana fermions but so far not verified in unbiased microscopic simulations. Using the fuzzy sphere regularization, we identify the low-energy spectrum at this transition with the 3D gauged Majorana conformal field theory. We show that the transition is driven by the closing of the neutral fermion gap, and we directly extract the operator content in both integer and half-integer spin sectors. Our results resolve the long-standing question of the nature of a topological phase transition in a setting relevant to quantum Hall experiments, while also providing the first realization of a fermionic theory on the fuzzy sphere, previously limited to bosonic theories. △ Less

Submitted 25 March, 2026; v1 submitted 9 September, 2025; originally announced September 2025.

Comments: 8 pages, 4 figures (main text); 6 pages, 4 figures (supplemental material)

Journal ref: Phys. Rev. Lett. 136, 076601 (2026)

ZTF SNe Ia DR2: Towards cosmology-grade ZTF supernova light curves using scene modeling photometry

Authors: L. Lacroix, N. Regnault, T. de Jaeger, M. Le Jeune, M. Betoule, J. -M. Colley, M. Bernard, M. Rigault, M. Smith, A. Goobar, K. Maguire, G. Dimitriadis, J. Nordin, J. Johansson, M. Aubert, C. Barjou, E. C. Bellm, S. Bongard, U. Burgaz, B. Carreres, D. Fouchez, F. Feinstein, L. Galbany, M. Ginolin, M. Graham , et al. (14 additional authors not shown)

Abstract: The Zwicky Transient Facility (ZTF) is conducting a wide-field survey of the northern sky in three optical bands and the collaboration cosmology working group has released 3628 spectroscopically confirmed Type Ia supernovae (SNe Ia) discovered during its first 2.5 years of operation. This "ZTF SN Ia DR2" sample is the largest SN Ia dataset to date. Fully exploiting this dataset to improve unders… ▽ More The Zwicky Transient Facility (ZTF) is conducting a wide-field survey of the northern sky in three optical bands and the collaboration cosmology working group has released 3628 spectroscopically confirmed Type Ia supernovae (SNe Ia) discovered during its first 2.5 years of operation. This "ZTF SN Ia DR2" sample is the largest SN Ia dataset to date. Fully exploiting this dataset to improve understanding of the properties of dark energy requires a photometric accuracy of O(0.1%). This can be achieved using Scene Modeling Photometry (SMP), which is optimal to extract a transient signal (SN) from a complex background (its host), while ensuring a common flux estimator with nearby stars used as calibration reference. In this paper, we present the status of the SMP development and use it to assess the precision and accuracy of the ZTF SN Ia DR2 force photometry light curves. We reach a repeatability of the star observations better than 1%. However, we have identified a new sensor effect, dubbed "pocket-effect", which distorts the Point Spread Function (PSF) in a flux-dependent manner leading to non-linearities in the photometry of a few percent. Correcting for this effect requires time- and sensor-dependent corrections to be applied at the pixel level, which is currently under development. This effects affects all light curve releases to date -- both from forced photometry and scene modelling preventing ZTF SN Ia DR2 to be used for accurate cosmological inference. Comparing the SMP and forced photometry measurements, we find that stretch and color estimated from both processings are consistent, aside from a 10 mmag shift in color. This assess the robustness of results presented as part of the the ZTF SN Ia DR2 release. The absolute calibration however shifts by 90 mmag. A reprocessing of the full ZTF SN Ia DR2 dataset using the SMP method is currently in progress. △ Less

Submitted 4 September, 2025; originally announced September 2025.

Comments: ZTF SN Ia DR2: photometry paper, Submitted to A&A

Symmetry Resolved Entanglement Entropy in a Non-Abelian Fractional Quantum Hall State

Authors: Mark J. Arildsen, Valentin Crépel, Nicolas Regnault, Benoit Estienne

Abstract: Symmetry-resolved entanglement entropy provides a powerful framework for probing the internal structure of quantum many-body states by decomposing entanglement into contributions from distinct symmetry sectors. In this work, we apply matrix product state techniques to study the bosonic, non-Abelian Moore-Read quantum Hall state, enabling precise numerical evaluation of both the full counting stati… ▽ More Symmetry-resolved entanglement entropy provides a powerful framework for probing the internal structure of quantum many-body states by decomposing entanglement into contributions from distinct symmetry sectors. In this work, we apply matrix product state techniques to study the bosonic, non-Abelian Moore-Read quantum Hall state, enabling precise numerical evaluation of both the full counting statistics and symmetry-resolved entanglement entropies. Our results reveal an approximate equipartition of entanglement among symmetry sectors, consistent with theoretical expectations and subject to finite-size corrections. The results also show that these expectations for symmetry-resolved entanglement entropy remain valid in the case of a non-Abelian state where the topological sectors cannot be distinguished by the Abelian $\mathrm{U}(1)$ symmetry alone, and where neutral and charged modes possess distinct velocities. We additionally perform a detailed comparison of the entanglement spectrum with predictions from the Li-Haldane conjecture, finding remarkable agreement, and enabling a more precise understanding of the effects of the distinct neutral and charged velocities. This not only provides a stringent test of the conjecture but also highlights its explanatory power in understanding the origin and structure of finite-size effects across different symmetry sectors. △ Less

Submitted 7 August, 2025; originally announced August 2025.

Comments: 28 pages, 21 figures, 6 tables

Journal ref: Phys. Rev. B 113, 075108 (2026)

Higher Chern bands in helical homotrilayer transition metal dichalcogenides

Authors: Jungho Daniel Choi, Nicolás Morales-Durán, Yves H. Kwan, Andrew J. Millis, Nicolas Regnault, Daniele Guerci

Abstract: We propose helically twisted homotrilayer transition metal dichalcogenides as a platform for realizing correlated topological phases of matter with higher and tunable Chern numbers. We show that a clear separation of scales emerges for small twist angles, allowing us to derive a low-energy continuum model that captures the physics within moiré-scale domains. We identify regimes of twist angle and… ▽ More We propose helically twisted homotrilayer transition metal dichalcogenides as a platform for realizing correlated topological phases of matter with higher and tunable Chern numbers. We show that a clear separation of scales emerges for small twist angles, allowing us to derive a low-energy continuum model that captures the physics within moiré-scale domains. We identify regimes of twist angle and displacement field for which the highest-lying hole band is isolated from other bands and is topological with $K$-valley Chern number $C=-2$. We demonstrate that varying the displacement field can induce a transition from $C=-2$ to $C=-1$, as well as from a topologically trivial band to a $C=-1$ band. We derive an effective tight-binding description for a high-symmetry stacking domain which is valid for a wide range of twist angles, and we show that the $C=-2$ band can remain stable at filling fraction $ν=-1$ in the presence of interactions in Hartree-Fock calculations. △ Less

Submitted 20 November, 2025; v1 submitted 23 July, 2025; originally announced July 2025.

Comments: 30 pages, 19 figures. Published version

Journal ref: Phys. Rev. B 112, 205122 (2025)

Spinless and spinful charge excitations in moiré Fractional Chern Insulators

Authors: Miguel Gonçalves, Juan Felipe Mendez-Valderrama, Jonah Herzog-Arbeitman, Jiabin Yu, Xiaodong Xu, Di Xiao, B. Andrei Bernevig, Nicolas Regnault

Abstract: Fractionally charged elementary excitations, the quasi-electron and quasi-hole, are one of the hallmarks of the fractional Chern insulator (FCI). In this work, we observe that spontaneous spin polarization in twisted MoTe$_2$ leads to multiple species of low-energy quasi-particles distinguished by their spin quantum numbers. We perform large-scale exact diagonalization (ED) calculations to investi… ▽ More Fractionally charged elementary excitations, the quasi-electron and quasi-hole, are one of the hallmarks of the fractional Chern insulator (FCI). In this work, we observe that spontaneous spin polarization in twisted MoTe$_2$ leads to multiple species of low-energy quasi-particles distinguished by their spin quantum numbers. We perform large-scale exact diagonalization (ED) calculations to investigate the nature of these excitations and develop a method to extract their fundamental energetic properties. Focusing on $θ= 3.7^{\circ}$ and filling factor $ν= -2/3$ relevant to recent experiments, we show that spin-preserving (spinless) charge excitations have smaller gap than spin-flipping (spinful) excitations both with and without band mixing. This result is in qualitative agreement with the measured magnetic field dependence of the transport gaps. Beyond the spinless and spinful quasi-particle gaps, we extract the full quasi-electron and quasi-hole ``band structure'' and find significant dispersion with emergent magnetic translation symmetry -- a fundamental departure from the immobile excitations of the quantum Hall fluid. Our results establish a framework for computing the properties of novel elementary excitations in FCIs. △ Less

Submitted 5 June, 2025; originally announced June 2025.

Multi-Band Exact Diagonalization and an Iteration Approach to Hunt For Fractional Chern Insulators in Rhombohedral Multilayer Graphene

Authors: Heqiu Li, B. Andrei Bernevig, Nicolas Regnault

Abstract: We perform a multi-band exact diagonalization (ED) study of rhombohedral pentalayer graphene twisted on hexagonal boron nitride with a focus on fractional Chern insulators (FCI) in systems with weak moiré gaps, complementing the results of [Yu et al., arXiv:2407.13770]. We consider both the charge-neutrality (CN) and average (AVE) interaction schemes. Saliently and surprisingly, we now find using… ▽ More We perform a multi-band exact diagonalization (ED) study of rhombohedral pentalayer graphene twisted on hexagonal boron nitride with a focus on fractional Chern insulators (FCI) in systems with weak moiré gaps, complementing the results of [Yu et al., arXiv:2407.13770]. We consider both the charge-neutrality (CN) and average (AVE) interaction schemes. Saliently and surprisingly, we now find using the particle entanglement spectrum that the FCI at filling factor 1/3 in the CN scheme predicted by single-(Hartree-Fock) band ED is unstable towards a transition to charge density wave once a small fraction of electrons is allowed to occupy the higher bands. Meanwhile, the FCI at filling 2/3 in the AVE scheme remains more robust under similar band mixing until being suppressed when increasing band mixing. To tackle truncation errors that arise from including multiple bands in larger system sizes, we propose an ED iteration method that iteratively optimizes the single-particle basis so that the particles in the ground state should reside mainly in the lowest band. Nevertheless, we find that the FCI gap remains absent after convergence when the mixing with higher bands is considered. These findings highlight the delicate sensitivity of FCIs to multi-band effects and the shortcoming of all of the current models to explain the experimental emergence of such phases. △ Less

Submitted 28 April, 2025; originally announced April 2025.

