Showing 1–50 of 72 results for author: Devakul, T

Skyrmion Fractional Chern Insulator: An Intrinsically Multiband Route to Fractionalization in Rhombohedral Graphene

Authors: Julian May-Mann, Tixuan Tan, Patrick J. Ledwith, Zhengyan Darius Shi, Trithep Devakul

Abstract: We propose an unconventional microscopic origin for the fractional quantum anomalous Hall (FQAH) effect in rhombohedral graphene moiré superlattices: skyrmion fractionalization. We view the state at filling $ν<1$ as a metal of skyrmion vacancies, charge $+e$ objects formed by removing layer-pseudospin skyrmions from the interaction-generated skyrmion lattice Chern insulator at $ν=1$. These vacanci… ▽ More We propose an unconventional microscopic origin for the fractional quantum anomalous Hall (FQAH) effect in rhombohedral graphene moiré superlattices: skyrmion fractionalization. We view the state at filling $ν<1$ as a metal of skyrmion vacancies, charge $+e$ objects formed by removing layer-pseudospin skyrmions from the interaction-generated skyrmion lattice Chern insulator at $ν=1$. These vacancies are intrinsically multiband degrees of freedom, absent in single Chern band-projected studies. Building on a recently proposed ideal limit, we first develop an effective field theory showing that skyrmion vacancies can themselves fractionalize, thereby inducing charge fractionalization. Focusing on $ν=\frac{2}{3}$, we then construct explicit variational trial wavefunctions for the resulting skyrmion fractional Chern insulator and provide numerical evidence, together with general arguments, showing that this process is energetically favored. Our results establish a realistic route to the FQAH that does not rely on a partially filled Chern band, but instead arises from fractionalization of collective pseudospin textures. △ Less

Submitted 14 August, 2026; originally announced August 2026.

Fermiology and the Candidate Chiral Superconductor in Rhombohedral Tetralayer Graphene

Authors: Sandesh S. Kalantre, Ben H. Alexander, Julian May-Mann, Jonah Herzog-Arbeitman, Marisa Hocking, Qingrui Cao, Kenji Watanabe, Takashi Taniguchi, David Goldhaber-Gordon, Andrew J. Mannix, Trithep Devakul, Yves H. Kwan, Daniel E. Parker, Aaron Sharpe

Abstract: Chiral superconductivity, in which the phase of the superconducting order parameter winds in momentum space, has long been sought for its close link to topological superconductivity. Recent work reported a superconductor in rhombohedral multilayer graphene emerging from a time-reversal symmetry broken normal state, suggesting that it could be a chiral superconductor. However, the possibility of ch… ▽ More Chiral superconductivity, in which the phase of the superconducting order parameter winds in momentum space, has long been sought for its close link to topological superconductivity. Recent work reported a superconductor in rhombohedral multilayer graphene emerging from a time-reversal symmetry broken normal state, suggesting that it could be a chiral superconductor. However, the possibility of chirality depends on the symmetry and structure of the normal-state Fermi surface, which have not been directly measured. Here we measure quantum oscillations in rhombohedral tetralayer graphene over a broad range of the phase diagram, including the superconducting region. At densities well above the onset of superconductivity, we reproduce previously-reported oscillations consistent with a spin- and valley-polarized quarter metal with a single simply-connected Fermi pocket. As the carrier density is reduced, we find a transition to a complex "multitone" state that persists through the superconducting region. This state's spectrum of quantum oscillations is incompatible with a simply-connected quarter metal. The next-simplest candidate normal states suggested by our microscopic modeling (fully-polarized annular, nematic, and three-pocket states) are inconsistent with our measurements, albeit difficult to rule out entirely. The normal state is thus seen to be richer than previously envisaged, reshaping the search for the superconducting mechanism and the possible chirality of the pairing channel. △ Less

Submitted 3 June, 2026; originally announced June 2026.

Comments: 12+60 pages, 4+52 figures

Visualizing orbital magnetism in electron doped rhombohedral multilayer graphene

Authors: Owen I. Sheekey, Trevor B. Arp, Benjamin A. Foutty, Ruoxi Zhang, Tixuan Tan, Ludwig F. W. Holleis, Yi Guo, Sandesh S. Kalantre, Canxun Zhang, Mark Zakharyan, David Gong, Aidan Keough, Youngjoon Choi, Ysun Choi, Siyuan Xu, Tian Xie, Ben Hodder Alexander, Marisa Hocking, Qingrui Cao, Martin E. Huber, Takashi Taniguchi, Kenji Watanabe, Chenhao Jin, Etienne Lantagne-Hurtubise, Aaron Sharpe , et al. (2 additional authors not shown)

Abstract: Electron doped rhombohedral multilayer graphene at high displacement field features an exceptionally flat band minimum with near-ideal quantum geometry. Experiments in this regime observe the formation of a 'quarter metal,' in which the electron liquid condenses into a single spin- and valley flavor. Remarkably, recent experiments have found a zero resistance state in the same region of the densit… ▽ More Electron doped rhombohedral multilayer graphene at high displacement field features an exceptionally flat band minimum with near-ideal quantum geometry. Experiments in this regime observe the formation of a 'quarter metal,' in which the electron liquid condenses into a single spin- and valley flavor. Remarkably, recent experiments have found a zero resistance state in the same region of the density- and displacement-field-tuned parameter space, attributed to the formation of a chiral superconductor from an orbitally ferromagnetic normal state. Here, we use nanoSQUID-on-tip magnetometry to map the orbital magnetization of electron-doped rhombohedral graphene devices ranging in thickness between 3 and 15 layers. Magnetization within the quarter metal phases peaks at finite density, consistent with concentration of the Berry curvature in a finite-momentum 'ring of fire'. Correlating transport and local magnetometry data in a superconducting tetralayer sample reveals a finite orbital ferromagnetic moment, providing direct evidence of valley polarization in the superconducting ground state. We further show that widely observed stochastic switching of the resistivity in both metallic and superconducting regimes arises from a density-tuned sign change in the valley-resolved total magnetic moment. This leads to the formation of metastable magnetic domains under typical gate control sequences and can also be harnessed for electric-field controlled switching of the magnetization across the entire device. Finally, high resolution measurements of the magnetization across a superconducting transition allow us to put an upper bound on the 'condensation magnetization' of 0.1 Bohr magneton per carrier, placing a strong quantitative restriction on theoretical models for ferromagnetic superconductivity. △ Less

Submitted 4 August, 2026; v1 submitted 28 May, 2026; originally announced May 2026.

Mesoscopic transport in a Chern mosaic

Authors: Sayak Bhattacharjee, Julian May-Mann, Yves H. Kwan, Trithep Devakul, Aaron Sharpe

Abstract: We analyze mesoscopic electronic transport in a Chern mosaic: a regular pattern of domains whose electronic bands carry differing local Chern numbers. An example platform where a Chern mosaic can arise is a moiré heterostructure, where variations in the local moiré parameters can produce such domains. We compute resistances at linear response for a variety of domain wall network geometries at zero… ▽ More We analyze mesoscopic electronic transport in a Chern mosaic: a regular pattern of domains whose electronic bands carry differing local Chern numbers. An example platform where a Chern mosaic can arise is a moiré heterostructure, where variations in the local moiré parameters can produce such domains. We compute resistances at linear response for a variety of domain wall network geometries at zero temperature and magnetic field. Simple domain configurations can exhibit zero, integer, or fractional multiples of the quantum of resistance in both the longitudinal and transverse (Hall) responses. Our simple semi-classical analysis provides a useful computational method and comparative catalog for ongoing experiments in two-dimensional topological materials. △ Less

Submitted 22 April, 2026; v1 submitted 9 April, 2026; originally announced April 2026.

Comments: 24 pages, 13 figures, 2 tables

Electrically controllable valence-conduction band reversals in helical trilayer graphene

Authors: Matan Bocarsly, Indranil Roy, Weifeng Zhi, Li-Qiao Xia, Aviram Uri, Yves H. Kwan, Aaron Sharpe, Matan Uzan, Yuri Myasoedov, Kenji Watanabe, Takashi Taniguchi, Trithep Devakul, Pablo Jarillo-Herrero, Eli Zeldov

Abstract: In moiré graphene systems, electronic interactions lift spin and valley degeneracies, leading to symmetry-broken ground states. In helical trilayer graphene (HTG), we uncover a distinct interaction-driven mechanism in which the roles of sublattice-polarized valence and conduction bands are cyclically reversed. Using scanning nano-SQUID magnetometry, we detect a series of sharp magnetic signatures… ▽ More In moiré graphene systems, electronic interactions lift spin and valley degeneracies, leading to symmetry-broken ground states. In helical trilayer graphene (HTG), we uncover a distinct interaction-driven mechanism in which the roles of sublattice-polarized valence and conduction bands are cyclically reversed. Using scanning nano-SQUID magnetometry, we detect a series of sharp magnetic signatures consistent with seesaw-like transitions, where occupied and unoccupied valence and conduction bands interchange repeatedly with doping, accompanied by a novel form of magnetic hysteresis. These transitions occur entirely within metallic regimes and leave only weak fingerprints in transport measurements. Self-consistent Hartree-Fock calculations reveal that interactions reorganize all eight low-energy flat bands, driving abrupt changes in orbital magnetization. Our results establish HTG as the first system where electronic interactions provide doping-controlled access to all three internal degrees of freedom - spin, valley, and sublattice - introducing a new class of correlated phase transitions. △ Less

Submitted 23 March, 2026; originally announced March 2026.

