Showing 1–50 of 141 results for author: Law, K

Switchable half-quantum flux states in a ring of the kagome superconductor CsV$_3$Sb$_5$

Authors: Shuo Wang, Ilaria Maccari, Xilin Feng, Ze-Nan Wu, Jia-Peng Peng, Kam Tuen Law, Y. X. Zhao, Andras Szabo, Andreas Schnyder, Ning Kang, Xiao-Song Wu, Jingchao Liu, Xuewen Fu, Mark H. Fischer, Manfred Sigrist, Dapeng Yu, Ben-Chuan Lin

Abstract: Magnetic flux quantization in units of $Φ_0 = h/2e$ is a defining feature of superconductivity, rooted in the charge-2e nature of Cooper pairs. In a ring geometry, the flux quantization leads to oscillations in the critical temperature with magnetic flux, known as the Little-Parks effect. While the maximal critical temperature is conventionally at zero flux, departures from this rule, for instance… ▽ More Magnetic flux quantization in units of $Φ_0 = h/2e$ is a defining feature of superconductivity, rooted in the charge-2e nature of Cooper pairs. In a ring geometry, the flux quantization leads to oscillations in the critical temperature with magnetic flux, known as the Little-Parks effect. While the maximal critical temperature is conventionally at zero flux, departures from this rule, for instance shifts by a half-quantum flux $Φ_0/2$, clearly signal unconventional superconducting states and require sign-changing order parameters. Historically, such $π$-phase shifts in Little-Parks oscillations have been found in tricrystals or engineered ring structures that intentionally incorporate a $π$-phase shift. Here we report the discovery of switchable half-quantum flux states in rings made from single crystals of the kagome superconductor CsV$_3$Sb$_5$. We observe Little-Parks oscillations with a $π$-phase shift at zero bias current, which can be reversibly tuned to conventional Little-Parks oscillations upon applying a bias current. Between the $π$-phase and 0-phase regimes, $h/4e$ periodic oscillations appear. Our observations suggest unconventional pairing, potentially in the form of a multicomponent order parameter in the kagome superconductor CsV$_3$Sb$_5$, and reveal an electrically tunable landscape of competing superconducting condensates and fractional flux states. △ Less

Submitted 16 December, 2025; v1 submitted 10 December, 2025; originally announced December 2025.

Comments: 49 pages, 23 figures

Quantum geometric planar magnetotransport: a probe for magnetic geometry in altermagnets

Authors: Zhichun Ouyang, Wei-Jing Dai, Zi-Ting Sun, Jin-Xin Hu, K. T. Law

Abstract: Nonlinear and nonreciprocal transport phenomena provide a direct probe of band quantum geometry in noncentrosymmetric magnetic materials, such as the nonlinear Hall effect induced by the quantum metric dipole. In altermagnets, a recently discovered class of even-parity collinear magnets with $C_n\mathcal{T}$ symmetry, conventional second-order responses are prohibited by an emergent $C_{2z}$ symme… ▽ More Nonlinear and nonreciprocal transport phenomena provide a direct probe of band quantum geometry in noncentrosymmetric magnetic materials, such as the nonlinear Hall effect induced by the quantum metric dipole. In altermagnets, a recently discovered class of even-parity collinear magnets with $C_n\mathcal{T}$ symmetry, conventional second-order responses are prohibited by an emergent $C_{2z}$ symmetry. In this work, we demonstrate that an in-plane magnetic field lifts this prohibition, inducing a planar magnetotransport that directly probes the intrinsic quantum geometry and the distinctive $C_n\mathcal{T}$ nature of altermagnetic orders. We show that the field-dependent quantum geometric susceptibility generates versatile planar magnetotransport, including the planar Hall effects and nonreciprocal responses. Our work establishes distinctive signatures of altermagnetism in linear and nonlinear magnetotransport, providing a general framework for measuring quantum geometric responses and probing altermagnetic order. △ Less

Submitted 3 December, 2025; originally announced December 2025.