Journal ref: Phys. Rev. B 112, 075130 (2025)

Observation of High-Temperature Dissipationless Fractional Chern Insulator

Authors: Heonjoon Park, Weijie Li, Chaowei Hu, Christiano Beach, Miguel Gonçalves, Juan Felipe Mendez-Valderrama, Jonah Herzog-Arbeitman, Takashi Taniguchi, Kenji Watanabe, David Cobden, Liang Fu, B. Andrei Bernevig, Nicolas Regnault, Jiun-Haw Chu, Di Xiao, Xiaodong Xu

Abstract: The fractional quantum anomalous Hall effect has recently been experimentally observed in zero-field fractional Chern insulators (FCI). However, an outstanding challenge is the presence of a substantial longitudinal resistance $R_{xx}$ (a few k$Ω$), even though the anomalous Hall resistance $R_{xy}$ is quantized. This dissipative behavior is likely linked to imperfect sample quality. Here, we repo… ▽ More The fractional quantum anomalous Hall effect has recently been experimentally observed in zero-field fractional Chern insulators (FCI). However, an outstanding challenge is the presence of a substantial longitudinal resistance $R_{xx}$ (a few k$Ω$), even though the anomalous Hall resistance $R_{xy}$ is quantized. This dissipative behavior is likely linked to imperfect sample quality. Here, we report transport measurements of a drastically improved twisted $\text{MoTe}_2$ bilayer device, which exhibits quantized $R_{xy}$ and vanishing $R_{xx}$ for the $-2/3$ state, marking a dissipationless FCI. Contrary to fractional quantum Hall states where the energy gap increases with magnetic field, we find that the thermal activation gap of the observed FCI states decreases rapidly as the magnetic field rises from zero, then plateaus above a few teslas. This observation is attributed to the interplay between spin and charge gaps. Due to the spontaneous ferromagnetism, the spin gap dominates at low field, while the charge gap becomes appreciable once the magnetic field freezes spin fluctuations. For the $-2/3$ state, we estimate the spin and FCI gap of about 55 and 20 K, respectively. Our results provide insights into the energy scale of FCI and offer a pathway for quantum engineering of exotic correlated topological states. △ Less

Submitted 13 March, 2025; originally announced March 2025.

Comments: 27 pages, 4 figures

Fractional topological states in rhombohedral multilayer graphene modulated by kagome superlattice

Authors: Yanran Shi, Bo Xie, Fengfan Ren, Xinyu Cai, Zhongqing Guo, Qiao Li, Xin Lu, Nicolas Regnault, Zhongkai Liu, Jianpeng Liu

Abstract: Fractional quantum anomalous Hall effects realized in twisted bilayer MoTe$_2$ and multilayer-graphene-based moiré heterostructures have captured a tremendous growth of interest. In this work, we propose that rhombohedral multilayer graphene coupled with an artificial kagome superlattice potential is a new platform to realize various fractional topological phases. Taking Bernal bilayer graphene as… ▽ More Fractional quantum anomalous Hall effects realized in twisted bilayer MoTe$_2$ and multilayer-graphene-based moiré heterostructures have captured a tremendous growth of interest. In this work, we propose that rhombohedral multilayer graphene coupled with an artificial kagome superlattice potential is a new platform to realize various fractional topological phases. Taking Bernal bilayer graphene as the simplest example, when it is placed on top of a prepatterned SiO$_2$ substrate with periodic arrays of holes arranged into kagome lattice, the system would be subject to a tunable kagome superlattice potential once an electrostatic voltage drop between the top and bottom gates is applied. Then, we theoretically study the electronic band structures, topological properties, and quantum geometric properties of the Bloch states of Bernal bilayer graphene coupled with a realistic kagome superlattice potential, which is well benchmarked by transport measurements in the weak superlattice-potential regime. We find that the system may exhibit nearly ideal topological flat bands in a substantial region of the parameter space spanned by superlattice constant and electrostatic potential strength. When these topological flat bands are fractionally filled, exact diagonalization calculations suggest that the system would exhibit rich fractional topological phases at 1/3, 2/3, 2/5, 3/5 and 1/2 fillings including both fractional Chern insulators and anomalous composite Fermi liquids under zero magnetic field. △ Less

Submitted 14 March, 2025; v1 submitted 24 February, 2025; originally announced February 2025.

Comments: 5 pages main text, 16 pages Supplemental Materials

Kekulé Spiral Order from Strained Topological Heavy Fermions

Authors: Jonah Herzog-Arbeitman, Dumitru Călugăru, Haoyu Hu, Jiabin Yu, Nicolas Regnault, Jian Kang, B. Andrei Bernevig, Oskar Vafek

Abstract: The topological heavy fermion (THF) model of twisted bilayer graphene is a framework for treating its strongly interacting topological flat bands. In this work, we employ the THF model with heterostrain and particle-hole symmetry breaking corrections to study its symmetry-broken ground states. We find that the heterostrain correction motivates a specific parent-state wavefunction which dictates th… ▽ More The topological heavy fermion (THF) model of twisted bilayer graphene is a framework for treating its strongly interacting topological flat bands. In this work, we employ the THF model with heterostrain and particle-hole symmetry breaking corrections to study its symmetry-broken ground states. We find that the heterostrain correction motivates a specific parent-state wavefunction which dictates the presence or absence of an incommensurate Kekulé spiral (IKS) at each integer filling by invoking Dirac node braiding and annihilation as a mechanism to achieve low energy gapped states. We then show that one-shot Hartree-Fock faithfully replicates the numerical results of fully self-consistent states and motivates an analytical approximation for the IKS wavevector. We can also account for the particle-hole asymmetry in the correlated insulator gaps. In particular, the THF model predicts stronger correlated states on the electron side rather than hole side in agreement with magic angle experiments, despite the electron side being more dispersive in the single-particle band structure. This work demonstrates that we can analytically explain even the more subtle symmetry breaking order properties observed in experiments where heterostrain, relaxation, and interactions together determine the ground state. △ Less

Submitted 18 February, 2025; v1 submitted 12 February, 2025; originally announced February 2025.

Journal ref: Phys. Rev. B 112, 125129, 9/15/2025

Regularizing 3D conformal field theories via anyons on the fuzzy sphere

Authors: Cristian Voinea, Ruihua Fan, Nicolas Regnault, Zlatko Papić

Abstract: Recently introduced ''fuzzy sphere'' method has enabled accurate numerical regularizations of certain three-dimensional (3D) conformal field theories (CFTs). The regularization is provided by the non-commutative geometry of the lowest Landau level filled by electrons, such that the charge is trivially gapped due to the Pauli exclusion principle at filling factor $ν=1$, while the electron spins enc… ▽ More Recently introduced ''fuzzy sphere'' method has enabled accurate numerical regularizations of certain three-dimensional (3D) conformal field theories (CFTs). The regularization is provided by the non-commutative geometry of the lowest Landau level filled by electrons, such that the charge is trivially gapped due to the Pauli exclusion principle at filling factor $ν=1$, while the electron spins encode the desired CFT. Successful applications of the fuzzy sphere to paradigmatic CFTs, such as the 3D Ising model, raise an important question: how finely tuned does the underlying electron system need to be? Here, we show that the 3D Ising CFT can also be realized at fractional electron fillings. In such cases, the CFT spectrum is intertwined with the charge-neutral spectrum of the underlying fractional quantum Hall (FQH) state -- a feature that is trivially absent in the previously studied $ν=1$ case. Remarkably, we show that the mixing between the CFT spectrum and the FQH spectrum is strongly suppressed within the numerically-accessible system sizes. Moreover, we demonstrate that the CFT critical point is unaffected by the exchange statistics of the particles and by the nature of topological order in the charge sector. Our results set the stage for the fuzzy-sphere exploration of conformal critical points between topologically-ordered states. △ Less

Submitted 24 July, 2025; v1 submitted 22 November, 2024; originally announced November 2024.

Comments: 16 pages, 15 figures

Journal ref: Phys. Rev. X 15, 031007 (2025)

2D Theoretically Twistable Material Database

Authors: Yi Jiang, Urko Petralanda, Grigorii Skorupskii, Qiaoling Xu, Hanqi Pi, Dumitru Călugăru, Haoyu Hu, Jiaze Xie, Rose Albu Mustaf, Peter Höhn, Vicky Haase, Maia G. Vergniory, Martin Claassen, Luis Elcoro, Nicolas Regnault, Jie Shan, Kin Fai Mak, Dmitri K. Efetov, Emilia Morosan, Dante M. Kennes, Angel Rubio, Lede Xian, Claudia Felser, Leslie M. Schoop, B. Andrei Bernevig

Abstract: The study of twisted two-dimensional (2D) materials, where twisting layers create moiré superlattices, has opened new opportunities for investigating topological phases and strongly correlated physics. While systems such as twisted bilayer graphene (TBG) and twisted transition metal dichalcogenides (TMDs) have been extensively studied, the broader potential of a seemingly infinite set of other twi… ▽ More The study of twisted two-dimensional (2D) materials, where twisting layers create moiré superlattices, has opened new opportunities for investigating topological phases and strongly correlated physics. While systems such as twisted bilayer graphene (TBG) and twisted transition metal dichalcogenides (TMDs) have been extensively studied, the broader potential of a seemingly infinite set of other twistable 2D materials remains largely unexplored. In this paper, we define "theoretically twistable materials" as single- or multi-layer structures that allow for the construction of simple continuum models of their moiré structures. This excludes, for example, materials with a "spaghetti" of bands or those with numerous crossing points at the Fermi level, for which theoretical moiré modeling is unfeasible. We present a high-throughput algorithm that systematically searches for theoretically twistable semimetals and insulators based on the Topological 2D Materials Database. By analyzing key electronic properties, we identify thousands of new candidate materials that could host rich topological and strongly correlated phenomena when twisted. We propose representative twistable materials for realizing different types of moiré systems, including materials with different Bravais lattices, valleys, and strength of spin-orbital coupling. We provide examples of crystal growth for several of these materials and showcase twisted bilayer band structures along with simplified twisted continuum models. Our results significantly broaden the scope of moiré heterostructures and provide a valuable resource for future experimental and theoretical studies on novel moiré systems. △ Less

Submitted 14 November, 2024; originally announced November 2024.