Comments: 15 pages, 4 figures

The ideal limit of rhombohedral graphene: Interaction-induced layer-skyrmion lattices and their collective excitations

Authors: Tixuan Tan, Patrick J. Ledwith, Trithep Devakul

Abstract: We introduce an ideal limit of rhombohedral graphene multilayers. In this limit, we show analytically how short-range repulsion stabilizes a layer-pseudospin skyrmion lattice, which generates an effective magnetic field and gives rise to a Chern band. This establishes the real-space origin of interaction-driven topology in moiré rhombohedral graphene. The resulting interaction-induced skyrmion lat… ▽ More We introduce an ideal limit of rhombohedral graphene multilayers. In this limit, we show analytically how short-range repulsion stabilizes a layer-pseudospin skyrmion lattice, which generates an effective magnetic field and gives rise to a Chern band. This establishes the real-space origin of interaction-driven topology in moiré rhombohedral graphene. The resulting interaction-induced skyrmion lattice is physically analogous to magnetic skyrmion crystals and hosts a hierarchy of collective excitations naturally described within the framework of skyrmion-lattice dynamics. △ Less

Submitted 10 November, 2025; originally announced November 2025.

Nonvolatile Switching of Magnetism via Gate-Induced Sliding in Tetralayer Graphene

Authors: Daniel Brandon, Tixuan Tan, Yiwen Ai, Peter Golemis, Akshat Gandhi, Lujin Min, Kenji Watanabe, Takashi Taniguchi, Trithep Devakul, Kenji Yasuda

Abstract: Interlayer sliding degrees of freedom often determine the physical properties of two-dimensional (2D) materials. In graphene, for instance, the metastable rhombohedral stacking arrangement hosts correlated and topological electronic phases, which are absent in conventional Bernal stacking. Here, we demonstrate a sliding-induced first-order structural phase transition between Bernal and rhombohedra… ▽ More Interlayer sliding degrees of freedom often determine the physical properties of two-dimensional (2D) materials. In graphene, for instance, the metastable rhombohedral stacking arrangement hosts correlated and topological electronic phases, which are absent in conventional Bernal stacking. Here, we demonstrate a sliding-induced first-order structural phase transition between Bernal and rhombohedral tetralayer graphene driven by gate voltages. Through transport measurement, we observe bistable switching between a Bernal-dominant state and a rhombohedral-Bernal mixed state across a wide space of the gate-voltage phase diagram. The structural phase transition results in nonvolatile switching between a paramagnet and a ferromagnet accompanied by the anomalous Hall effect. The sign reversal of the anomalous Hall effect under opposite displacement fields suggests that it may originate from domain boundaries between the Bernal and rhombohedral regions. Our discovery paves the way for on-demand toggling of quantum phases based on the sliding phase transition of 2D materials and offers a playground to explore unconventional physics at the stacking domain boundaries. △ Less

Submitted 30 September, 2025; originally announced October 2025.

Link between thermodynamic correlation signatures and superconductivity in twisted trilayer graphene

Authors: Jesse C. Hoke, Yifan Li, Yuwen Hu, Julian May-Mann, Kenji Watanabe, Takashi Taniguchi, Trithep Devakul, Aaron Sharpe, Benjamin E. Feldman

Abstract: Twisted graphene multilayers exhibit strong electronic correlations, which manifest in a range of experimental signatures. Yet how these signatures relate to each other and the microscopic ground states-and how twist angle and band structure reshape them-remains poorly understood. Here we study this interplay by correlating local thermodynamic and transport measurements in a twisted trilayer graph… ▽ More Twisted graphene multilayers exhibit strong electronic correlations, which manifest in a range of experimental signatures. Yet how these signatures relate to each other and the microscopic ground states-and how twist angle and band structure reshape them-remains poorly understood. Here we study this interplay by correlating local thermodynamic and transport measurements in a twisted trilayer graphene (TTG) sample with unequal angles and flat electronic bands. We use a scanning single-electron transistor to map the impact of electron-electron interactions in a region of the sample where the local twist angle evolves smoothly. We observe gapped correlated insulators and a sawtooth in electronic compressibility, both exhibiting pronounced electron-hole (e-h) asymmetry with distinct magic angles for conduction and valence bands. Subsequent transport measurements in the same region reveal robust superconductivity with a similar e-h asymmetry. Our measurements indicate that superconductivity is not directly tied to the correlated insulators. Instead, its critical temperature correlates closely with the strength of the sawtooth in compressibility, suggesting a common origin or link between the two. By combining a local probe with transport measurements, we uncover connections between superconductivity and thermodynamic correlation signatures that are not apparent from either technique in isolation, highlighting the power of our dual approach and establishing their dependence on interlayer twist angles in TTG. △ Less

Submitted 18 July, 2026; v1 submitted 9 September, 2025; originally announced September 2025.

Magic continuum in multi-moiré twisted trilayer graphene

Authors: Li-Qiao Xia, Aviram Uri, Jiaojie Yan, Aaron Sharpe, Filippo Gaggioli, Nicole S. Ticea, Julian May-Mann, Kenji Watanabe, Takashi Taniguchi, Liang Fu, Trithep Devakul, Jurgen H. Smet, Pablo Jarillo-Herrero

Abstract: Moiré lattices provide a highly tunable platform for exploring the interplay between electronic correlations and band topology. Introducing a second moiré pattern extends this paradigm: interference between the two moiré patterns produces a supermoiré modulation, opening a route to further tailor electronic properties. Twisted trilayer graphene generally exemplifies such a system: two distinct moi… ▽ More Moiré lattices provide a highly tunable platform for exploring the interplay between electronic correlations and band topology. Introducing a second moiré pattern extends this paradigm: interference between the two moiré patterns produces a supermoiré modulation, opening a route to further tailor electronic properties. Twisted trilayer graphene generally exemplifies such a system: two distinct moiré patterns arise from the relative twists between adjacent graphene layers. Here, we report the observation of correlated phenomena across a wide range of twisted trilayer graphene devices whose twist angles lie along two continuous lines in the twist-angle parameter space. Depending on the degree of lattice relaxation, twisted trilayer graphene falls into two classes: moiré polycrystals, composed of periodic domains with locally commensurate moiré order, and moiré quasicrystals, characterized by smoothly varying local moiré configurations. In helically twisted moiré polycrystals, we observe an anomalous Hall effect, consistent with topological bands arising from domains with broken $xy$-inversion symmetry. In contrast, superconductivity appears generically in our moiré quasicrystals. A subset of these systems exhibits signatures of spatially modulated superconductivity, which we attribute to the supermoiré structure. Our findings uncover the organizing principles of the observed correlated phases in twisted trilayer graphene, highlight the critical roles of the supermoiré modulation and lattice relaxation, and suggest a broader framework in which magic conditions arise not as isolated points but as extended manifolds within the multi-dimensional twist-angle space of complex moiré materials. △ Less

Submitted 3 September, 2025; originally announced September 2025.

Shot noise in strongly correlated double quantum spin Hall edges

Authors: Andreas Tsantilas, Trithep Devakul, Julian May-Mann

Abstract: We consider the effects of interactions on the edges of ``double" quantum spin Hall insulators (DQSHIs), motivated by recent experiments on moiré twisted metal dichalcogenides. Without interactions, a DQSHI can be understood as two copies of a conventional quantum spin Hall insulator. If interactions are present and $s^z$-spin is conserved, we show that there are two possible phases for the DQSHI… ▽ More We consider the effects of interactions on the edges of ``double" quantum spin Hall insulators (DQSHIs), motivated by recent experiments on moiré twisted metal dichalcogenides. Without interactions, a DQSHI can be understood as two copies of a conventional quantum spin Hall insulator. If interactions are present and $s^z$-spin is conserved, we show that there are two possible phases for the DQSHI edge. First is a weakly correlated edge which has two pairs of helical modes and is adiabatically equivalent to two conventional quantum spin Hall edges. Second is a strongly correlated edge with only one pair of helical modes. The strongly correlated edge also has a gap to single electrons, but is gapless to pairs of electrons. In a quantum point contact geometry, this single-electron gap leads to a Fano factor of $2$ in shot noise measurements, compared to a Fano factor of $1$ for a weakly correlated edge. △ Less

Submitted 14 January, 2026; v1 submitted 28 April, 2025; originally announced April 2025.

How pairing mechanism dictates topology in valley-polarized superconductors with Berry curvature

Authors: Julian May-Mann, Tobias Helbig, Trithep Devakul

Abstract: We investigate how the pairing mechanism influences topological superconductivity in valley-polarized systems with Berry curvature. We demonstrate that short-range attractive interactions, such as those mediated by phonons, favor superconducting states where the Bogoliubov-de Gennes (BdG) Chern number has the same sign as the Berry curvature. In contrast, overscreened repulsive interactions, as in… ▽ More We investigate how the pairing mechanism influences topological superconductivity in valley-polarized systems with Berry curvature. We demonstrate that short-range attractive interactions, such as those mediated by phonons, favor superconducting states where the Bogoliubov-de Gennes (BdG) Chern number has the same sign as the Berry curvature. In contrast, overscreened repulsive interactions, as in the Kohn-Luttinger mechanism, favor superconducting states where the BdG Chern number has the opposite sign as the Berry curvature. We establish these trends in a fully controlled limit and apply them to a recently reported chiral superconductor in rhombohedral multilayer graphene. Our theory provides a concrete experimental criterion for distinguishing between different pairing mechanisms in valley-polarized topological superconductors. △ Less

Submitted 7 March, 2025; originally announced March 2025.