Comments: 7 pages, 6 figures

Spin Symmetry Criteria for Odd-parity Magnets

Authors: Xun-Jiang Luo, Jin-Xin Hu, K. T. Law

Abstract: Inspired by the discovery of altermagnets, which exhibit even-parity nonrelativistic spin splitting, odd-parity magnets (OPMs) have been proposed and emerged as a novel research frontier. In this study, we perform a comprehensive spin group symmetry analysis to establish symmetry criteria for the emergence of OPMs. We identify eight distinct symmetry-driven cases that support OPMs, enabling their… ▽ More Inspired by the discovery of altermagnets, which exhibit even-parity nonrelativistic spin splitting, odd-parity magnets (OPMs) have been proposed and emerged as a novel research frontier. In this study, we perform a comprehensive spin group symmetry analysis to establish symmetry criteria for the emergence of OPMs. We identify eight distinct symmetry-driven cases that support OPMs, enabling their realization in collinear, coplanar, and noncoplanar magnetic orders. These OPMs are categorized into three types based on their spin textures for Bloch states: collinear (type-I), coplanar (type-II), and noncoplanar (type-III). For type-I OPMs, we further delineate additional symmetry requirements for $p$-wave and $f$-wave spin splitting. We identify 48 candidate materials in the Magndata database that satisfy these symmetry criteria. Additionally, we construct two theoretical models to validate the effectiveness of the established symmetry criteria. Finally, we show that OPMs can exhibit an intrinsic $\mathbb{Z}_2$ topology and construct a theoretical model to realize this phase. △ Less

Submitted 12 October, 2025; v1 submitted 6 October, 2025; originally announced October 2025.

Comments: 7 pages, 2 figures

Tunable quantum metric and band topology in bilayer Dirac models

Authors: Xun-Jiang Luo, Xing-Lei Ma, K. T. Law

Abstract: Quantum metric, a fundamental component of quantum geometry, has attracted broad interest in recent years due to its critical role in various quantum phenomena. Meanwhile, band topology, which serves as an important framework in condensed matter physics, has led to the discovery of various topological phases. In this work, we introduce a bilayer Dirac model that allows precise tuning of both prope… ▽ More Quantum metric, a fundamental component of quantum geometry, has attracted broad interest in recent years due to its critical role in various quantum phenomena. Meanwhile, band topology, which serves as an important framework in condensed matter physics, has led to the discovery of various topological phases. In this work, we introduce a bilayer Dirac model that allows precise tuning of both properties. Our approach combines two Dirac Hamiltonians with distinct energy scales; one producing relatively dispersive bands and the other yielding relatively flat bands. The dispersive and flat bands are weakly coupled via hybridization $λ$. By inducing a band inversion in the layer subspace, we achieve flexible tuning of band topology across all Altland-Zirnbauer symmetry classes and quantum metric scaling as $g \propto 1/λ^2$ near band inversion point. Using the bilayer Su-Schrieffer-Heeger model, we investigate the localization properties of gapless boundary states, which are affected by quantum metric. Our work lays a foundation for exploring the interplay between band topology and quantum metric. △ Less

Submitted 17 October, 2025; v1 submitted 27 September, 2025; originally announced September 2025.

Comments: 8 pages, 5 figures

Electrically Controlled 0-$π$ Oscillations and Josephson Giant Magnetoresistor with PT-Symmetric Antiferromagnetic Bilayers

Authors: Jin-Xin Hu, Mengli Hu, Ying-Ming Xie, K. T. Law

Abstract: We propose that unconventional Josephson effects can typically emerge in {\it PT}-symmetric antiferromagnetic (AFM) bilayer systems. When proximitized by a conventional superconductor, these heterostructures host dominant interlayer Cooper pairing that features a distinctive spin texture enabled by the strong exchange field. Specifically, we demonstrate a novel mechanism for electrically tunable 0… ▽ More We propose that unconventional Josephson effects can typically emerge in {\it PT}-symmetric antiferromagnetic (AFM) bilayer systems. When proximitized by a conventional superconductor, these heterostructures host dominant interlayer Cooper pairing that features a distinctive spin texture enabled by the strong exchange field. Specifically, we demonstrate a novel mechanism for electrically tunable 0-$π$ oscillations in lateral Josephson junctions, controlled by an out-of-plane electric displacement field. This behavior originates from field-induced finite-momentum Cooper pairing, a hallmark of the unique layer-pseudospin structure in {\it PT}-symmetric AFM bilayers. Furthermore, we introduce a Josephson giant magnetoresistor based on these exotic spin-layer-locked Cooper pairs, in which the supercurrent exhibits a strong dependence on the internal Néel order. Our findings establish {\it PT}-symmetric AFM bilayers as a versatile platform for phase-controllable Josephson junctions and superconducting magnetic random-access memory, with promising applications in superconducting circuits and ultralow-power computing. △ Less

Submitted 28 October, 2025; v1 submitted 9 September, 2025; originally announced September 2025.