Comments: 15+81 pages, 5+187 figures, 4+104 tables. The Topological 2D Materials Database is available at https://topologicalquantumchemistry.com/topo2d/index.html . See also the accompanying paper "Two-dimensional Topological Quantum Chemistry and Catalog of Topological Materials"

Two-dimensional Topological Quantum Chemistry and Catalog of Topological Materials

Authors: Urko Petralanda, Yi Jiang, B. Andrei Bernevig, Nicolas Regnault, Luis Elcoro

Abstract: We adapt the topological quantum chemistry formalism to layer groups, and apply it to study the band topology of 8,872 entries from the computational two-dimensional (2D) materials databases C2DB and MC2D. In our analysis, we find 4,073 topologically non-trivial or obstructed atomic insulator entries, including 905 topological insulators, 602 even-electron number topological semimetals, and 1,003… ▽ More We adapt the topological quantum chemistry formalism to layer groups, and apply it to study the band topology of 8,872 entries from the computational two-dimensional (2D) materials databases C2DB and MC2D. In our analysis, we find 4,073 topologically non-trivial or obstructed atomic insulator entries, including 905 topological insulators, 602 even-electron number topological semimetals, and 1,003 obstructed atomic insulators. We thus largely expand the library of known topological or obstructed materials in two dimensions, beyond the few hundreds known to date. We additionally classify the materials into four categories: experimentally existing, stable, computationally exfoliated, and not stable. We present a detailed analysis of the edge states emerging in a number of selected new materials, and compile a Topological 2D Materials Database (2D-TQCDB) containing the band structures and detailed topological properties of all the materials studied in this work. The methodology here developed is implemented in new programs available to the public, designed to study the topology of any non-magnetic monolayer or multilayer 2D material. △ Less

Submitted 13 November, 2024; originally announced November 2024.

Comments: 167 pages, 21 figures, 28 tables. The Topological 2D Materials Database is available at https://www.topologicalquantumchemistry.org/topo2d/index.html . The new programs on the Bilbao Crystallographic Server is available at https://www.cryst.ehu.es/

Universal Moiré-Model-Building Method without Fitting: Application to Twisted MoTe$_2$ and WSe$_2$

Authors: Yan Zhang, Hanqi Pi, Jiaxuan Liu, Wangqian Miao, Ziyue Qi, Nicolas Regnault, Hongming Weng, Xi Dai, B. Andrei Bernevig, Quansheng Wu, Jiabin Yu

Abstract: We develop a comprehensive method to construct analytical continuum models for moiré systems directly from first-principle calculations without any parameter fitting. The core idea of this method is to interpret the terms in the continuum model as a basis, allowing us to determine model parameters as coefficients of this basis through Gram-Schmidt orthogonalization. We apply our method to twisted… ▽ More We develop a comprehensive method to construct analytical continuum models for moiré systems directly from first-principle calculations without any parameter fitting. The core idea of this method is to interpret the terms in the continuum model as a basis, allowing us to determine model parameters as coefficients of this basis through Gram-Schmidt orthogonalization. We apply our method to twisted MoTe$_2$ and WSe$_2$ with twist angles ranging from 2.13$^\circ$ to 3.89$^\circ$, producing continuum models that exhibit excellent agreement with both energy bands and wavefunctions obtained from first-principles calculations. We further propose a strategy to integrate out the higher-energy degrees of freedom to reduce the number of the parameters in the model without sacrificing the accuracy for low-energy bands. Our findings reveal that decreasing twist angles typically need an increasing number of harmonics in the moiré potentials to accurately replicate first-principles results. We provide parameter values for all derived continuum models, facilitating further robust many-body calculations. Our approach is general and applicable to any commensurate moiré materials accessible by first-principles calculations. △ Less

Submitted 12 November, 2024; originally announced November 2024.

Comments: 14+47 pages, 5+8 figures, 20 tables

How the StarDICE photometric calibration of standard stars can improve cosmological constraints?

Authors: T. Souverin, J. Neveu, M. Betoule, S. Bongard, P. E. Blanc, J. Cohen Tanugi, S. Dagoret-Campagne, F. Feinstein, M. Ferrari, F. Hazenberg, C. Juramy, L. Le Guillou, A. Le Van Suu, M. Moniez, E. Nuss, B. Plez, N. Regnault, E. Sepulveda, K. Sommer

Abstract: The number of type Ia supernova (SNe Ia) observations will grow significantly within the next decade, mainly thanks to the Legacy Survey of Space and Time (LSST) undertaken by the Vera Rubin Observatory in Chile. With this improvement, statistical uncertainties will decrease, and flux calibration will become the main uncertainty for the characterization of dark energy. Currently, the astronomical… ▽ More The number of type Ia supernova (SNe Ia) observations will grow significantly within the next decade, mainly thanks to the Legacy Survey of Space and Time (LSST) undertaken by the Vera Rubin Observatory in Chile. With this improvement, statistical uncertainties will decrease, and flux calibration will become the main uncertainty for the characterization of dark energy. Currently, the astronomical flux scale is anchored on the numerical models of white dwarf atmospheres from the CALSPEC catalog, and every error on the model can induce a bias over cosmological parameters inference. The StarDICE experiment proposes a new calibration reference that only relies on observations from the optical watt defined by the NIST towards the magnitude of standard stars. It is currently operating at l'Observatoire de Haute-Provence and has been collecting data since the beginning of 2023. To overcome the photometric calibration uncertainty and reach a sub-percent precision, the instrument throughput has been calibrated with a Collimated Beam Projector. It will be monitored on-site with a LED-based artificial star source calibrated with NIST photodiodes. In this proceeding, we will first illustrate how an error in the photometric calibration can impact the SNe Ia distance moduli and thus bias the measurement of cosmological parameters. Then we will present the StarDICE experiment and how we can recalibrate the CALSPEC catalog at the millimagnitude level on the NIST scale with photometric analysis. △ Less

Submitted 8 January, 2025; v1 submitted 5 November, 2024; originally announced November 2024.

Comments: 4 pages, 3 figures, contribution to the 2024 Cosmology session of the 58th Rencontres de Moriond

StarDICE III: Characterization of the photometric instrument with a Collimated Beam Projector

Authors: Thierry Souverin, Jérémy Neveu, Marc Betoule, Sébastien Bongard, Christopher W. Stubbs, Elana Urbach, Sasha Brownsberger, Pierre Éric Blanc, Johann Cohen Tanugi, Sylvie Dagoret-Campagne, Fabrice Feinstein, Delphine Hardin, Claire Juramy, Laurent Le Guillou, Auguste Le Van Suu, Marc Moniez, Bertrand Plez, Nicolas Regnault, Eduardo Sepulveda, Kélian Sommer, the LSST Dark Energy Science Collaboration

Abstract: The measurement of type Ia supernovae magnitudes provides cosmological distances, which can be used to constrain dark energy parameters. Large photometric surveys require a substantial improvement in the calibration precision of their photometry to reduce systematic uncertainties in cosmological constraints. The StarDICE experiment is designed to establish accurate broadband flux references for th… ▽ More The measurement of type Ia supernovae magnitudes provides cosmological distances, which can be used to constrain dark energy parameters. Large photometric surveys require a substantial improvement in the calibration precision of their photometry to reduce systematic uncertainties in cosmological constraints. The StarDICE experiment is designed to establish accurate broadband flux references for these surveys, aiming for sub-percent precision in magnitude measurements. This requires a precise measurement of the filter bandpasses of both the StarDICE and survey instruments with sub-nanometer accuracy. To that end, we have developed the Collimated Beam Projector (CBP), an optical device capable of calibrating the throughput of an astronomical telescope and of its filters. The CBP is built from a tunable laser source and a reversed telescope to emit a parallel monochromatic light beam that is continuously monitored in flux and wavelength. The CBP output light flux is measured using a large area photodiode, previously calibrated relative to a NIST photodiode. We derive the StarDICE telescope throughput and filter transmissions from the CBP measurements, anchoring it to the absolute calibration provided by the NIST. After analyzing the systematic uncertainties, we achieved sub-nanometer accuracy in determining filter central wavelengths, measured each filter transmission with a precision of 0.5% per 1nm bin, and detected out-of-band leakages at 0.01%. Furthermore, we have synthesized the equivalent transmission for full pupil illumination from four sample positions in the StarDICE telescope mirror, with an accuracy of approximately 0.2nm for central wavelengths and 7mmag for broadband fluxes. We demonstrated our ability to characterize a telescope throughput down to the mmag, and paved the way for future developments, such as a portable CBP version for in-situ transmission monitoring. △ Less

Submitted 4 November, 2024; v1 submitted 31 October, 2024; originally announced October 2024.

Comments: 29 pages, 50 figures

Catalogue of Phonon Instabilities in Symmetry Group 191 Kagome MT$_6$Z$_6$ Materials

Authors: X. Feng, Y. Jiang, H. Hu, D. Călugăru, N. Regnault, M. G. Vergniory, C. Felser, S. Blanco-Canosa, B. Andrei Bernevig

Abstract: Kagome materials manifest rich physical properties due to the emergence of abundant electronic phases. Here, we carry out a high-throughput first-principles study of the kagome 1:6:6 family MT$_6$Z$_6$ materials in space group 191, focusing on their phonon instability and electronic flat bands. Different MT$_6$Z$_6$ kagome candidates reveal a remarkable variety of kagome flat bands ranging from un… ▽ More Kagome materials manifest rich physical properties due to the emergence of abundant electronic phases. Here, we carry out a high-throughput first-principles study of the kagome 1:6:6 family MT$_6$Z$_6$ materials in space group 191, focusing on their phonon instability and electronic flat bands. Different MT$_6$Z$_6$ kagome candidates reveal a remarkable variety of kagome flat bands ranging from unfilled, partially filled, to fully filled. Notably, the Mn/Fe-166 compounds exhibit partially filled flat bands with a pronounced sharp peak in the density of states near the Fermi level, leading to magnetic orders that polarize the bands and stabilize the otherwise unstable phonon. When the flat bands are located away from the Fermi level, we find a large number of phonon instabilities, which can be classified into three types, based on the phonon dispersion and vibrational modes. Type-I instabilities involve the in-plane distortion of kagome nets, while type-II and type-III present out-of-plane distortion of trigonal M and Z atoms. We take MgNi$_6$Ge$_6$ and HfNi$_6$In$_6$ as examples to illustrate the possible CDW structures derived from the emergent type-I and type-II instabilities. The type-I instability in MgNi$_6$Ge$_6$ suggests a nematic phase transition, governed by the local twisting of kagome nets. The type-II instability in HfNi$_6$In$_6$ may result in a hexagonal-to-orthorhombic transition, offering insight into the formation of MT$_6$Z$_6$ in other space groups. Additionally, the predicted ScNb$_6$Sn$_6$ is analyzed as an example of the type-III instability. Our predictions suggest a vast kagome family with rich properties induced by the flat bands, possible CDW transitions, and their interplay with magnetism. △ Less

Submitted 17 September, 2024; originally announced September 2024.