Comments: 5 pages, 4 figures, plus supplemental material

Magnetic Hofstadter cascade in a twisted semiconductor homobilayer

Authors: Benjamin A. Foutty, Aidan P. Reddy, Carlos R. Kometter, Kenji Watanabe, Takashi Taniguchi, Trithep Devakul, Benjamin E. Feldman

Abstract: Transition metal dichalcogenide moiré homobilayers have emerged as a platform in which magnetism, strong correlations, and topology are intertwined. In a large magnetic field, the energetic alignment of states with different spin in these systems is dictated by both strong Zeeman splitting and the structure of the Hofstadter's butterfly spectrum, yet the latter has been difficult to probe experime… ▽ More Transition metal dichalcogenide moiré homobilayers have emerged as a platform in which magnetism, strong correlations, and topology are intertwined. In a large magnetic field, the energetic alignment of states with different spin in these systems is dictated by both strong Zeeman splitting and the structure of the Hofstadter's butterfly spectrum, yet the latter has been difficult to probe experimentally. Here we conduct local thermodynamic measurements of twisted WSe$_2$ homobilayers that reveal a cascade of magnetic phase transitions. We understand these transitions as the filling of individual Hofstadter subbands, allowing us to extract the structure and connectivity of the Hofstadter spectrum of a single spin. The onset of magnetic transitions is independent of twist angle, indicating that the exchange interactions of the component layers are only weakly modified by the moiré potential. In contrast, the magnetic transitions are associated with stark changes in the insulating states at commensurate filling. Our work achieves a spin-resolved measurement of Hofstadter's butterfly despite overlapping states, and it disentangles the role of material and moiré effects on the nature of the correlated ground states. △ Less

Submitted 28 December, 2024; originally announced December 2024.

Fractional Chern mosaic in supermoiré graphene

Authors: Yves H. Kwan, Tixuan Tan, Trithep Devakul

Abstract: We propose the realization of a fractional Chern mosaic: a state characterized by a spatially varying topological order. This state is enabled by a separation of length scales that emerges when three graphene sheets are sequentially rotated by a small twist angle. The resulting structure features not only conventional moiré lattices, but also a much larger supermoiré lattice. We demonstrate that a… ▽ More We propose the realization of a fractional Chern mosaic: a state characterized by a spatially varying topological order. This state is enabled by a separation of length scales that emerges when three graphene sheets are sequentially rotated by a small twist angle. The resulting structure features not only conventional moiré lattices, but also a much larger supermoiré lattice. We demonstrate that a fractional Chern mosaic arises when electron correlations induce fractionalization locally on the moiré scale, while the pattern of fractionalization varies at the supermoiré scale. △ Less

Submitted 13 November, 2024; originally announced November 2024.

Comments: 5+11 pages

Imaging supermoiré relaxation in helical trilayer graphene

Authors: Jesse C. Hoke, Yifan Li, Yuwen Hu, Julian May-Mann, Kenji Watanabe, Takashi Taniguchi, Trithep Devakul, Benjamin E. Feldman

Abstract: In twisted van der Waals materials, local atomic relaxation can alter the underlying electronic structure. Characterizing lattice reconstruction and its susceptibility to strain is essential for understanding emergent electronic states, especially in multilayers in which interference between moiré lattices yields larger supermoiré patterns whose energy is highly sensitive to local stacking. Here w… ▽ More In twisted van der Waals materials, local atomic relaxation can alter the underlying electronic structure. Characterizing lattice reconstruction and its susceptibility to strain is essential for understanding emergent electronic states, especially in multilayers in which interference between moiré lattices yields larger supermoiré patterns whose energy is highly sensitive to local stacking. Here we image spatial modulations in the electronic character of helical trilayer graphene, which indicate relaxation into a superstructure of large domains with uniform moiré periodicity. We show that the supermoiré domain size is increased by strain and can be altered in the same device while preserving the local properties within each domain. Finally, we observe a higher conductance at the domain boundaries, consistent with predictions that they host counter-propagating edge modes. Our work provides a real-space visualization of moiré-periodic domains, reveals two independently tunable length scales and demonstrates strain engineering as a route towards designing correlated topological networks at the supermoiré scale. △ Less

Submitted 24 January, 2026; v1 submitted 21 October, 2024; originally announced October 2024.

Wavefunction approach to the fractional anomalous Hall crystal

Authors: Tixuan Tan, Julian May-Mann, Trithep Devakul

Abstract: We propose fractional anomalous Hall crystals (FAHCs) as possible ground states of strongly interacting electrons in parent bands with Berry curvature. FAHCs are exotic states of matter that spontaneously break continuous translation symmetry to form a fractional Chern insulator. We construct a unified family of variational wavefunctions that describe FAHCs and their competing states in the presen… ▽ More We propose fractional anomalous Hall crystals (FAHCs) as possible ground states of strongly interacting electrons in parent bands with Berry curvature. FAHCs are exotic states of matter that spontaneously break continuous translation symmetry to form a fractional Chern insulator. We construct a unified family of variational wavefunctions that describe FAHCs and their competing states in the presence of uniform parent Berry curvature. We calculate their variational energy with Coulomb interactions semi-analytically in the thermodynamic limit. Our analysis reveals that FAHCs can be energetically favorable over both Wigner crystals and integer anomalous Hall crystals for sufficiently strong interactions or flat dispersion. △ Less

Submitted 10 September, 2024; originally announced September 2024.

Parent Berry curvature and the ideal anomalous Hall crystal

Authors: Tixuan Tan, Trithep Devakul

Abstract: We study a model of electrons moving in a parent band of uniform Berry curvature. At sufficiently high parent Berry curvature, we show that strong repulsive interactions generically lead to the formation of an anomalous Hall crystal: a topological state with spontaneously broken continuous translation symmetry. Our results are established via a mapping to a problem of Wigner crystallization in a r… ▽ More We study a model of electrons moving in a parent band of uniform Berry curvature. At sufficiently high parent Berry curvature, we show that strong repulsive interactions generically lead to the formation of an anomalous Hall crystal: a topological state with spontaneously broken continuous translation symmetry. Our results are established via a mapping to a problem of Wigner crystallization in a regular 2D electron gas. Interestingly, we find that a periodic electrostatic potential induces a competing state with opposite Chern number. Our theory offers a unified perspective for understanding several aspects of the recently observed integer and fractional quantum anomalous Hall effects in rhombohedral multilayer graphene and provides a recipe for engineering new topological states. △ Less

Submitted 8 July, 2024; v1 submitted 6 March, 2024; originally announced March 2024.

Theory of Half-Integer Fractional Quantum Spin Hall Insulator Edges

Authors: Julian May-Mann, Ady Stern, Trithep Devakul

Abstract: We study the edges of fractional quantum spin Hall insulators (FQSH) with half-integer spin Hall conductance. These states can be viewed as symmetric combinations of a spin-up and spin-down half-integer fractional quantum Hall state (FQH) that are time-reversal invariant, and conserve the z-component of spin. We consider the non-Abelian states based on the Pfaffian, anti-Pfaffian, PH-Pfaffian, and… ▽ More We study the edges of fractional quantum spin Hall insulators (FQSH) with half-integer spin Hall conductance. These states can be viewed as symmetric combinations of a spin-up and spin-down half-integer fractional quantum Hall state (FQH) that are time-reversal invariant, and conserve the z-component of spin. We consider the non-Abelian states based on the Pfaffian, anti-Pfaffian, PH-Pfaffian, and 221 FQH, and generic Abelian FQH. For strong enough spin-conserving interactions, we find that all the non-Abelian and Abelian edges flow to the same fixed point that consists of a single pair of charged counter-propagating bosonic modes. If spin-conservation is broken, the Abelian edge can be fully gapped in a time-reversal symmetric fashion. The non-Abelian edge with broken spin-conservation remains gapless due to time-reversal symmetry, and can flow to a new fixed point with a helical gapless pair of Majorana fermions. We discuss the possible relevance of our results to the recent observation of a half-integer edge conductance in twisted MoTe2. △ Less

Submitted 4 March, 2024; originally announced March 2024.

Comments: 9 pages

Stability of quasiperiodic superconductors

Authors: Nicole Sabina Ticea, Julian May-Mann, Jiewen Xiao, Erez Berg, Trithep Devakul

Abstract: We study the effects of quasiperiodicity on the stability of conventional and unconventional superconductors. Quasiperiodicity is modelled using the three-dimensional Aubry-Andre model, a system in which electrons are coupled to a translation-symmetry-breaking potential that is incommensurate with the underlying lattice. Upon increasing the strength of the quasiperiodic potential, the single-parti… ▽ More We study the effects of quasiperiodicity on the stability of conventional and unconventional superconductors. Quasiperiodicity is modelled using the three-dimensional Aubry-Andre model, a system in which electrons are coupled to a translation-symmetry-breaking potential that is incommensurate with the underlying lattice. Upon increasing the strength of the quasiperiodic potential, the single-particle eigenstates undergo a transition from a ballistic to a diffusive character. Here, we study the instability of the model towards superconductivity. We find that in the ballistic regime, the system is unstable towards both $s$-wave and $p$-wave superconductivity. In contrast, only the conventional $s$-wave instability survives in the intermediate diffusive regime. Our results suggest a version of Anderson's theorem for quasiperiodic systems, relating the normal state dynamics to the stability of conventional and unconventional superconductivity. These findings are relevant vis-a-vis recent studies of superconductivity in quasiperiodic moire structures. △ Less

Submitted 16 February, 2024; originally announced February 2024.

Comments: 5 pages, 4 figures

Journal ref: PhysRevB.110.L060501 (2024)

Designing topology and fractionalization in narrow gap semiconductor films via electrostatic engineering

Authors: Tixuan Tan, Aidan P. Reddy, Liang Fu, Trithep Devakul

Abstract: We show that topological flat minibands can be engineered in a class of narrow gap semiconductor films using only an external electrostatic superlattice potential. We demonstrate that, for realistic material parameters, these bands are capable of hosting correlated topological phases such as integer and fractional quantum anomalous Hall states and composite Fermi liquid phases at zero magnetic fie… ▽ More We show that topological flat minibands can be engineered in a class of narrow gap semiconductor films using only an external electrostatic superlattice potential. We demonstrate that, for realistic material parameters, these bands are capable of hosting correlated topological phases such as integer and fractional quantum anomalous Hall states and composite Fermi liquid phases at zero magnetic field. Our results provide a path towards the realization of fractionalized topological states in a broad range of materials. △ Less

Submitted 10 January, 2025; v1 submitted 5 February, 2024; originally announced February 2024.