Comments: 6 pages, 4 figures

Universal Boundary-Modes Localization from Quantum Metric Length

Authors: Xing-Lei Ma, Jin-Xin Hu, K. T. Law

Abstract: The presence of localized boundary modes is an unambiguous hallmark of topological quantum matter. While these modes are typically protected by topological invariants such as the Chern number, here we demonstrate that the {\it quantum metric length} (QML), a quantity inherent in multi-band topological systems, governs the spatial extent of flat-band topological boundary modes. We introduce a frame… ▽ More The presence of localized boundary modes is an unambiguous hallmark of topological quantum matter. While these modes are typically protected by topological invariants such as the Chern number, here we demonstrate that the {\it quantum metric length} (QML), a quantity inherent in multi-band topological systems, governs the spatial extent of flat-band topological boundary modes. We introduce a framework for constructing topological flat bands from degenerate manifolds with large quantum metric and find that the boundary modes exhibit dual phases of spatial behaviors: a conventional oscillatory decay arising from bare band dispersion, followed by another exponential decay controlled by quantum geometry. Crucially, the QML, derived from the quantum metric of the degenerate manifolds, sets a lower bound on the spatial spread of boundary states in the flat-band limit. Applying our framework to concrete models, we validate the universal role of the QML in shaping the long-range behavior of topological boundary modes. Furthermore, by tuning the QML, we unveil extraordinary non-local transport phenomena, including QML-shaped quantum Hall plateaus and anomalous Fraunhofer patterns. Our theoretical framework paves the way for engineering boundary-modes localization in topological flat-band systems. △ Less

Submitted 22 December, 2025; v1 submitted 5 September, 2025; originally announced September 2025.

Correlation-driven quantum geometry effects in a Kondo system

Authors: Ruizi Liu, Zehan Chen, Xingkai Cheng, Xiaolin Ren, Yiyang Zhang, Xuezhao Wu, Chengping Zhang, Kun Qian, Ching Ho Chan, Junwei Liu, Kam Tuen Law, Qiming Shao

Abstract: Quantum geometry, including quantum metric and Berry curvature, which describes the topology of electronic states, can induce fascinating physical properties. Symmetry-dependent nonlinear transport has emerged as a sensitive probe of these quantum geometric properties. However, its interplay with strong electronic correlations has rarely been explored in bulk materials, particularly in a Kondo lat… ▽ More Quantum geometry, including quantum metric and Berry curvature, which describes the topology of electronic states, can induce fascinating physical properties. Symmetry-dependent nonlinear transport has emerged as a sensitive probe of these quantum geometric properties. However, its interplay with strong electronic correlations has rarely been explored in bulk materials, particularly in a Kondo lattice system. Here, we uncover correlation-driven quantum geometry in centrosymmetric antiferromagnetic iron telluride (FeTe). We experimentally observe the quantum metric quadrupole-induced third-order nonlinear transport, whose angular dependence reflects magnetic structure in FeTe. The nonlinear transport signals follow Kondo lattice crossover and vanish at high temperatures. Our theory suggests that a Kondo lattice formed at low temperatures explains the emergence of quantum geometry, which is induced by the opening of a hybridization gap near the Fermi energy. This discovery establishes a paradigm where quantum geometry arises not from static symmetry breaking but from dynamic many-body effects and provides a zero-field probe for sensing antiferromagnetic order. △ Less

Submitted 2 July, 2025; originally announced July 2025.

Comments: 19 pages, 4 figures for the manuscript

Layer Pseudospin Superconductivity in Twisted MoTe$_2$

Authors: Jin-Xin Hu, Akito Daido, Zi-Ting Sun, Ying-Ming Xie, K. T. Law

Abstract: Recent experiments have observed signatures of spin-valley-polarized unconventional superconductivity in twisted bilayer MoTe$_2$ (tMoTe$_2$). Here, we explore the rich physics of superconducting tMoTe$_2$, enabled by its unique layer-pseudospin structure. Within a minimal two-orbital layer-pseudospin model framework, both interlayer and intralayer Cooper pairings can be effectively visualized usi… ▽ More Recent experiments have observed signatures of spin-valley-polarized unconventional superconductivity in twisted bilayer MoTe$_2$ (tMoTe$_2$). Here, we explore the rich physics of superconducting tMoTe$_2$, enabled by its unique layer-pseudospin structure. Within a minimal two-orbital layer-pseudospin model framework, both interlayer and intralayer Cooper pairings can be effectively visualized using a layer-space Bloch sphere representation. Remarkably, we find that interlayer pairing prevails in the spin-valley-polarized state, whereas intralayer pairing dominates in the spin-valley-unpolarized state. Strikingly, we further predict that for spin-valley-polarized intravalley superconducting state, experimentally feasible weak displacement fields can stabilize finite-momentum pairings at low temperatures. Additionally, in-plane magnetic fields, which break three-fold rotational symmetry, induce field-direction-dependent finite-momentum pairing states, leading to a versatile momentum-selection phase diagram. Our work highlights the crucial role of layer pseudospin in tMoTe$_2$'s unconventional superconductivity and demonstrates its unique tunability via external fields. △ Less

Submitted 15 June, 2025; originally announced June 2025.