Comments: 14 pages, 7 figures, with 1000 pages of additional supplemental materials

ZTF SN Ia DR2: Simulations and volume limited sample

Authors: M. Amenouche, M. Smith, P. Rosnet, M. Rigault, M. Aubert, C. Barjou-Delayre, U. Burgaz, B. Carreres, G. Dimitriadis, F. Feinstein, L. Galbany, M. Ginolin, A. Goobar, L. Harvey, Y. -L. Kim, K. Maguire, T. E. Müller-Bravo, J. Nordin, P. Nugent, B. Racine, D. Rosselli, N. Regnault, J. Sollerman, J. H. Terwel, A. Townsend , et al. (5 additional authors not shown)

Abstract: Type Ia supernovae (SNe Ia) constitute an historical probe to derive cosmological parameters through the fit of the Hubble-Lemaître diagram, i.e. SN Ia distance modulus versus their redshift. In the era of precision cosmology, realistic simulation of SNe Ia for any survey entering in an Hubble-Lemaître diagram is a key tool to address observational systematics, like Malmquist bias. As the distance… ▽ More Type Ia supernovae (SNe Ia) constitute an historical probe to derive cosmological parameters through the fit of the Hubble-Lemaître diagram, i.e. SN Ia distance modulus versus their redshift. In the era of precision cosmology, realistic simulation of SNe Ia for any survey entering in an Hubble-Lemaître diagram is a key tool to address observational systematics, like Malmquist bias. As the distance modulus of SNe Ia is derived from the fit of their light-curves, a robust simulation framework is required. In this paper, we present the performances of the simulation framework skysurvey to reproduce the the Zwicky Transient Facility (ZTF) SN Ia DR2 covering the first phase of ZTF running from April 2018 up to December 2020. The ZTF SN Ia DR2 sample correspond to almost 3000 classified SNe Ia of cosmological quality. First, a targeted simulation of the ZTF SN Ia DR2 was carried on to check the validity of the framework after some fine tuning of the observing conditions and instrument performance. Then, a realistic simulation has been run using observing ZTF logs and ZTF SN Ia DR2 selection criteria on simulated light-curves to demonstrate the ability of the simulation framework to match the ZTF SN Ia DR2 sample. Furthermore a redshift dependency of SALT2 light-curve parameters (stretch and colour) was conducted to deduce a volume limited sample, i.e. an unbiased SNe Ia sample, characterized with $z_{lim} \leq 0.06$. This volume limited sample of about 1000 SNe Ia is unique to carry on new analysis on standardization procedure with a precision never reached (those analysis are presented in companion papers). △ Less

Submitted 6 September, 2024; originally announced September 2024.

Comments: 10 pages, 10 figures. Submitted to A & A

ZTF SN Ia DR2: Overview

Authors: Mickael Rigault, Mathew Smith, Ariel Goobar, Kate Maguire, Georgios Dimitriadis, Umut Burgaz, Suhail Dhawan, Jesper Sollerman, Nicolas Regnault, Marek Kowalski, Melissa Amenouche, Marie Aubert, Chloé Barjou-Delayre, Julian Bautista, Josh S. Bloom, Bastien Carreres, Tracy X. Chen, Yannick Copin, Maxime Deckers, Dominique Fouchez, Christoffer Fremling, Lluis Galbany, Madeleine Ginolin, Matthew Graham, Mancy M. Kasliwal , et al. (31 additional authors not shown)

Abstract: We present the first homogeneous release of several thousand Type Ia supernovae (SNe Ia), all having spectroscopic classification, and spectroscopic redshifts for half the sample. This release, named the "DR2", contains 3628 nearby (z < 0.3) SNe Ia discovered, followed and classified by the Zwicky Transient Facility survey between March 2018 and December 2020. Of these, 3000 have good-to-excellent… ▽ More We present the first homogeneous release of several thousand Type Ia supernovae (SNe Ia), all having spectroscopic classification, and spectroscopic redshifts for half the sample. This release, named the "DR2", contains 3628 nearby (z < 0.3) SNe Ia discovered, followed and classified by the Zwicky Transient Facility survey between March 2018 and December 2020. Of these, 3000 have good-to-excellent sampling and 2667 pass standard cosmology light-curve quality cuts. This release is thus the largest SN Ia release to date, increasing by an order of magnitude the number of well characterized low-redshift objects. With the "DR2", we also provide a volume-limited (z < 0.06) sample of nearly a thousand SNe Ia. With such a large, homogeneous and well controlled dataset, we are studying key current questions on SN cosmology, such as the linearity SNe Ia standardization, the SN and host dependencies, the diversity of the SN Ia population, and the accuracy of the current light-curve modeling. These, and more, are studied in detail in a series of articles associated with this release. Alongside the SN Ia parameters, we publish our force-photometry gri-band light curves, 5138 spectra, local and global host properties, observing logs, and a python tool to ease use and access of these data. The photometric accuracy of the "DR2" is not yet suited for cosmological parameter inference, which will follow as "DR2.5" release. We nonetheless demonstrate that the multi-thousand SN Ia Hubble Diagram has a typical 0.15 mag scatter. △ Less

Submitted 2 December, 2024; v1 submitted 6 September, 2024; originally announced September 2024.

Comments: ZTF SN Ia DR2 release paper. Accepted for publication (Astronomy and Astrophysics). Reference paper for the ZTF SN Ia DR2 A&A Special Issue

New magnetic topological materials from high-throughput search

Authors: Iñigo Robredo, Yuanfeng Xu, Yi Jiang, Claudia Felser, B. Andrei Bernevig, Luis Elcoro, Nicolas Regnault, Maia G. Vergniory

Abstract: We conducted a high-throughput search for topological magnetic materials on 522 new, experimentally reported commensurate magnetic structures from MAGNDATA, doubling the number of available materials on the Topological Magnetic Materials database. This brings up to date the previous studies which had become incomplete due to the discovery of new materials. For each material, we performed first-pri… ▽ More We conducted a high-throughput search for topological magnetic materials on 522 new, experimentally reported commensurate magnetic structures from MAGNDATA, doubling the number of available materials on the Topological Magnetic Materials database. This brings up to date the previous studies which had become incomplete due to the discovery of new materials. For each material, we performed first-principle electronic calculations and diagnosed the topology as a function of the Hubbard U parameter. Our high-throughput calculation led us to the prediction of 250 experimentally relevant topologically non-trivial materials, which represent 47.89% of the newly analyzed materials. We present five remarkable examples of these materials, each showcasing a different topological phase: Mn${}_2$AlB${}_2$ (BCSID 1.508), which exhibits a nodal line semimetal to topological insulator transition as a function of SOC, CaMnSi (BCSID 0.599), a narrow gap axion insulator, UAsS (BCSID 0.594) a 5f-orbital Weyl semimetal, CsMnF${}_4$ (BCSID 0.327), a material presenting a new type of quasi-symmetry protected closed nodal surface and FeCr${}_2$S${}_4$ (BCSID 0.613), a symmetry-enforced semimetal with double Weyls and spin-polarised surface states. △ Less

Submitted 29 August, 2024; originally announced August 2024.

Comments: 249 pages, Full topologies and band structures are provided on the Topological Magnetic Materials Database https://www.topologicalquantumchemistry.fr/magnetic/

Moiré Fractional Chern Insulators IV: Fluctuation-Driven Collapse of FCIs in Multi-Band Exact Diagonalization Calculations on Rhombohedral Graphene

Authors: Jiabin Yu, Jonah Herzog-Arbeitman, Yves H. Kwan, Nicolas Regnault, B. Andrei Bernevig

Abstract: The fractional Chern insulators (FCIs) observed in pentalayer rhombohedral graphene/hexagonal boron nitride superlattices have a unique origin contrary to theoretical expectations: their non-interacting band structure is gapless, unlike standard FCIs and the Landau level. Hartree-Fock (HF) calculations at filling $ν=1$ yield a gapped ground state with Chern number 1 through band mixing, identifyin… ▽ More The fractional Chern insulators (FCIs) observed in pentalayer rhombohedral graphene/hexagonal boron nitride superlattices have a unique origin contrary to theoretical expectations: their non-interacting band structure is gapless, unlike standard FCIs and the Landau level. Hartree-Fock (HF) calculations at filling $ν=1$ yield a gapped ground state with Chern number 1 through band mixing, identifying a possible parent state. However, many-body calculations restricted to the occupied HF band predispose the system towards FCIs and are essentially uncontrolled. In this work, we use unbiased multi-band exact diagonalization (ED) to allow fluctuations into the gapless bands for two normal-ordering schemes. In the "charge neutrality" scheme, the weak moiré potential leads to theoretical proposals based on Wigner crystal-like states. However, we find that FCIs seen in 1-band ED calculations are destroyed by band mixing, becoming gapless as fluctuations are included. In the "average" scheme, the Coulomb interaction with the periodic valence charge background sets up a stronger moiré potential. On small systems, FCIs at $ν=1/3$ are destroyed in multi-band calculations, while those at $ν=2/3$ are initially strengthened. However we do not converge to a stable FCI at $ν=2/3$ even on the largest accessible systems. These findings question prior results obtained within projection to a single HF band. They suggest that current models do not support FCIs with correlation length small enough to be converged in accessible, unbiased ED calculations, or do not support FCIs at all. △ Less

Submitted 18 July, 2024; originally announced July 2024.