Wigner Molecular Crystals from Multi-electron Moiré Artificial Atoms

Authors: Hongyuan Li, Ziyu Xiang, Aidan P. Reddy, Trithep Devakul, Renee Sailus, Rounak Banerjee, Takashi Taniguchi, Kenji Watanabe, Sefaattin Tongay, Alex Zettl, Liang Fu, Michael F. Crommie, Feng Wang

Abstract: Semiconductor moiré superlattices provide a versatile platform to engineer new quantum solids composed of artificial atoms on moiré sites. Previous studies have mostly focused on the simplest correlated quantum solid - the Fermi-Hubbard model - where intra-atom interactions are simplified to a single onsite repulsion energy U. These studies have revealed novel quantum phases ranging from Mott insu… ▽ More Semiconductor moiré superlattices provide a versatile platform to engineer new quantum solids composed of artificial atoms on moiré sites. Previous studies have mostly focused on the simplest correlated quantum solid - the Fermi-Hubbard model - where intra-atom interactions are simplified to a single onsite repulsion energy U. These studies have revealed novel quantum phases ranging from Mott insulators to quantum anomalous Hall insulators at a filling of one electron per moiré unit cell. New types of quantum solids should arise at even higher filling factors where the multi-electron configuration of moiré artificial atoms provides new degrees of freedom. Here we report the experimental observation of Wigner molecular crystals emerging from multi-electron artificial atoms in twisted bilayer WS2 moiré superlattices. Moiré artificial atoms, unlike natural atoms, can host qualitatively different electron states due to the interplay between quantized energy levels and Coulomb interactions. Using scanning tunneling microscopy (STM), we demonstrate that Wigner molecules appear in multi-electron artificial atoms when Coulomb interactions dominate. Three-electron Wigner molecules, for example, are seen to exhibit a characteristic trimer pattern. The array of Wigner molecules observed in a moiré superlattice comprises a new crystalline phase of electrons: the Wigner molecular crystal. We show that these Wigner molecular crystals are highly tunable through mechanical strain, moiré period, and carrier charge type. Our study presents new opportunities for exploring quantum phenomena in moiré quantum solids composed of multi-electron artificial atoms. △ Less

Submitted 11 December, 2023; originally announced December 2023.

Multi-moiré trilayer graphene: lattice relaxation, electronic structure, and magic angles

Authors: Charles Yang, Julian May-Mann, Ziyan Zhu, Trithep Devakul

Abstract: We systematically explore the structural and electronic properties of twisted trilayer graphene systems. In general, these systems are characterized by two twist angles, which lead to two incommensurate moiré periods. We show that lattice relaxation results in the formation of domains of periodic single-moiré structures only for twist angles close to the simplest fractions. For the majority of oth… ▽ More We systematically explore the structural and electronic properties of twisted trilayer graphene systems. In general, these systems are characterized by two twist angles, which lead to two incommensurate moiré periods. We show that lattice relaxation results in the formation of domains of periodic single-moiré structures only for twist angles close to the simplest fractions. For the majority of other twist angles, the incommensurate moiré periods lead to a quasicrystalline structure. We identify experimentally relevant magic angles at which the electronic density of states is sharply peaked and strongly correlated physics is most likely to be realized. △ Less

Submitted 29 October, 2023; v1 submitted 19 October, 2023; originally announced October 2023.

Comments: 11+7 pages, 10 figures

Helical trilayer graphene: a moiré platform for strongly-interacting topological bands

Authors: Li-Qiao Xia, Sergio C. de la Barrera, Aviram Uri, Aaron Sharpe, Yves H. Kwan, Ziyan Zhu, Kenji Watanabe, Takashi Taniguchi, David Goldhaber-Gordon, Liang Fu, Trithep Devakul, Pablo Jarillo-Herrero

Abstract: Quantum geometry of electronic wavefunctions results in fascinating topological phenomena. A prominent example is the intrinsic anomalous Hall effect (AHE) in which a Hall voltage arises in the absence of an applied magnetic field. The AHE requires a coexistence of Berry curvature and spontaneous time-reversal symmetry breaking. These conditions can be realized in two-dimensional moiré systems wit… ▽ More Quantum geometry of electronic wavefunctions results in fascinating topological phenomena. A prominent example is the intrinsic anomalous Hall effect (AHE) in which a Hall voltage arises in the absence of an applied magnetic field. The AHE requires a coexistence of Berry curvature and spontaneous time-reversal symmetry breaking. These conditions can be realized in two-dimensional moiré systems with broken $xy$-inversion symmetry ($C_{2z}$) that host flat electronic bands. Here, we explore helical trilayer graphene (HTG), three graphene layers twisted sequentially by the same angle forming two misoriented moiré patterns. Although HTG is globally $C_{2z}$-symmetric, surprisingly we observe clear signatures of topological bands. At a magic angle $θ_\mathrm{m}\approx 1.8^\circ$, we uncover a robust phase diagram of correlated and magnetic states using magnetotransport measurements. Lattice relaxation leads to large periodic domains in which $C_{2z}$ is broken on the moiré scale. Each domain harbors flat topological bands with valley-contrasting Chern numbers $\pm(1,-2)$. We find correlated states at integer electron fillings per moiré unit cell $ν=1,2,3$ and fractional fillings $2/3,7/2$ with the AHE arising at $ν=1,3$ and $2/3,7/2$. At $ν=1$, a time-reversal symmetric phase appears beyond a critical electric displacement field, indicating a topological phase transition. Finally, hysteresis upon sweeping $ν$ points to first-order phase transitions across a spatial mosaic of Chern domains separated by a network of topological gapless edge states. We establish HTG as an important platform that realizes ideal conditions for exploring strongly interacting topological phases and, due to its emergent moiré-scale symmetries, demonstrates a novel way to engineer topology. △ Less

Submitted 18 October, 2023; originally announced October 2023.

Journal ref: Nature Physics 21.2 (2025): 239-244

Strong-coupling topological states and phase transitions in helical trilayer graphene

Authors: Yves H. Kwan, Patrick J. Ledwith, Chiu Fan Bowen Lo, Trithep Devakul

Abstract: Magic-angle helical trilayer graphene relaxes into commensurate moiré domains, whose topological and well-isolated set of narrow bands possess ideal characteristics for realizing robust correlated topological phases, compared with other graphene-based moiré heterostructures. Combining strong-coupling analysis and Hartree-Fock calculations, we investigate the ground states at integer fillings $ν$,… ▽ More Magic-angle helical trilayer graphene relaxes into commensurate moiré domains, whose topological and well-isolated set of narrow bands possess ideal characteristics for realizing robust correlated topological phases, compared with other graphene-based moiré heterostructures. Combining strong-coupling analysis and Hartree-Fock calculations, we investigate the ground states at integer fillings $ν$, and uncover a rich phase diagram of correlated insulators tuned by an external displacement field $D$. For small $D$, the system realizes several competing families of symmetry-broken generalized flavor ferromagnets, which exhibit various anomalous Hall signatures and Chern numbers as high as $|C|=6$. The interaction-induced dispersion renormalization is weak, so that the band flatness and the validity of strong-coupling theory are maintained at all integer fillings. For experimentally accessible displacement fields, the strong-coupling insulators at all $ν$ undergo topological phase transitions, which appear continuous or weakly first-order. For larger $D$, we also find translation symmetry-broken phases such as Kekulé spiral order. Our results demonstrate the robust capability of helical trilayer graphene to host gate-tunable topological and symmetry-broken correlated phases, and lay the groundwork for future theoretical studies on other aspects such as fractional topological states. △ Less

Submitted 18 August, 2023; originally announced August 2023.

Comments: 16+9 pages

Electronic ratchet effect in a moiré system: signatures of excitonic ferroelectricity

Authors: Zhiren Zheng, Xueqiao Wang, Ziyan Zhu, Stephen Carr, Trithep Devakul, Sergio de la Barrera, Nisarga Paul, Zumeng Huang, Anyuan Gao, Yang Zhang, Damien Bérubé, Kathryn Natasha Evancho, Kenji Watanabe, Takashi Taniguchi, Liang Fu, Yao Wang, Su-Yang Xu, Efthimios Kaxiras, Pablo Jarillo-Herrero, Qiong Ma

Abstract: Electronic ferroelectricity represents a new paradigm where spontaneous symmetry breaking driven by electronic correlations, in contrast to traditional lattice-driven ferroelectricity, leads to the formation of electric dipoles. Despite the potential application advantages arising from its electronic nature, switchable electronic ferroelectricity remains exceedingly rare. Here, we report the disco… ▽ More Electronic ferroelectricity represents a new paradigm where spontaneous symmetry breaking driven by electronic correlations, in contrast to traditional lattice-driven ferroelectricity, leads to the formation of electric dipoles. Despite the potential application advantages arising from its electronic nature, switchable electronic ferroelectricity remains exceedingly rare. Here, we report the discovery of an electronic ratchet effect that manifests itself as switchable electronic ferroelectricity in a layer-contrasting graphene-boron nitride moiré heterostructure. Our engineered layer-asymmetric moiré potential landscapes result in layer-polarized localized and itinerant electronic subsystems. At particular fillings of the localized subsystem, we find a ratcheting injection of itinerant carriers in a non-volatile manner, leading to a highly unusual ferroelectric response. Strikingly, the remnant polarization can be stabilized at multiple (quasi-continuous) states with behavior markedly distinct from known ferroelectrics. Our experimental observations, simulations, and theoretical analysis suggest that dipolar excitons are the driving force and elementary ferroelectric units in our system. This signifies a new type of electronic ferroelectricity where the formation of dipolar excitons with aligned moments generates a macroscopic polarization and leads to an electronically-driven ferroelectric response, which we term excitonic ferroelectricity. Such new ferroelectrics, driven by quantum objects like dipolar excitons, could pave the way to innovative quantum analog memory and synaptic devices. △ Less

Submitted 6 June, 2023; originally announced June 2023.