Journal ref: Phys. Rev. B 112, 075110 (2025)

When Could Abelian Fractional Topological Insulators Exist in Twisted MoTe$_2$ (and Other Systems)

Authors: Yves H. Kwan, Glenn Wagner, Jiabin Yu, Andrea Kouta Dagnino, Yi Jiang, Xiaodong Xu, B. Andrei Bernevig, Titus Neupert, Nicolas Regnault

Abstract: Using comprehensive exact diagonalization calculations on $θ\approx 3.7 ^{\circ}$ twisted bilayer MoTe$_2$ ($t$MoTe$_2$), as well as idealized Landau level models also relevant for lower $θ$, we extract general principles for engineering fractional topological insulators (FTIs) in realistic situations. First, in a Landau level setup at $ν=1/3+1/3$, we investigate what features of the interaction d… ▽ More Using comprehensive exact diagonalization calculations on $θ\approx 3.7 ^{\circ}$ twisted bilayer MoTe$_2$ ($t$MoTe$_2$), as well as idealized Landau level models also relevant for lower $θ$, we extract general principles for engineering fractional topological insulators (FTIs) in realistic situations. First, in a Landau level setup at $ν=1/3+1/3$, we investigate what features of the interaction destroy an FTI. For both pseudopotential interactions and realistic screened Coulomb interactions, we find that sufficient suppression of the short-range repulsion is needed for stabilizing an FTI. We then study $θ\approx 3.7 ^{\circ}$ $t$MoTe$_2$ with realistic band-mixing and anisotropic non-local dielectric screening. Our finite-size calculations only find an FTI phase at $ν=-4/3$ in the presence of a significant additional short-range attraction $g$ that acts to counter the Coulomb repulsion at short distances. We discuss how further finite-size drifts, dielectric engineering, Landau level character, and band-mixing effects may reduce the required value of $g$ closer towards the experimentally relevant conditions of $t$MoTe$_2$. Projective calculations into the $n=1$ Landau level, which resembles the second valence band of $θ\simeq 2.1^\circ$ $t$MoTe$_2$, do not yield FTIs for any $g$, suggesting that FTIs at low-angle $t$MoTe$_2$ for $ν=-8/3$ and $-10/3$ may be unlikely. While our study highlights the challenges, at least for the fillings considered, to obtaining an FTI with transport plateaus, even in large-angle $t$MoTe$_2$ where fractional Chern insulators are experimentally established, we also provide potential sample-engineering routes to improve the stability of FTI phases. △ Less

Submitted 2 July, 2024; originally announced July 2024.

Comments: 6+36 pages

ZTF SN Ia DR2: Exploring SN Ia properties in the vicinity of under-dense environments

Authors: M. Aubert, P. Rosnet, B. Popovic, F. Ruppin, M. Smith, M. Rigault, G. Dimitriadis, A. Goobar, J. Johansson, C. Barjou-Delayre, U. Burgaz, B. Carreres, F. Feinstein, D. Fouchez, L. Galbany, M. Ginolin, T. de Jaeger, M. M. Kasliwal, Y. -L. Kim, L. Lacroix, F. J. Masci, T. E. Müller-Bravo, B. Racine, C. Ravoux, N. Regnault , et al. (7 additional authors not shown)

Abstract: The unprecedented statistics of detected Type Ia supernovae (SNe Ia) brought by the Zwicky Transient Facility enables us to probe the impact of the Large-Scale Structure on the properties of these objects. The goal of this paper is to explore the possible impact of the under-dense part of the large-scale structure on the intrinsic SALT2 light curve properties of SNe Ia and uncover possible biases… ▽ More The unprecedented statistics of detected Type Ia supernovae (SNe Ia) brought by the Zwicky Transient Facility enables us to probe the impact of the Large-Scale Structure on the properties of these objects. The goal of this paper is to explore the possible impact of the under-dense part of the large-scale structure on the intrinsic SALT2 light curve properties of SNe Ia and uncover possible biases in SN Ia analyses. With a volume-limited selection of ZTF-Cosmo-DR2 Type Ia supernovae overlapping with the SDSS-DR7 survey footprint, we investigate the distribution of their properties with regard to voids detected in the SDSS-DR7 galaxy sample. We further use Voronoi volumes as proxy for local density environments within the large-scale structure. We find a moderate dependency of the stretch toward the localisation around the void centre and none when considering colour. The local Voronoi volumes mostly affect the fraction of low/high stretch supernovae. With the current statistics available, we consider that the impact of high or low local density environment can be considered as a proxy for the colour of the host galaxy. Under-dense environments should not cause any biases in supernova analyses. △ Less

Submitted 17 June, 2024; originally announced June 2024.

Comments: 10 pages, 8 figures. Submitted to A&A

Journal ref: A&A 694, A7 (2025)

Ferromagnetism and Topology of the Higher Flat Band in a Fractional Chern Insulator

Authors: Heonjoon Park, Jiaqi Cai, Eric Anderson, Xiao-Wei Zhang, Xiaoyu Liu, William Holtzmann, Weijie Li, Chong Wang, Chaowei Hu, Yuzhou Zhao, Takashi Taniguchi, Kenji Watanabe, Jihui Yang, David Cobden, Jiun-Haw Chu, Nicolas Regnault, B. Andrei Bernevig, Liang Fu, Ting Cao, Di Xiao, Xiaodong Xu

Abstract: The recent observation of the fractional quantum anomalous Hall effect in moiré fractional Chern insulators provides an opportunity to investigate zero magnetic field anyons. To potentially realize non-Abelian anyons, one approach is to engineer higher flat Chern bands that mimic higher Landau levels. Here, we investigate the interaction, topology, and ferromagnetism of the second moiré miniband i… ▽ More The recent observation of the fractional quantum anomalous Hall effect in moiré fractional Chern insulators provides an opportunity to investigate zero magnetic field anyons. To potentially realize non-Abelian anyons, one approach is to engineer higher flat Chern bands that mimic higher Landau levels. Here, we investigate the interaction, topology, and ferromagnetism of the second moiré miniband in twisted MoTe2 bilayers. At half filling of the second miniband, we observe spontaneous ferromagnetism and an incipient Chern insulator state. The Chern numbers of the top two moiré flat bands exhibit opposite signs for twist angles above 3.1°, but share the same sign near 2.6°, consistent with theoretical predictions. In the 2.6° device, increasing magnetic field induces a topological phase transition via band crossing between opposite valleys, resulting in an emergent state with Chern number C = -2. Additionally, an insulating state at half filling of the second valley-polarized band suggests a charge-ordered state is favored over the fractional Chern insulator state. These findings lay a foundation for understanding the higher flat Chern bands, crucial for the discovery of non-Abelian fractional Chern insulators. △ Less

Submitted 16 December, 2024; v1 submitted 13 June, 2024; originally announced June 2024.

Comments: 26 pages, 4 figures, updated version

ZTF SN Ia DR2: Study of Type Ia Supernova lightcurve fits

Authors: M. Rigault, M. Smith, N. Regnault, D. W. Kenworthy, K. Maguire, A. Goobar, G. Dimitriadis, M. Amenouche, M. Aubert, C. Barjou-Delayre, C. E. Bellm, U. Burgaz, B. Carreres, Y. Copin, M. Deckers, T. de Jaeger, S. Dhawan, F. Feinstein, D. Fouchez, L. Galbany, M. Ginolin, J. M. Graham, Y. -L. Kim, M. Kowalski, D. Kuhn , et al. (12 additional authors not shown)

Abstract: Type Ia supernova (SN Ia) cosmology relies on the estimation of lightcurve parameters to derive precision distances that leads to the estimation of cosmological parameters. The empirical SALT2 lightcurve modeling that relies on only two parameters, a stretch x1, and a color c, has been used by the community for almost two decades. In this paper we study the ability of the SALT2 model to fit the ne… ▽ More Type Ia supernova (SN Ia) cosmology relies on the estimation of lightcurve parameters to derive precision distances that leads to the estimation of cosmological parameters. The empirical SALT2 lightcurve modeling that relies on only two parameters, a stretch x1, and a color c, has been used by the community for almost two decades. In this paper we study the ability of the SALT2 model to fit the nearly 3000 cosmology-grade SN Ia lightcurves from the second release of the Zwicky Transient Facility (ZTF) cosmology science working group. While the ZTF data was not used to train SALT2, the algorithm is modeling the ZTF SN Ia optical lightcurves remarkably well, except for lightcurve points prior to -10 d from maximum, where the training critically lacks statistics. We find that the lightcurve fitting is robust against the considered choice of phase-range, but we show the [-10; +40] d range to be optimal in terms of statistics and accuracy. We do not detect any significant features in the lightcurve fit residuals that could be connected to the host environment. Potential systematic population differences related to the SN Ia host properties might thus not be accountable for by the addition of extra lightcurve parameters. However, a small but significant inconsistency between residuals of blue- and red-SN Ia strongly suggests the existence of a phase-dependent color term, with potential implications for the use of SNe Ia in precision cosmology. We thus encourage modellers to explore this avenue and we emphasize the importance that SN Ia cosmology must include a SALT2 retraining to accurately model the lightcurves and avoid biasing the derivation of cosmological parameters. △ Less

Submitted 2 December, 2024; v1 submitted 4 June, 2024; originally announced June 2024.

Comments: 10 pages, 9 figures. Accepted for publication (Astronomy and Astrophysics)

Journal ref: A&A 694, A2 (2025)

Enhanced fractional quantum Hall gaps in a two-dimensional electron gas coupled to a hovering split-ring resonator

Authors: Josefine Enkner, Lorenzo Graziotto, Dalin Boriçi, Felice Appugliese, Christian Reichl, Giacomo Scalari, Nicolas Regnault, Werner Wegscheider, Cristiano Ciuti, Jérôme Faist

Abstract: The magnetotransport of a high-mobility two-dimensional electron gas coupled to a hovering split-ring resonator with controllable distance is studied in the quantum Hall regime. The measurements reveal an enhancement by more than a factor 2 of the quantum Hall energy gaps at the fractional filling factors 4/3, 5/3, and 7/5, alongside a concurrent reduction in exchange splitting at odd integer fill… ▽ More The magnetotransport of a high-mobility two-dimensional electron gas coupled to a hovering split-ring resonator with controllable distance is studied in the quantum Hall regime. The measurements reveal an enhancement by more than a factor 2 of the quantum Hall energy gaps at the fractional filling factors 4/3, 5/3, and 7/5, alongside a concurrent reduction in exchange splitting at odd integer filling factors. Theoretically, we show the strength of both effects to be quantitatively compatible with the emergence of an effective electron-electron long-range attractive interaction mediated by the exchange of virtual cavity photons in the presence of significant spatial gradients of the cavity electric vacuum fields. These results unveil a compelling interplay between cavity quantum electrodynamics and electronic correlations in two-dimensional systems, with profound implications for the manipulation and control of quantum phases in 2D materials. △ Less

Submitted 28 May, 2024; originally announced May 2024.