Diverse magnetic orders and quantum anomalous Hall effect in twisted bilayer MoTe2 and WSe2

Authors: Taige Wang, Trithep Devakul, Michael P. Zaletel, Liang Fu

Abstract: Twisted homobilayer transition metal dichalcogenide (TMD) offers a versatile platform for exploring band topology, interaction-driven phases, and magnetic orders. We study the interaction-driven phases in twisted TMD homobilayers and their low-energy collective excitations, focusing on the effect of band topology on magnetism and its thermal stability. From Hartree-Fock theory of the continuum mod… ▽ More Twisted homobilayer transition metal dichalcogenide (TMD) offers a versatile platform for exploring band topology, interaction-driven phases, and magnetic orders. We study the interaction-driven phases in twisted TMD homobilayers and their low-energy collective excitations, focusing on the effect of band topology on magnetism and its thermal stability. From Hartree-Fock theory of the continuum model, we identify several magnetic and topological phases. By tuning the displacement field, we find two phase transitions involving a change in topology and magnetism respectively. We analyze the magnon spectrum, revealing the crucial role of band topology in stabilizing 2D ferromagnetism by amplifying easy-axis magnetic anisotropy, resulting in a large magnon gap of up to 7meV. As the magnon gap is directly tied to the stability of the magnetic phase to thermal fluctuations, our findings have several important experimental implications. △ Less

Submitted 11 September, 2024; v1 submitted 4 June, 2023; originally announced June 2023.

Comments: 5 pages, 5 figures. (v2) Added SM. (v3) Improved convergence, added NLSM analysis

Magic-angle helical trilayer graphene

Authors: Trithep Devakul, Patrick J. Ledwith, Li-Qiao Xia, Aviram Uri, Sergio de la Barrera, Pablo Jarillo-Herrero, Liang Fu

Abstract: We propose helical trilayer graphene (HTG), a helical structure featuring identical rotation angles $θ\approx 1.5^\circ$ between three consecutive layers of graphene, as a unique and experimentally accessible platform for realizing exotic correlated topological states of matter. While nominally forming a supermoiré (or moiré-of-moiré) structure, we show that HTG locally relaxes into large regions… ▽ More We propose helical trilayer graphene (HTG), a helical structure featuring identical rotation angles $θ\approx 1.5^\circ$ between three consecutive layers of graphene, as a unique and experimentally accessible platform for realizing exotic correlated topological states of matter. While nominally forming a supermoiré (or moiré-of-moiré) structure, we show that HTG locally relaxes into large regions of a periodic single-moiré structure in which $C_{2z}$ is broken, giving rise to flat topological bands carrying valley-Chern numbers $C=\pm(1,-2)$. These bands feature near-ideal quantum geometry and are isolated from remote bands by a large gap $E_{\mathrm{gap}}\sim 100$ meV, making HTG a promising platform for experimental realization of correlated topological states such as integer and fractional quantum anomalous Hall states in $C=1$ and $2$ bands. △ Less

Submitted 4 May, 2023; originally announced May 2023.

Fractional quantum anomalous Hall states in twisted bilayer MoTe$_2$ and WSe$_2$

Authors: Aidan P. Reddy, Faisal F. Alsallom, Yang Zhang, Trithep Devakul, Liang Fu

Abstract: We demonstrate via exact diagonalization that AA-stacked TMD homobilayers host fractional quantum anomalous Hall (FQAH) states with fractionally quantized Hall conductance at fractional fillings $n=\frac{1}{3},\, \frac{2}{3}$ and zero magnetic field. While both states are most robust at angles near $θ\approx 2^{\circ}$, the $n=\frac{1}{3}$ state gives way to a charge density wave with increasing t… ▽ More We demonstrate via exact diagonalization that AA-stacked TMD homobilayers host fractional quantum anomalous Hall (FQAH) states with fractionally quantized Hall conductance at fractional fillings $n=\frac{1}{3},\, \frac{2}{3}$ and zero magnetic field. While both states are most robust at angles near $θ\approx 2^{\circ}$, the $n=\frac{1}{3}$ state gives way to a charge density wave with increasing twist angle whereas the $n=\frac{2}{3}$ state survives across a much broader range of twist angles. We show that the competition between FQAH states and charge density wave or metallic phases is primarily controlled by the wavefunctions and dispersion of the underlying Chern band, respectively. Additionally, Ising ferromagnetism is found across a broad range of fillings where the system is insulating or metallic alike. The spin gap is enhanced at filling fractions where integer and fractional quantum anomalous Hall states are formed. △ Less

Submitted 22 August, 2023; v1 submitted 24 April, 2023; originally announced April 2023.

Comments: Journal version (PRB, Editor's suggestion). Supplementary Material added. Main: 10 pages, 9 figures. SM: 8 pages, 5 figures

Journal ref: Phys. Rev. B, 108, 085117 (2023)

Mapping twist-tuned multiband topology in bilayer WSe$_2$

Authors: Benjamin A. Foutty, Carlos R. Kometter, Trithep Devakul, Aidan P. Reddy, Kenji Watanabe, Takashi Taniguchi, Liang Fu, Benjamin E. Feldman

Abstract: Semiconductor moiré superlattices have been shown to host a wide array of interaction-driven ground states. However, twisted homobilayers have been difficult to study in the limit of large moiré wavelength, where interactions are most dominant. Here, we conduct local electronic compressibility measurements of twisted bilayer WSe$_2$ (tWSe$_2$) at small twist angles. We demonstrate multiple topolog… ▽ More Semiconductor moiré superlattices have been shown to host a wide array of interaction-driven ground states. However, twisted homobilayers have been difficult to study in the limit of large moiré wavelength, where interactions are most dominant. Here, we conduct local electronic compressibility measurements of twisted bilayer WSe$_2$ (tWSe$_2$) at small twist angles. We demonstrate multiple topological bands which host a series of Chern insulators at zero magnetic field near a 'magic angle' around $1.23^\circ$. Using a locally applied electric field, we induce a topological quantum phase transition at one hole per moiré unit cell. Our work establishes the topological phase diagram of a generalized Kane-Mele-Hubbard model in tWSe$_2$, demonstrating a tunable platform for strongly correlated topological phases. △ Less

Submitted 29 April, 2024; v1 submitted 19 April, 2023; originally announced April 2023.

Comments: This is the author's version of the work. It is posted here by permission of the AAAS for personal use, not for redistribution. The definitive version was published in Science 384 (doi below)

Journal ref: Science 384 (6693), 343-347 (2024)

Artificial intelligence for artificial materials: moiré atom

Authors: Di Luo, Aidan P. Reddy, Trithep Devakul, Liang Fu

Abstract: Moiré engineering in atomically thin van der Waals heterostructures creates artificial quantum materials with designer properties. We solve the many-body problem of interacting electrons confined to a moiré superlattice potential minimum (the moiré atom) using a 2D fermionic neural network. We show that strong Coulomb interactions in combination with the anisotropic moiré potential lead to strikin… ▽ More Moiré engineering in atomically thin van der Waals heterostructures creates artificial quantum materials with designer properties. We solve the many-body problem of interacting electrons confined to a moiré superlattice potential minimum (the moiré atom) using a 2D fermionic neural network. We show that strong Coulomb interactions in combination with the anisotropic moiré potential lead to striking ``Wigner molecule" charge density distributions observable with scanning tunneling microscopy. △ Less

Submitted 26 March, 2023; v1 submitted 14 March, 2023; originally announced March 2023.

Report number: MIT-CTP/5534

Superconductivity and strong interactions in a tunable moiré quasiperiodic crystal

Authors: Aviram Uri, Sergio C. de la Barrera, Mallika T. Randeria, Daniel Rodan-Legrain, Trithep Devakul, Philip J. D. Crowley, Nisarga Paul, Kenji Watanabe, Takashi Taniguchi, Ron Lifshitz, Liang Fu, Raymond C. Ashoori, Pablo Jarillo-Herrero

Abstract: Electronic states in quasiperiodic crystals generally preclude a Bloch description, rendering them simultaneously fascinating and enigmatic. Owing to their complexity and relative scarcity, quasiperiodic crystals are underexplored relative to periodic and amorphous structures. Here, we introduce a new type of highly tunable quasiperiodic crystal easily assembled from periodic components. By twisti… ▽ More Electronic states in quasiperiodic crystals generally preclude a Bloch description, rendering them simultaneously fascinating and enigmatic. Owing to their complexity and relative scarcity, quasiperiodic crystals are underexplored relative to periodic and amorphous structures. Here, we introduce a new type of highly tunable quasiperiodic crystal easily assembled from periodic components. By twisting three layers of graphene with two different twist angles, we form two moiré patterns with incommensurate moiré unit cells. In contrast to many common quasiperiodic structures that are defined on the atomic scale, the quasiperiodicity in our system is defined on moiré length scales of several nanometers. This novel "moiré quasiperiodic crystal" allows us to tune the chemical potential and thus the electronic system between a periodic-like regime at low energies and a strongly quasiperiodic regime at higher energies, the latter hosting a large density of weakly dispersing states. Interestingly, in the quasiperiodic regime we observe superconductivity near a flavor-symmetry-breaking phase transition, the latter indicative of the important role electronic interactions play in that regime. The prevalence of interacting phenomena in future systems with in situ tunability is not only useful for the study of quasiperiodic systems, but it may also provide insights into electronic ordering in related periodic moiré crystals. We anticipate that extending this new platform to engineer quasiperiodic crystals by varying the number of layers and twist angles, and by using different two-dimensional components, will lead to a new family of quantum materials to investigate the properties of strongly interacting quasiperiodic crystals. △ Less

Submitted 1 February, 2023; originally announced February 2023.