Heavy Fermions as an Efficient Representation of Atomistic Strain and Relaxation in Twisted Bilayer Graphene

Authors: Jonah Herzog-Arbeitman, Jiabin Yu, Dumitru Călugăru, Haoyu Hu, Nicolas Regnault, Oskar Vafek, Jian Kang, B. Andrei Bernevig

Abstract: Although the strongly interacting flat bands in twisted bilayer graphene (TBG) have been approached using the minimal Bistritzer-MacDonald (BM) Hamiltonian, there is mounting evidence that strain and lattice relaxation are essential in correctly determining the order of the correlated insulator groundstates. These effects can be incorporated in an enhanced continuum model by introducing additional… ▽ More Although the strongly interacting flat bands in twisted bilayer graphene (TBG) have been approached using the minimal Bistritzer-MacDonald (BM) Hamiltonian, there is mounting evidence that strain and lattice relaxation are essential in correctly determining the order of the correlated insulator groundstates. These effects can be incorporated in an enhanced continuum model by introducing additional terms computed from the relaxation profile. To develop an analytical and physical understanding of these effects, we include strain and relaxation in the topological heavy fermion (HF) model of TBG. We find that strain and relaxation are very well captured in first order perturbation theory by projection onto the fully symmetric HF Hilbert space, and remarkably do not alter the interacting terms in the periodic Anderson model. Their effects are fully incorporated in the single-particle HF Hamiltonian, and can be reproduced in a minimal model with only 4 symmetry-breaking terms. Our results demonstrate that the heavy fermion framework of TBG is an efficient and robust representation of the perturbations encountered in experiment. △ Less

Submitted 18 February, 2025; v1 submitted 22 May, 2024; originally announced May 2024.

Journal ref: Phys. Rev. B 112, 125128 (2025)

Fractional quantum Hall effect of partons and the nature of the 8/17 state in the zeroth Landau level of bilayer graphene

Authors: Ajit C. Balram, Nicolas Regnault

Abstract: We consider the fractional quantum Hall effect (FQHE) at the filling factor $8/17$, where signatures of incompressibility have been observed in the zeroth Landau level of bilayer graphene. We propose an Abelian state described by the ``$\overline{(8/3)}\bar{2}1^{3}$" parton wave function, where a parton itself forms an FQHE state. This state is topologically distinct from the $8/17$ Levin-Halperin… ▽ More We consider the fractional quantum Hall effect (FQHE) at the filling factor $8/17$, where signatures of incompressibility have been observed in the zeroth Landau level of bilayer graphene. We propose an Abelian state described by the ``$\overline{(8/3)}\bar{2}1^{3}$" parton wave function, where a parton itself forms an FQHE state. This state is topologically distinct from the $8/17$ Levin-Halperin state, a daughter state of the Moore-Read state. We carry out extensive numerical exact diagonalization of the Coulomb interaction at 8/17 in the zeroth Landau level of bilayer graphene but find that our results cannot conclusively determine the topological order of the underlying ground state. We work out the low-energy effective theory of the $\overline{(8/3)}\bar{2}1^{3}$ edge and make predictions for experimentally measurable properties of the state which can tell it apart from the 8/17 Levin-Halperin state. △ Less

Submitted 26 August, 2024; v1 submitted 23 April, 2024; originally announced April 2024.

Comments: 9 pages, 2 figures and includes supplemental material

Journal ref: Phys. Rev. B 110, L081114 (2024)

Topological Heavy Fermion Principle For Flat (Narrow) Bands With Concentrated Quantum Geometry

Authors: Jonah Herzog-Arbeitman, Jiabin Yu, Dumitru Călugăru, Haoyu Hu, Nicolas Regnault, Chaoxing Liu, Oskar Vafek, Piers Coleman, Alexei Tsvelik, Zhi-da Song, B. Andrei Bernevig

Abstract: We propose a general principle for the low-energy theory of narrow bands with concentrated Berry curvature and Fubini-Study metric in the form of a map to Anderson-"+" models composed of heavy fermions hybridizing and interacting with semi-metallic modes. This map resolves the obstruction preventing topological bands from being realized in a local Hamiltonian acting on the low-energy degrees of fr… ▽ More We propose a general principle for the low-energy theory of narrow bands with concentrated Berry curvature and Fubini-Study metric in the form of a map to Anderson-"+" models composed of heavy fermions hybridizing and interacting with semi-metallic modes. This map resolves the obstruction preventing topological bands from being realized in a local Hamiltonian acting on the low-energy degrees of freedom. The concentrated quantum geometry is reproduced through band inversion with a dispersive semi-metal, leaving a nearly flat, trivial band which becomes the heavy fermion. This representation is natural when the narrow band is not energetically isolated on the scale of the interaction and an enlarged Hilbert space is inescapable, but also provides analytical insight into the projected-interaction limit. First exemplified in twisted bilayer graphene (TBG), we extend it to (1) the twisted checkerboard, which we find has a chiral symmetric stable anomaly that forbids a lattice realization at all energies, and (2) the Lieb lattice with gapless flat bands, where we show the heavy fermions can be obtained by minimizing a Euclidean instanton action to saturate its BPS bound. The heavy fermion approach is widely applicable and physically transparent: heavy electrons carry the strong correlations and dispersive electrons carry the topology. This simple picture unifies the dichotomous phenomena observed in TBG and points to connections between moiré and stoichiometric materials. △ Less

Submitted 17 October, 2024; v1 submitted 10 April, 2024; originally announced April 2024.

Topologically protected flatness in chiral moiré heterostructures

Authors: Valentin Crépel, Peize Ding, Nishchhal Verma, Nicolas Regnault, Raquel Queiroz

Abstract: The observation of delicate correlated phases in twisted heterostructures of graphene and transition metal dichalcogenides suggests that moiré flat bands are intrinsically resilient against certain types of disorder. Here, we investigate the robustness of moiré flat bands in the chiral limit of the Bistrizer-MacDonald model -- applicable to both platforms in certain limits -- and demonstrate drast… ▽ More The observation of delicate correlated phases in twisted heterostructures of graphene and transition metal dichalcogenides suggests that moiré flat bands are intrinsically resilient against certain types of disorder. Here, we investigate the robustness of moiré flat bands in the chiral limit of the Bistrizer-MacDonald model -- applicable to both platforms in certain limits -- and demonstrate drastic differences between the first magic angle and higher magic angles in response to chiral symmetric disorder that arise, for instance, from lattice relaxation. Using a hidden constant of motion, we decompose the non-abelian gauge field induced by interlayer tunnelings into two decoupled abelian ones, whose effective magnetic field splits into an anomalous contribution and a fluctuating part. The anomalous field maps the moiré flat bands onto a zeroth Dirac Landau level, whose flatness withstands any chiral symmetric perturbation due to a topological index theorem -- thereby underscoring a topological mechanism for band flatness. Only the first magic angle can fully harness this topological protection due to its weak fluctuating magnetic field. In higher magic angles, the amplitude of fluctuations largely exceeds the anomalous contribution, which we find results in an extremely large sensitivity to microscopic details. Through numerical simulations, we study various types of disorder and identify the processes that are enhanced or suppressed in the chiral limit. Interestingly, we find that the topological suppression of disorder broadening persists away from the chiral limit and is further accentuated by isolating a single sublattice polarized flat band in energy. Our analysis suggests the Berry curvature hotspot at the top of the $K$ and $K'$ valence band in the transition metal dichalcogenide monolayers is essential for the stability of its moiré flat bands and their correlated states. △ Less

Submitted 25 November, 2024; v1 submitted 28 March, 2024; originally announced March 2024.

Attractive Haldane bilayers for trapping non-Abelian anyons

Authors: Valentin Crépel, Nicolas Regnault

Abstract: We study the interplay between intrinsic topological order and superconductivity in a two-component Haldane bilayer, where the two layers are coupled by an attractive force. We obtain the phase diagram of the model with exact diagonalization in finite size, and develop arguments to assess the stability of the observed phases in the thermodynamic limit. Our main result is that a finite critical att… ▽ More We study the interplay between intrinsic topological order and superconductivity in a two-component Haldane bilayer, where the two layers are coupled by an attractive force. We obtain the phase diagram of the model with exact diagonalization in finite size, and develop arguments to assess the stability of the observed phases in the thermodynamic limit. Our main result is that a finite critical attraction strength is needed to pair fermions forming a fractional topological order. This behavior can be harnessed to create clean interfaces between a fractional topological insulator and a superconductor by gating, wherein non-Abelian parafermionic modes are trapped. We discuss realization of such interfaces in the bulk of double bilayers of transition metal dichalcogenides by inhomogenous electrostatic gating, which should mitigate the spurious effects of disorder and crystalline defects present on physical edges. △ Less

Submitted 10 September, 2024; v1 submitted 8 March, 2024; originally announced March 2024.

Journal ref: Phys. Rev. B 110, 115109 (2024)

The Thermoelectric Effect and Its Natural Heavy Fermion Explanation in Twisted Bilayer and Trilayer Graphene

Authors: Dumitru Călugăru, Haoyu Hu, Rafael Luque Merino, Nicolas Regnault, Dmitri K. Efetov, B. Andrei Bernevig

Abstract: We study the interacting transport properties of twisted bilayer graphene (TBG) using the topological heavy-fermion (THF) model. In the THF model, TBG comprises localized, correlated $f$-electrons and itinerant, dispersive $c$-electrons. We focus on the Seebeck coefficient, which quantifies the voltage difference arising from a temperature gradient. We find that the TBG's Seebeck coefficient shows… ▽ More We study the interacting transport properties of twisted bilayer graphene (TBG) using the topological heavy-fermion (THF) model. In the THF model, TBG comprises localized, correlated $f$-electrons and itinerant, dispersive $c$-electrons. We focus on the Seebeck coefficient, which quantifies the voltage difference arising from a temperature gradient. We find that the TBG's Seebeck coefficient shows unconventional (strongly-interacting) traits: negative values with sawtooth oscillations at positive fillings, contrasting typical band-theory expectations. This behavior is naturally attributed to the presence of heavy (correlated, short-lived $f$-electrons) and light (dispersive, long-lived $c$-electrons) electronic bands. Their longer lifetime and stronger dispersion lead to a dominant transport contribution from the $c$-electrons. At positive integer fillings, the correlated TBG insulators feature $c$- ($f$-)electron bands on the electron (hole) doping side, leading to an overall negative Seebeck coefficient. Additionally, sawtooth oscillations occur around each integer filling due to gap openings. Our results highlight the essential importance of electron correlations in understanding the transport properties of TBG and, in particular, of the lifetime asymmetry between the two fermionic species (naturally captured by the THF model). Our findings are corroborated by new experiments in both twisted bilayer and trilayer graphene, and show the natural presence of strongly-correlated heavy and light carriers in the system. △ Less

Submitted 21 February, 2024; originally announced February 2024.