Artificial atoms, Wigner molecules, and emergent Kagome lattice in semiconductor moiré superlattices

Authors: Aidan P. Reddy, Trithep Devakul, Liang Fu

Abstract: Semiconductor moiré superlattices comprise an array of artificial atoms and provide a highly tunable platform for exploring novel electronic phases. We introduce a theoretical framework for studying moiré quantum matter that treats intra-moiré-atom interactions exactly and is controlled in the limit of large moiré period. We reveal an abundance of new physics arising from strong electron interacti… ▽ More Semiconductor moiré superlattices comprise an array of artificial atoms and provide a highly tunable platform for exploring novel electronic phases. We introduce a theoretical framework for studying moiré quantum matter that treats intra-moiré-atom interactions exactly and is controlled in the limit of large moiré period. We reveal an abundance of new physics arising from strong electron interactions when there are multiple electrons within a moiré unit cell. In particular, at filling factor $n=3$, the Coulomb interaction within each three-electron moiré atom leads to a three-lobed ``Wigner molecule''. When their size is comparable to the moiré period, the Wigner molecules form an emergent Kagome lattice. Our work identifies two universal length scales characterizing the kinetic and interaction energies in moiré materials and demonstrates a rich phase diagram due to their interplay. △ Less

Submitted 20 November, 2023; v1 submitted 2 January, 2023; originally announced January 2023.

Comments: Accepted by PRL. main 5 pages, 4 figures; supplement 12 pages, 4 figures

Hofstadter states and reentrant charge order in a semiconductor moiré lattice

Authors: Carlos R. Kometter, Jiachen Yu, Trithep Devakul, Aidan P. Reddy, Yang Zhang, Benjamin A. Foutty, Kenji Watanabe, Takashi Taniguchi, Liang Fu, Benjamin E. Feldman

Abstract: The emergence of moiré materials with flat bands provides a platform to systematically investigate and precisely control correlated electronic phases. Here, we report local electronic compressibility measurements of a twisted WSe$_2$/MoSe$_2$ heterobilayer which reveal a rich phase diagram of interpenetrating Hofstadter states and electron solids. We show that this reflects the presence of both fl… ▽ More The emergence of moiré materials with flat bands provides a platform to systematically investigate and precisely control correlated electronic phases. Here, we report local electronic compressibility measurements of a twisted WSe$_2$/MoSe$_2$ heterobilayer which reveal a rich phase diagram of interpenetrating Hofstadter states and electron solids. We show that this reflects the presence of both flat and dispersive moiré bands whose relative energies, and therefore occupations, are tuned by density and magnetic field. At low densities, competition between moiré bands leads to a transition from commensurate arrangements of singlets at doubly occupied sites to triplet configurations at high fields. Hofstadter states (i.e., Chern insulators) are generally favored at high densities as dispersive bands are populated, but are suppressed by an intervening region of reentrant charge-ordered states in which holes originating from multiple bands cooperatively crystallize. Our results reveal the key microscopic ingredients that favor distinct correlated ground states in semiconductor moiré systems, and they demonstrate an emergent lattice model system in which both interactions and band dispersion can be experimentally controlled. △ Less

Submitted 9 December, 2022; originally announced December 2022.

Journal ref: Nature Physics 19, 1861-1867 (2023)

Tunable spin and valley excitations of correlated insulators in $Γ$-valley moiré bands

Authors: Benjamin A. Foutty, Jiachen Yu, Trithep Devakul, Carlos R. Kometter, Yang Zhang, Kenji Watanabe, Takashi Taniguchi, Liang Fu, Benjamin E. Feldman

Abstract: Moiré superlattices formed from transition metal dichalcogenides (TMDs) have been shown to support a variety of quantum electronic phases that are highly tunable using applied electromagnetic fields. While the valley character of the low-energy states dramatically affects optoelectronic properties in the constituent TMDs, this degree of freedom has yet to be fully explored in moiré systems. Here,… ▽ More Moiré superlattices formed from transition metal dichalcogenides (TMDs) have been shown to support a variety of quantum electronic phases that are highly tunable using applied electromagnetic fields. While the valley character of the low-energy states dramatically affects optoelectronic properties in the constituent TMDs, this degree of freedom has yet to be fully explored in moiré systems. Here, we establish twisted double bilayer WSe$_2$ as an experimental platform to study electronic correlations within $Γ$-valley moiré bands. Through a combination of local and global electronic compressibility measurements, we identify charge-ordered phases at multiple integer and fractional moiré band fillings $ν$. By measuring the magnetic field dependence of their energy gaps and the chemical potential upon doping, we reveal spin-polarized ground states with novel spin polaron quasiparticle excitations. In addition, an applied displacement field allows us to realize a new mechanism of metal-insulator transition at $ν= -1$ driven by tuning between $Γ$- and $K$-valley moiré bands. Together, our results demonstrate control over both the spin and valley character of the correlated ground and excited states in this system. △ Less

Submitted 23 October, 2023; v1 submitted 21 June, 2022; originally announced June 2022.

Moiré Landau fans and magic zeros

Authors: Nisarga Paul, Philip J. D. Crowley, Trithep Devakul, Liang Fu

Abstract: We study the energy spectrum of moiré systems under a uniform magnetic field. The superlattice potential generally broadens Landau levels into Chern bands with finite bandwidth. However, we find that these Chern bands become flat at a discrete set of magnetic fields which we dub "magic zeros". The flat band subspace is generally different from the Landau level subspace in the absence of the moiré… ▽ More We study the energy spectrum of moiré systems under a uniform magnetic field. The superlattice potential generally broadens Landau levels into Chern bands with finite bandwidth. However, we find that these Chern bands become flat at a discrete set of magnetic fields which we dub "magic zeros". The flat band subspace is generally different from the Landau level subspace in the absence of the moiré superlattice. By developing a semiclassical quantization method and taking account of superlattice induced Bragg reflection, we prove that magic zeros arise from the simultaneous quantization of two distinct $k$-space orbits. The flat bands at magic zeros provide a new setting for exploring crystalline fractional quantum Hall physics. △ Less

Submitted 30 August, 2022; v1 submitted 11 February, 2022; originally announced February 2022.

Comments: 5+4 pages; version to appear in PRL

Anomaly Inflow for Subsystem Symmetries

Authors: Fiona J. Burnell, Trithep Devakul, Pranay Gorantla, Ho Tat Lam, Shu-Heng Shao

Abstract: We study 't Hooft anomalies and the related anomaly inflow for subsystem global symmetries. These symmetries and anomalies arise in a number of exotic systems, including models with fracton order such as the X-cube model. As is the case for ordinary global symmetries, anomalies for subsystem symmetries can be canceled by anomaly inflow from a bulk theory in one higher dimension; the corresponding… ▽ More We study 't Hooft anomalies and the related anomaly inflow for subsystem global symmetries. These symmetries and anomalies arise in a number of exotic systems, including models with fracton order such as the X-cube model. As is the case for ordinary global symmetries, anomalies for subsystem symmetries can be canceled by anomaly inflow from a bulk theory in one higher dimension; the corresponding bulk is therefore a non-trivial subsystem symmetry protected topological (SSPT) phase. We demonstrate these phenomena in several examples with continuous and discrete subsystem global symmetries, as well as time-reversal symmetry. For each example we describe the boundary anomaly, and present classical continuum actions for the corresponding bulk SSPT phases, which describe the response of background gauge fields associated with the subsystem symmetries. Interestingly, we show that the anomaly does not uniquely specify the bulk SSPT phase. In general, the latter may also depend on how the symmetry and the associated foliation structure on the boundary are extended into the bulk. △ Less

Submitted 18 October, 2021; originally announced October 2021.

Comments: 41 pages, 2 figures; the authors were ordered alphabetically

Quantum anomalous Hall effect from inverted charge transfer gap

Authors: Trithep Devakul, Liang Fu

Abstract: A general mechanism is presented by which topological physics arises in strongly correlated systems without flat bands. Starting from a charge transfer insulator, topology emerges when the charge transfer energy between the cation and anion is reduced to invert the lower Hubbard band and the spin-degenerate charge transfer band. A universal low-energy theory is developed for the inversion of charg… ▽ More A general mechanism is presented by which topological physics arises in strongly correlated systems without flat bands. Starting from a charge transfer insulator, topology emerges when the charge transfer energy between the cation and anion is reduced to invert the lower Hubbard band and the spin-degenerate charge transfer band. A universal low-energy theory is developed for the inversion of charge transfer gap in a quantum antiferromagnet. The inverted state is found to be a quantum anomalous Hall (QAH) insulator with non-coplanar magnetism. Interactions play two essential roles in this mechanism: producing the insulating gap and quasiparticle bands prior to the band inversion, and causing the change of magnetic order necessary for the QAH effect after inversion. Our theory explains the electric field induced transition from correlated insulator to QAH state in AB-stacked TMD bilayer MoTe$_2$/WSe$_2$. △ Less

Submitted 26 January, 2022; v1 submitted 28 September, 2021; originally announced September 2021.

One-Dimensional Luttinger Liquids in a Two-Dimensional Moiré Lattice

Authors: Pengjie Wang, Guo Yu, Yves H. Kwan, Yanyu Jia, Shiming Lei, Sebastian Klemenz, F. Alexandre Cevallos, Ratnadwip Singha, Trithep Devakul, Kenji Watanabe, Takashi Taniguchi, Shivaji L. Sondhi, Robert J. Cava, Leslie M. Schoop, Siddharth A. Parameswaran, Sanfeng Wu

Abstract: The Luttinger liquid (LL) model of one-dimensional (1D) electronic systems provides a powerful tool for understanding strongly correlated physics including phenomena such as spin-charge separation. Substantial theoretical efforts have attempted to extend the LL phenomenology to two dimensions (2D), especially in models of closely packed arrays of 1D quantum wires, each being described as a LL. Suc… ▽ More The Luttinger liquid (LL) model of one-dimensional (1D) electronic systems provides a powerful tool for understanding strongly correlated physics including phenomena such as spin-charge separation. Substantial theoretical efforts have attempted to extend the LL phenomenology to two dimensions (2D), especially in models of closely packed arrays of 1D quantum wires, each being described as a LL. Such coupled-wire models have been successfully used to construct 2D anisotropic non-Fermi liquids, quantum Hall states, topological phases, and quantum spin liquids. However, an experimental demonstration of high-quality arrays of 1D LLs suitable for realizing these models remains absent. Here we report the experimental realization of 2D arrays of 1D LLs with crystalline quality in a moiré superlattice made of twisted bilayer tungsten ditelluride (tWTe$_{2}$). Originating from the anisotropic lattice of the monolayer, the moiré pattern of tWTe$_{2}$ hosts identical, parallel 1D electronic channels, separated by a fixed nanoscale distance, which is tunable by the interlayer twist angle. At a twist angle of ~ 5 degrees, we find that hole-doped tWTe$_{2}$ exhibits exceptionally large transport anisotropy with a resistance ratio of ~ 1000 between two orthogonal in-plane directions. The across-wire conductance exhibits power-law scaling behaviors, consistent with the formation of a 2D anisotropic phase that resembles an array of LLs. Our results open the door for realizing a variety of correlated and topological quantum phases based on coupled-wire models and LL physics. △ Less

Submitted 13 December, 2021; v1 submitted 9 September, 2021; originally announced September 2021.

Comments: 29 pages, 4 Main Figures + 13 Extended Data Figures

Journal ref: Nature 605, 57-62 (2022)

Spin-textured Chern bands in AB-stacked transition metal dichalcogenide bilayers

Authors: Yang Zhang, Trithep Devakul, Liang Fu

Abstract: While transition metal dichalcogenide (TMD) based moire materials have been shown to host various correlated electronic phenomena, topological states have not been experimentally observed until now. In this work, using first principles calculations and continuum modeling, we reveal the displacement field induced topological moire bands in AB-stacked TMD heterobilayer MoTe2/WSe2. Valley contrasting… ▽ More While transition metal dichalcogenide (TMD) based moire materials have been shown to host various correlated electronic phenomena, topological states have not been experimentally observed until now. In this work, using first principles calculations and continuum modeling, we reveal the displacement field induced topological moire bands in AB-stacked TMD heterobilayer MoTe2/WSe2. Valley contrasting Chern bands with non-trivial spin texture are formed from interlayer hybridization between MoTe2 and WSe2 bands of nominally opposite spins. Our study establishes a recipe for creating topological bands in AB stacked TMD bilayers in general, which provides a highly tunable platform for realizing quantum spin Hall and interaction induced quantum anomalous Hall effects. △ Less

Submitted 2 August, 2021; v1 submitted 5 July, 2021; originally announced July 2021.

Comments: 6 pages, 6 figures. Accepted at PNAS

Quantum anomalous Hall effect from intertwined moiré bands

Authors: Tingxin Li, Shengwei Jiang, Bowen Shen, Yang Zhang, Lizhong Li, Trithep Devakul, Kenji Watanabe, Takashi Taniguchi, Liang Fu, Jie Shan, Kin Fai Mak

Abstract: Electron correlation and topology are two central threads of modern condensed matter physics. Semiconductor moiré materials provide a highly tunable platform for studies of electron correlation. Correlation-driven phenomena, including the Mott insulator, generalized Wigner crystals, stripe phases and continuous Mott transition, have been demonstrated. However, nontrivial band topology has remained… ▽ More Electron correlation and topology are two central threads of modern condensed matter physics. Semiconductor moiré materials provide a highly tunable platform for studies of electron correlation. Correlation-driven phenomena, including the Mott insulator, generalized Wigner crystals, stripe phases and continuous Mott transition, have been demonstrated. However, nontrivial band topology has remained elusive. Here we report the observation of a quantum anomalous Hall (QAH) effect in AB-stacked MoTe2/WSe2 moiré heterobilayers. Unlike in the AA-stacked structures, an out-of-plane electric field controls not only the bandwidth but also the band topology by intertwining moiré bands centered at different high-symmetry stacking sites. At half band filling, corresponding to one particle per moiré unit cell, we observe quantized Hall resistance, h/e2 (with h and e denoting the Planck's constant and electron charge, respectively), and vanishing longitudinal resistance at zero magnetic field. The electric-field-induced topological phase transition from a Mott insulator to a QAH insulator precedes an insulator-to-metal transition; contrary to most known topological phase transitions, it is not accompanied by a bulk charge gap closure. Our study paves the path for discovery of a wealth of emergent phenomena arising from the combined influence of strong correlation and topology in semiconductor moiré materials. △ Less

Submitted 5 July, 2021; originally announced July 2021.

Magic in twisted transition metal dichalcogenide bilayers

Authors: Trithep Devakul, Valentin Crépel, Yang Zhang, Liang Fu

Abstract: The long wavelength moiré superlattices in twisted 2D structures have emerged as a highly tunable platform for strongly correlated electron physics. We study the moiré bands in twisted transition metal dichalcogenide homobilayers, focusing on WSe$_2$, at small twist angles using a combination of first principles density functional theory, continuum modeling, and Hartree-Fock approximation. We reve… ▽ More The long wavelength moiré superlattices in twisted 2D structures have emerged as a highly tunable platform for strongly correlated electron physics. We study the moiré bands in twisted transition metal dichalcogenide homobilayers, focusing on WSe$_2$, at small twist angles using a combination of first principles density functional theory, continuum modeling, and Hartree-Fock approximation. We reveal the rich physics at small twist angles $θ<4^\circ$, and identify a particular magic angle at which the top valence moiré band achieves almost perfect flatness. In the vicinity of this magic angle, we predict the realization of a generalized Kane-Mele model with a topological flat band, interaction-driven Haldane insulator, and Mott insulators at the filling of one hole per moiré unit cell. The combination of flat dispersion and uniformity of Berry curvature near the magic angle holds promise for realizing fractional quantum anomalous Hall effect at fractional filling. We also identify twist angles favorable for quantum spin Hall insulators and interaction-induced quantum anomalous Hall insulators at other integer fillings. △ Less

Submitted 18 November, 2021; v1 submitted 22 June, 2021; originally announced June 2021.

Journal ref: Nature Communications 12, 6730 (2021)

Quantum oscillations in the zeroth Landau Level and the serpentine Landau fan

Authors: T. Devakul, Yves H. Kwan, S. L. Sondhi, S. A. Parameswaran

Abstract: We identify an unusual mechanism for quantum oscillations in nodal semimetals, driven by a single pair of Landau levels periodically closing their gap at the Fermi energy as a magnetic field is varied. These `zero Landau level' quantum oscillations (ZQOs) appear in the nodal limit where the zero-field Fermi volume vanishes, and have distinctive periodicity and temperature dependence. We link the L… ▽ More We identify an unusual mechanism for quantum oscillations in nodal semimetals, driven by a single pair of Landau levels periodically closing their gap at the Fermi energy as a magnetic field is varied. These `zero Landau level' quantum oscillations (ZQOs) appear in the nodal limit where the zero-field Fermi volume vanishes, and have distinctive periodicity and temperature dependence. We link the Landau spectrum of a two-dimensional (2D) nodal semimetal to the Rabi model, and show by exact solution that across the entire Landau fan, pairs of opposite-parity Landau levels are intertwined in a `serpentine' manner. We propose 2D surfaces of topological crystalline insulators as natural settings for ZQOs, and comment on implications for anomaly physics in 3D nodal semimetals. △ Less

Submitted 10 August, 2021; v1 submitted 13 January, 2021; originally announced January 2021.

Journal ref: Phys. Rev. Lett. 127, 116602 (2021)

Theory of competing excitonic orders in insulating WTe$_2$ monolayers

Authors: Yves H. Kwan, T. Devakul, S. L. Sondhi, S. A. Parameswaran

Abstract: We develop a theory of the excitonic phase recently proposed as the zero-field insulating state observed near charge neutrality in monolayer WTe$_2$. Using a Hartree-Fock approximation, we numerically identify two distinct gapped excitonic phases: a spin density wave state for weak non-zero interaction strength and spin spiral order at stronger interactions, separated by a narrow window of non-exc… ▽ More We develop a theory of the excitonic phase recently proposed as the zero-field insulating state observed near charge neutrality in monolayer WTe$_2$. Using a Hartree-Fock approximation, we numerically identify two distinct gapped excitonic phases: a spin density wave state for weak non-zero interaction strength and spin spiral order at stronger interactions, separated by a narrow window of non-excitonic quantum spin Hall insulator. We introduce a simplified model capturing key features of the WTe$_2$ band structure, in which these phases appear as distinct valley ferromagnetic orders. We link the competition between the excitonic phases to the orbital structure of electronic wavefunctions at the Fermi surface and hence its proximity to the underlying gapped Dirac point in WTe$_2$. We briefly discuss collective modes of the two excitonic states, and comment on implications for experiments. △ Less

Submitted 23 September, 2021; v1 submitted 9 December, 2020; originally announced December 2020.

Comments: 14 pages, 5 figures

Journal ref: Phys. Rev. B 104, 125133 (2021)

Fractalizing quantum codes

Authors: Trithep Devakul, Dominic J. Williamson

Abstract: We introduce "fractalization", a procedure by which spin models are extended to higher-dimensional "fractal" spin models. This allows us to interpret type-II fracton phases, fractal symmetry-protected topological phases, and more, in terms of well understood lower-dimensional spin models. Fractalization is also useful for deriving new spin models and quantum codes from known ones. We construct hig… ▽ More We introduce "fractalization", a procedure by which spin models are extended to higher-dimensional "fractal" spin models. This allows us to interpret type-II fracton phases, fractal symmetry-protected topological phases, and more, in terms of well understood lower-dimensional spin models. Fractalization is also useful for deriving new spin models and quantum codes from known ones. We construct higher dimensional generalizations of fracton models that host extended fractal excitations. Finally, by applying fractalization to a 2D subsystem code, we produce a family of locally generated 3D subsystem codes that are conjectured to saturate a quantum information storage tradeoff bound. △ Less

Submitted 15 April, 2021; v1 submitted 2 September, 2020; originally announced September 2020.