Comments: 5+106 pages, 3+36 figures, 6 tables. See also the accompanying experimental papers arXiv:2402.11749 and arXiv:2402.12296. The accompanying Ref. 252 will be posted soon

Quantum Fragmentation in the Extended Quantum Breakdown Model

Authors: Bo-Ting Chen, Abhinav Prem, Nicolas Regnault, Biao Lian

Abstract: We introduce a one-dimensional (1D) extended quantum breakdown model comprising a fermionic and a spin degree of freedom per site, and featuring a spatially asymmetric breakdown-type interaction between the fermions and spins. We analytically show that, in the absence of any magnetic field for the spins, the model exhibits Hilbert space fragmentation within each symmetry sector into exponentially… ▽ More We introduce a one-dimensional (1D) extended quantum breakdown model comprising a fermionic and a spin degree of freedom per site, and featuring a spatially asymmetric breakdown-type interaction between the fermions and spins. We analytically show that, in the absence of any magnetic field for the spins, the model exhibits Hilbert space fragmentation within each symmetry sector into exponentially many Krylov subspaces and hence displays non-thermal dynamics. Here, we demonstrate that the fragmentation naturally occurs in an entangled basis and thus provides an example of "quantum fragmentation." Besides establishing the nature of fragmentation analytically, we also study the long-time behavior of the entanglement entropy and its deviation from the expected Page value as a probe of ergodicity in the system. Upon introducing a non-trivial magnetic field for the spins, most of the Krylov subspaces merge and the model becomes chaotic. Finally, we study the effects of strong randomness on the system and observe behavior similar to that of many-body localized systems. △ Less

Submitted 29 January, 2024; originally announced January 2024.

Comments: 30 pages, 13 figures

Moiré Fractional Chern Insulators III: Hartree-Fock Phase Diagram, Magic Angle Regime for Chern Insulator States, the Role of the Moiré Potential and Goldstone Gaps in Rhombohedral Graphene Superlattices

Authors: Yves H. Kwan, Jiabin Yu, Jonah Herzog-Arbeitman, Dmitri K. Efetov, Nicolas Regnault, B. Andrei Bernevig

Abstract: We investigate in detail the $ν=+1$ displacement-field-tuned interacting phase diagram of $L=3,4,5,6,7$ layer rhombohedral graphene aligned to hBN (R$L$G/hBN). Our calculations account for the 3D nature of the Coulomb interaction, the inequivalent stacking orientations $ξ=0,1$, the effects of the filled valence bands, and the choice of `interaction scheme' for specifying the many-body Hamiltonian.… ▽ More We investigate in detail the $ν=+1$ displacement-field-tuned interacting phase diagram of $L=3,4,5,6,7$ layer rhombohedral graphene aligned to hBN (R$L$G/hBN). Our calculations account for the 3D nature of the Coulomb interaction, the inequivalent stacking orientations $ξ=0,1$, the effects of the filled valence bands, and the choice of `interaction scheme' for specifying the many-body Hamiltonian. We show that the latter has a dramatic impact on the Hartree-Fock phase boundaries and the properties of the phases, including for pentalayers (R5G/hBN) with large displacement field $D$ where recent experiments observed a Chern insulator at $ν=+1$ and fractional Chern insulators for $ν<1$. In this large $D$ regime, the low-energy conduction bands are polarized away from the aligned hBN layer, and are hence well-described by the folded bands of moiréless rhombohedral graphene at the non-interacting level. Despite this, the filled valence bands develop moiré-periodic charge density variations which can generate an effective moiré potential, thereby explicitly breaking the approximate continuous translation symmetry in the conduction bands, and leading to contrasting electronic topology in the ground state for the two stacking arrangements. Within time-dependent Hartree-Fock theory, we further characterize the strength of the moiré pinning potential in the Chern insulator phase by computing the low-energy $\mathbf{q}=0$ collective mode spectrum, where we identify competing gapped pseudophonon and valley magnon excitations. Our results emphasize the importance of careful examination of both the single-particle and interaction model for a proper understanding of the correlated phases in R$L$G/hBN. △ Less

Submitted 18 December, 2023; originally announced December 2023.

Journal ref: Phys. Rev. B 112, 075109 (2025)

Fingerprints of Composite Fermion Lambda Levels in Scanning Tunneling Microscopy

Authors: Songyang Pu, Ajit C. Balram, Yuwen Hu, Yen-Chen Tsui, Minhao He, Nicolas Regnault, Michael P. Zaletel, Ali Yazdani, Zlatko Papić

Abstract: Composite fermion (CF) is a topological quasiparticle that emerges from a non-perturbative attachment of vortices to electrons in strongly correlated two-dimensional materials. Similar to non-interacting fermions that form Landau levels in a magnetic field, CFs can fill analogous ``Lambda'' levels, giving rise to the fractional quantum Hall (FQH) effect of electrons. Here, we show that Lambda leve… ▽ More Composite fermion (CF) is a topological quasiparticle that emerges from a non-perturbative attachment of vortices to electrons in strongly correlated two-dimensional materials. Similar to non-interacting fermions that form Landau levels in a magnetic field, CFs can fill analogous ``Lambda'' levels, giving rise to the fractional quantum Hall (FQH) effect of electrons. Here, we show that Lambda levels can be directly visualized through the characteristic peak structure in the signal obtained via spectroscopy with the scanning tunneling microscopy (STM) on a FQH state. Complementary to transport, which probes low-energy properties of CFs, we show that \emph{high-energy} features in STM spectra can be interpreted in terms of Lambda levels. We numerically demonstrate that STM spectra can be accurately modeled using Jain's CF theory. Our results show that STM provides a powerful tool for revealing the anatomy of FQH states and identifying physics beyond the non-interacting CF paradigm. △ Less

Submitted 15 August, 2024; v1 submitted 11 December, 2023; originally announced December 2023.

Comments: Seven figures including supplementary materials

Journal ref: Phys. Rev. B 110, L081107 (2024)

Moiré Fractional Chern Insulators II: First-principles Calculations and Continuum Models of Rhombohedral Graphene Superlattices

Authors: Jonah Herzog-Arbeitman, Yuzhi Wang, Jiaxuan Liu, Pok Man Tam, Ziyue Qi, Yujin Jia, Dmitri K. Efetov, Oskar Vafek, Nicolas Regnault, Hongming Weng, Quansheng Wu, B. Andrei Bernevig, Jiabin Yu

Abstract: The experimental discovery of fractional Chern insulators (FCIs) in rhombohedral pentalayer graphene twisted on hexagonal boron nitride (hBN) has preceded theoretical prediction. Supported by large-scale first principles relaxation calculations at the experimental twist angle of $0.77^\circ$, we obtain an accurate continuum model of $n=3,4,5,6,7$ layer rhombohedral graphene-hBN moiré systems. Focu… ▽ More The experimental discovery of fractional Chern insulators (FCIs) in rhombohedral pentalayer graphene twisted on hexagonal boron nitride (hBN) has preceded theoretical prediction. Supported by large-scale first principles relaxation calculations at the experimental twist angle of $0.77^\circ$, we obtain an accurate continuum model of $n=3,4,5,6,7$ layer rhombohedral graphene-hBN moiré systems. Focusing on the pentalayer case, we analytically explain the robust $|C|=0,5$ Chern numbers seen in the low-energy single-particle bands and their flattening with displacement field, making use of a minimal two-flavor continuum Hamiltonian derived from the full model. We then predict nonzero valley Chern numbers at the $ν= -4,0$ insulators observed in experiment. Our analysis makes clear the importance of displacement field and the moiré potential in producing localized "heavy fermion" charge density in the top valence band, in addition to the nearly free conduction band. Lastly, we study doubly aligned devices as additional platforms for moiré FCIs with higher Chern number bands. △ Less

Submitted 21 November, 2023; originally announced November 2023.

Comments: Second paper in the moiré FCI series

Journal ref: Phys. Rev. B 109, 205122 (2024)

Moiré Fractional Chern Insulators I: First-principles calculations and Continuum Models of Twisted Bilayer MoTe$_2$

Authors: Yujin Jia, Jiabin Yu, Jiaxuan Liu, Jonah Herzog-Arbeitman, Ziyue Qi, Nicolas Regnault, Hongming Weng, B. Andrei Bernevig, Quansheng Wu

Abstract: Recent experiments observed fractional Chern insulators (FCI) in twisted bilayer MoTe$_2$ at zero magnetic field, yet even the single-particle model of this material is controversial, leading to unreliable predictions of the experimental phase diagram as discussed in [Yu et al., 2023]. In this light, we revisit the single-particle model of twisted bilayer MoTe$_2$. Utilizing large-scale density fu… ▽ More Recent experiments observed fractional Chern insulators (FCI) in twisted bilayer MoTe$_2$ at zero magnetic field, yet even the single-particle model of this material is controversial, leading to unreliable predictions of the experimental phase diagram as discussed in [Yu et al., 2023]. In this light, we revisit the single-particle model of twisted bilayer MoTe$_2$. Utilizing large-scale density functional theory, we calculate the band structure of twisted AA-stacked bilayer MoTe$_2$ at various twist angles relevant to experiment. We find that a band inversion occurs near $4.41^\circ$ between the second and third bands. Our ab initio band structure is in qualitative agreement with [Wang et al., 2023], but shows important differences in the remote bands and in the $Γ$ valley. We incorporate two higher harmonic terms into the continuum model to capture the highest 3 valence bands per valley. We confirm that the two highest valence bands per valley have opposite Chern numbers with $|C|=1$ for small angles, and also use our model to predict a variety of Chern states in the remote bands accessible by displacement field. Finally, we perform DFT calculations and build models for the AB stacking configuration. Our work serves as a foundation for accurate determination of the correlated phases in twisted bilayer MoTe$_2$. △ Less

Submitted 8 November, 2023; originally announced November 2023.

Journal ref: Phys. Rev. B 109, 205121 (2024)

Fractional Chern Insulators vs. Non-Magnetic States in Twisted Bilayer MoTe$_2$

Authors: Jiabin Yu, Jonah Herzog-Arbeitman, Minxuan Wang, Oskar Vafek, B. Andrei Bernevig, Nicolas Regnault

Abstract: Fractionally filled Chern bands with strong interactions may give rise to fractional Chern insulator (FCI) states, the zero-field analogue of the fractional quantum Hall effect. Recent experiments have demonstrated the existence of FCIs in twisted bilayer MoTe$_2$ without external magnetic fields -- most robust at $ν=-2/3$ -- as well as Chern insulators (CIs) at $ν=-1$. Although the appearance of… ▽ More Fractionally filled Chern bands with strong interactions may give rise to fractional Chern insulator (FCI) states, the zero-field analogue of the fractional quantum Hall effect. Recent experiments have demonstrated the existence of FCIs in twisted bilayer MoTe$_2$ without external magnetic fields -- most robust at $ν=-2/3$ -- as well as Chern insulators (CIs) at $ν=-1$. Although the appearance of both of these states is theoretically natural in an interacting topological system, experiments repeatedly observe nonmagnetic states (lacking FCIs) at $ν=-1/3$ and $-4/3$, a puzzling result which has not been fully theoretically explained. In this work, we perform Hartree-Fock and exact diagonalization calculations to test whether the standard MoTe$_2$ moiré model with the (greatly varying) parameter values available in the literature can reproduce the non-magnetic states at $ν=-1/3$ and $-4/3$ in unison with the FCI at $ν=-2/3$ and CI state at $ν= -1$. We focus on the experimentally relevant twist angles and, crucially, include remote bands. We find that the parameters proposed in [Wang et al. (2023)] can nearly capture the experimental phenomena at $ν=-1/3,-2/3,-1,-4/3$ simultaneously, though the predicted ground states at $ν=-1/3$ are still mostly fully-spin-polarized and a larger dielectric constant $ε>10$ than is typical of hexagonal boron nitride (h-BN) substrate $ε\sim 6$ is required. Our results show the importance of remote bands in identifying the competing magnetic orders and lay the groundwork for further study of the realistic phase diagram. △ Less

Submitted 25 September, 2023; originally announced September 2023.

Comments: 16+32 pages, 10+28 figures, 2+1 tables

Journal ref: Phys. Rev. B 109, 045147 (2024)

Probing the fractional quantum Hall phases in valley-layer locked bilayer MoS$_{2}$

Authors: Siwen Zhao, Jinqiang Huang, Valentin Crépel, Xingguang Wu, Tongyao Zhang, Hanwen Wang, Xiangyan Han, Zhengyu Li, Chuanying Xi, Senyang Pan, Zhaosheng Wang, Kenji Watanabe, Takashi Taniguchi, Benjamin Sacépé, Jing Zhang, Ning Wang, Jianming Lu, Nicolas Regnault, Zheng Vitto Han

Abstract: Semiconducting transition-metal dichalcogenides (TMDs) exhibit high mobility, strong spin-orbit coupling, and large effective masses, which simultaneously leads to a rich wealth of Landau quantizations and inherently strong electronic interactions. However, in spite of their extensively explored Landau levels (LL) structure, probing electron correlations in the fractionally filled LL regime has no… ▽ More Semiconducting transition-metal dichalcogenides (TMDs) exhibit high mobility, strong spin-orbit coupling, and large effective masses, which simultaneously leads to a rich wealth of Landau quantizations and inherently strong electronic interactions. However, in spite of their extensively explored Landau levels (LL) structure, probing electron correlations in the fractionally filled LL regime has not been possible due to the difficulty of reaching the quantum limit. Here, we report evidence for fractional quantum Hall (FQH) states at filling fractions 4/5 and 2/5 in the lowest LL of bilayer MoS$_{2}$, manifested in fractionally quantized transverse conductance plateaus accompanied by longitudinal resistance minima. We further show that the observed FQH states sensitively depend on the dielectric and gate screening of the Coulomb interactions. Our findings establish a new FQH experimental platform which are a scarce resource: an intrinsic semiconducting high mobility electron gas, whose electronic interactions in the FQH regime are in principle tunable by Coulomb-screening engineering, and as such, could be the missing link between atomically thin graphene and semiconducting quantum wells. △ Less

Submitted 8 October, 2023; v1 submitted 5 August, 2023; originally announced August 2023.

Comments: 10 pages, 4 figures

Probing pre-supernova mass loss in double-peaked Type Ibc supernovae from the Zwicky Transient Facility

Authors: Kaustav K. Das, Mansi M. Kasliwal, Jesper Sollerman, Christoffer Fremling, I. Irani, Shing-Chi Leung, Sheng Yang, Samantha Wu, Jim Fuller, Shreya Anand, Igor Andreoni, C. Barbarino, Thomas G. Brink, Kishalay De, Alison Dugas, Steven L. Groom, George Helou, K-Ryan Hinds, Anna Y. Q. Ho, Viraj Karambelkar, S. R. Kulkarni, Daniel A. Perley, Josiah Purdum, Nicolas Regnault, Steve Schulze , et al. (12 additional authors not shown)

Abstract: Eruptive mass loss of massive stars prior to supernova (SN) explosion is key to understanding their evolution and end fate. An observational signature of pre-SN mass loss is the detection of an early, short-lived peak prior to the radioactive-powered peak in the lightcurve of the SN. This is usually attributed to the SN shock passing through an extended envelope or circumstellar medium (CSM). Such… ▽ More Eruptive mass loss of massive stars prior to supernova (SN) explosion is key to understanding their evolution and end fate. An observational signature of pre-SN mass loss is the detection of an early, short-lived peak prior to the radioactive-powered peak in the lightcurve of the SN. This is usually attributed to the SN shock passing through an extended envelope or circumstellar medium (CSM). Such an early peak is common for double-peaked Type IIb SNe with an extended Hydrogen envelope but is uncommon for normal Type Ibc SNe with very compact progenitors. In this paper, we systematically study a sample of 14 double-peaked Type Ibc SNe out of 475 Type Ibc SNe detected by the Zwicky Transient Facility. The rate of these events is ~ 3-9 % of Type Ibc SNe. A strong correlation is seen between the peak brightness of the first and the second peak. We perform a holistic analysis of this sample's photometric and spectroscopic properties. We find that six SNe have ejecta mass less than 1.5 Msun. Based on the nebular spectra and lightcurve properties, we estimate that the progenitor masses for these are less than ~ 12 Msun. The rest have an ejecta mass > 2.4 Msun and a higher progenitor mass. This sample suggests that the SNe with low progenitor masses undergo late-time binary mass transfer. Meanwhile, the SNe with higher progenitor masses are consistent with wave-driven mass loss or pulsation-pair instability-driven mass loss simulations. △ Less

Submitted 7 August, 2024; v1 submitted 7 June, 2023; originally announced June 2023.

Comments: Accepted for publication in ApJ

Chiral limit and origin of topological flat bands in twisted transition metal dichalcogenide homobilayers

Authors: Valentin Crépel, Nicolas Regnault, Raquel Queiroz

Abstract: The observation of zero field fractional quantum Hall analogs in twisted transition metal dichalcogenides (TMDs) asks for a deeper understanding of what mechanisms lead to topological flat bands in two-dimensional heterostructures, and what makes TMDs an excellent platform for topologically ordered phases, surpassing twisted bilayer graphene. To this aim, we explore the chiral limits of massive Di… ▽ More The observation of zero field fractional quantum Hall analogs in twisted transition metal dichalcogenides (TMDs) asks for a deeper understanding of what mechanisms lead to topological flat bands in two-dimensional heterostructures, and what makes TMDs an excellent platform for topologically ordered phases, surpassing twisted bilayer graphene. To this aim, we explore the chiral limits of massive Dirac theories applicable to $C_3$-symmetric moiré materials, and show their relevance for both bilayer graphene and TMD homobilayers. In the latter, the Berry curvature of valence bands leads to relativistic corrections of the moiré potential that promote band flattening, and permit a limit with exactly flat bands with nonzero Chern number. The relativistic corrections enter as a \emph{layer-orbit coupling}, analogous to spin-orbit coupling for relativistic Dirac fermions, which we show is non-negligible on the moiré scale. The Berry curvature of the TMD monolayers therefore plays an essential role in the flattening of moiré Chern bands in these heterostructures. △ Less

Submitted 9 May, 2024; v1 submitted 17 May, 2023; originally announced May 2023.

Journal ref: Communications Physics volume 7, Article number: 146 (2024)

Ideal Chern bands are Landau levels in curved space

Authors: B. Estienne, N. Regnault, V. Crépel

Abstract: We prove that all the criteria proposed in the literature to identify a Chern band hosting exact fractional Chern insulating ground states, in fact, describe an equivalence with a lowest Landau level defined in curved space under a non-uniform magnetic field. In addition, we design an operational test for the most general instance of such lowest Landau level mapping, which only relies on the compu… ▽ More We prove that all the criteria proposed in the literature to identify a Chern band hosting exact fractional Chern insulating ground states, in fact, describe an equivalence with a lowest Landau level defined in curved space under a non-uniform magnetic field. In addition, we design an operational test for the most general instance of such lowest Landau level mapping, which only relies on the computationally inexpensive evaluation of Bloch wavefunctions' derivatives. Our work clarifies the common origin of various Chern-idealness criteria, proves that these criteria exhaust all possible lowest Landau levels, and hints at classes of Chern bands that may posses interesting phases beyond Landau level physics. △ Less

Submitted 15 July, 2023; v1 submitted 3 April, 2023; originally announced April 2023.

Comments: 8 pages

Journal ref: Phys. Rev. Research 5, L032048 (2023)