Comments: 17 pages

Journal ref: Quantum 5, 438 (2021)

Type-II fractons from coupled spin chains and layers

Authors: Dominic J. Williamson, Trithep Devakul

Abstract: We describe a construction of topological orders from coupled lower dimensional symmetry-protected topological orders, which is closely related to gauging a subsystem symmetry. Our construction yields both conventional topological orders and exotic fracton topological orders of type-I and type-II. In particular, we find a coupled spin chain construction of Haah's cubic code, and a coupled layer co… ▽ More We describe a construction of topological orders from coupled lower dimensional symmetry-protected topological orders, which is closely related to gauging a subsystem symmetry. Our construction yields both conventional topological orders and exotic fracton topological orders of type-I and type-II. In particular, we find a coupled spin chain construction of Haah's cubic code, and a coupled layer construction of Yoshida's fractal spin liquids. △ Less

Submitted 22 April, 2021; v1 submitted 15 July, 2020; originally announced July 2020.

Comments: 8+9 pages, 4 figures; v2 published version

Journal ref: Phys. Rev. B 103, 155140 (2021)

Floating topological phases

Authors: Trithep Devakul, S. L. Sondhi, S. A. Kivelson, Erez Berg

Abstract: While quasi-two-dimensional (layered) materials can be highly anisotropic, their asymptotic long-distance behavior generally reflects the properties of a fully three dimensional phase of matter. However, certain topologically ordered quantum phases with an emergent 2+1 dimensional gauge symmetry can be asymptotically impervious to interplane couplings. We discuss the stability of such "floating to… ▽ More While quasi-two-dimensional (layered) materials can be highly anisotropic, their asymptotic long-distance behavior generally reflects the properties of a fully three dimensional phase of matter. However, certain topologically ordered quantum phases with an emergent 2+1 dimensional gauge symmetry can be asymptotically impervious to interplane couplings. We discuss the stability of such "floating topological phases", as well as their diagnosis by means of a non-local order parameter. Such a phase can produce a divergent ratio $ρ_{\perp}/ρ_{\parallel}$ of the inter-layer to intra-layer resistivity as $T\to 0$, even in an insulator where both $ρ_{\perp}$ and $ρ_\parallel$ individually diverge. Experimental observation of such a divergence would constitute proof of the existence of a topological (e.g. spin liquid) phase. △ Less

Submitted 8 June, 2020; originally announced June 2020.

Comments: 15 pages

Journal ref: Phys. Rev. B 102, 125136 (2020)

Strong planar subsystem symmetry-protected topological phases and their dual fracton orders

Authors: Trithep Devakul, Wilbur Shirley, Juven Wang

Abstract: We classify subsystem symmetry-protected topological (SSPT) phases in $3+1$D protected by planar subsystem symmetries, which are dual to abelian fracton topological orders. We distinguish between weak SSPTs, which can be constructed by stacking $2+1$D SPTs, and strong SSPTs, which cannot. We identify signatures of strong phases, and show by explicit construction that such phases exist. A classific… ▽ More We classify subsystem symmetry-protected topological (SSPT) phases in $3+1$D protected by planar subsystem symmetries, which are dual to abelian fracton topological orders. We distinguish between weak SSPTs, which can be constructed by stacking $2+1$D SPTs, and strong SSPTs, which cannot. We identify signatures of strong phases, and show by explicit construction that such phases exist. A classification of strong phases is presented for an arbitrary finite abelian group. Finally, we show that fracton orders realizable via $p$-string condensation are dual to weak SSPTs, while strong SSPTs do not admit such a realization. △ Less

Submitted 31 August, 2020; v1 submitted 3 October, 2019; originally announced October 2019.

Comments: 21 pages, 7 figures

Journal ref: Phys. Rev. Research 2, 012059(R) (2020)

Fractonic Chern-Simons and BF theories

Authors: Yizhi You, Trithep Devakul, S. L. Sondhi, F. J. Burnell

Abstract: Fracton order is an intriguing new type of order which shares many common features with topological order, such as topology-dependent ground state degeneracies, and excitations with mutual statistics. However, it also has several distinctive geometrical aspects, such as excitations with restricted mobility, which naturally lead to effective descriptions in terms of higher rank gauge fields. In thi… ▽ More Fracton order is an intriguing new type of order which shares many common features with topological order, such as topology-dependent ground state degeneracies, and excitations with mutual statistics. However, it also has several distinctive geometrical aspects, such as excitations with restricted mobility, which naturally lead to effective descriptions in terms of higher rank gauge fields. In this paper, we investigate possible effective field theories for 3D fracton order, by presenting a general philosophy whereby topological-like actions for such higher-rank gauge fields can be constructed. Our approach draws inspiration from Chern-Simons and BF theories in 2+1 dimensions, and imposes constraints binding higher-rank gauge charge to higher-rank gauge flux. We show that the resulting fractonic Chern-Simons and BF theories reproduce many of the interesting features of their familiar 2D cousins. We analyze one example of the resulting fractonic Chern-Simons theory in detail, and show that upon quantization it realizes a gapped fracton order with quasiparticle excitations that are mobile only along a sub-set of 1-dimensional lines, and display a form of fractional self-statistics. The ground state degeneracy of this theory is both topology- and geometry- dependent, scaling exponentially with the linear system size when the model is placed on a 3-dimensional torus. By studying the resulting quantum theory on the lattice, we show that it describes a $\mathbb{Z}_s$ generalization of the Chamon code. △ Less

Submitted 25 April, 2019; originally announced April 2019.

Journal ref: Phys. Rev. Research 2, 023249 (2020)

Classifying local fractal subsystem symmetry protected topological phases

Authors: Trithep Devakul

Abstract: We study symmetry-protected topological (SPT) phases of matter in 2D protected by symmetries acting on fractal subsystems of a certain type. Despite the total symmetry group of such systems being subextensively large, we show that only a small number of phases are actually realizable by local Hamiltonians. Which phases are possible depends crucially on the spatial structure of the symmetries, and… ▽ More We study symmetry-protected topological (SPT) phases of matter in 2D protected by symmetries acting on fractal subsystems of a certain type. Despite the total symmetry group of such systems being subextensively large, we show that only a small number of phases are actually realizable by local Hamiltonians. Which phases are possible depends crucially on the spatial structure of the symmetries, and we show that in many cases no non-trivial SPT phases are possible at all. In cases where non-trivial SPT phases do exist, we give an exhaustive enumeration of them in terms of their locality. △ Less

Submitted 12 June, 2019; v1 submitted 6 December, 2018; originally announced December 2018.

Comments: 22 pages, 5 figures

Journal ref: Phys. Rev. B 99, 235131 (2019)

An Extension of ETH to Non-Equilibrium Steady States

Authors: Sanjay Moudgalya, Trithep Devakul, D. P. Arovas, S. L. Sondhi

Abstract: We extend the notion of the Eigenstate Thermalization Hypothesis (ETH) to Open Quantum Systems governed by the Gorini-Kossakowski-Lindblad-Sudarshan (GKLS) Master Equation. We present evidence that the eigenstates of non-equilibrium steady state (NESS) density matrices obey a generalization of ETH in boundary-driven systems when the bulk Hamiltonian is non-integrable, just as eigenstates of Gibbs… ▽ More We extend the notion of the Eigenstate Thermalization Hypothesis (ETH) to Open Quantum Systems governed by the Gorini-Kossakowski-Lindblad-Sudarshan (GKLS) Master Equation. We present evidence that the eigenstates of non-equilibrium steady state (NESS) density matrices obey a generalization of ETH in boundary-driven systems when the bulk Hamiltonian is non-integrable, just as eigenstates of Gibbs density matrices are conjectured to do in equilibrium. This generalized ETH, which we call NESS-ETH, can be used to obtain representative pure states that reproduce the expectation values of few-body operators in the NESS. The density matrices of these representative pure states can be further interpreted as weak solutions of the GKLS Master Equation. Additionally, we explore the validity and breakdown of NESS-ETH in the presence of symmetries, integrability and many-body localization in the bulk Hamiltonian. △ Less

Submitted 9 July, 2019; v1 submitted 7 November, 2018; originally announced November 2018.

Comments: 16 pages, 5 figures v2: typos corrected, minor corrections to figures, new appendix, references added

Journal ref: Phys. Rev. B 100, 045112 (2019)

Classification of subsystem symmetry-protected topological phases

Authors: Trithep Devakul, Dominic J. Williamson, Yizhi You

Abstract: We consider symmetry-protected topological (SPT) phases in 2D protected by linear subsystem symmetries, i.e. those that act along rigid lines. There is a distinction between a "strong" subsystem SPT phase, and a "weak" one, which is composed of decoupled 1D SPTs with global symmetries. We propose a natural definition for strong equivalence of such phases, in terms of a linearly-symmetric local uni… ▽ More We consider symmetry-protected topological (SPT) phases in 2D protected by linear subsystem symmetries, i.e. those that act along rigid lines. There is a distinction between a "strong" subsystem SPT phase, and a "weak" one, which is composed of decoupled 1D SPTs with global symmetries. We propose a natural definition for strong equivalence of such phases, in terms of a linearly-symmetric local unitary transformation, under which a weak subsystem SPT is equivalent to the trivial phase. This leads to a number of distinct equivalence classes of strong subsystem SPTs, which we show are in one-to-one correspondence with elements of the group $\mathcal{C}[G_s] = \mathcal{H}^{2}[G_s^2,U(1)]/(\mathcal{H}^{2}[G_s,U(1)])^3$, where $G_s$ is the finite abelian onsite symmetry group. We also show that strong subsystem SPTs by our classification necessarily exhibit a spurious topological entanglement entropy on a cylinder. △ Less

Submitted 22 November, 2018; v1 submitted 15 August, 2018; originally announced August 2018.

Comments: 17 pages, 8 figures

Journal ref: Phys. Rev. B 98, 235121 (2018)