Comments: 10 pages, 5 figures

Spectroscopic evidence for possible quantum spin liquid behavior in a two-dimensional Mott insulator

Authors: Haiyang Chen, Fo-Hong Wang, Qiang Gao, Xue-Jian Gao, Zhenhua Chen, Yaobo Huang, Kam Tuen Law, Xiao Yan Xu, Peng Chen

Abstract: Mott insulators with localized magnetic moments will exhibit a quantum spin liquid (QSL) state when the quantum fluctuations are strong enough to suppress the ordering of the spins. Such an entangled state will give rise to collective excitations, in which spin and charge information are carried separately. Our angle-resolved photoemission spectroscopy (ARPES) measurements on single-layer 1T-TaS2… ▽ More Mott insulators with localized magnetic moments will exhibit a quantum spin liquid (QSL) state when the quantum fluctuations are strong enough to suppress the ordering of the spins. Such an entangled state will give rise to collective excitations, in which spin and charge information are carried separately. Our angle-resolved photoemission spectroscopy (ARPES) measurements on single-layer 1T-TaS2 show a flat band around the zone center and a gap opening of about 200 meV in the low temperature, indicating 2D Mott insulating nature in the system. This flat band is dispersionless in momentum space but shows anomalously broad width around the zone center and the spectral weight decays rapidly as momentum increases. The observation is described as a spectral continuum from electron fractionalization, corroborated by a low energy effective model.The intensity of the flat band is reduced by surface doping with magnetic adatoms and the gap is closing, a result from the interaction between spin impurities coupled with spinons and the chargons, which gives rise to a charge redistribution. Doping with nonmagnetic impurities behaves differently as the chemical potential shift dominates. These findings provide insight into the QSL states of strongly correlated electrons on 2D triangular lattices. △ Less

Submitted 16 April, 2025; originally announced April 2025.

Journal ref: Phys. Rev. Lett. 134, 066402 (2025)

Topological Fermi-arc-like surface states in Kramers nodal line metals

Authors: Zi-Ting Sun, Ruo-Peng Yu, Xue-Jian Gao, K. T. Law

Abstract: The discovery of Kramers nodal line metals (KNLMs) and Kramers Weyl semimetals (KWSs) has significantly expanded the range of metallic topological materials to all noncentrosymmetric crystals. However, a key characteristic of this topology - the presence of topologically protected surface states in KNLMs - is not well understood. In this work, we use a model of a $C_{1v}$ KNLM with curved Kramers… ▽ More The discovery of Kramers nodal line metals (KNLMs) and Kramers Weyl semimetals (KWSs) has significantly expanded the range of metallic topological materials to all noncentrosymmetric crystals. However, a key characteristic of this topology - the presence of topologically protected surface states in KNLMs - is not well understood. In this work, we use a model of a $C_{1v}$ KNLM with curved Kramers nodal lines (KNLs) to demonstrate that Fermi-arc-like surface states (FALSSs), which have a $\mathbb{Z}_2$ topological origin, appear on surfaces parallel to the mirror plane. These states connect two surface momenta, corresponding to the projections of two touching points on the Fermi surfaces. Notably, as achiral symmetries (mirrors and roto-inversions) are gradually broken, the KNLM transitions into a KWS, allowing the FALSSs to evolve continuously into the Fermi arc states of the KWS. We also explore the conditions under which FALSSs emerge in KNLMs with straight KNLs. Through bulk-boundary correspondence, we clarify the topological nature of KNLMs. △ Less

Submitted 6 April, 2025; originally announced April 2025.

Comments: 9 pages, 4 figures

Journal ref: Phys. Rev. B 112, L201111 (2025)

Nonreciprocal Current-Induced Zero-Resistance State in Valley-Polarized Superconductors

Authors: Akito Daido, Youichi Yanase, K. T. Law

Abstract: The recently observed nonreciprocal current-induced zero-resistance state (CIZRS) in twisted trilayer graphene/WSe$_2$ heterostructure has posed a significant theoretical challenge. In the experiment, the system shows a zero-resistance state only when a sufficiently large current is applied in a particular direction, while stays in an incipient superconducting state with small resistance when the… ▽ More The recently observed nonreciprocal current-induced zero-resistance state (CIZRS) in twisted trilayer graphene/WSe$_2$ heterostructure has posed a significant theoretical challenge. In the experiment, the system shows a zero-resistance state only when a sufficiently large current is applied in a particular direction, while stays in an incipient superconducting state with small resistance when the current is small or flows in the opposite direction. In this Letter, we provide a theory of CIZRS. We show that the threefold degenerate Fulde-Ferrell (FF) states are stabilized by the valley polarization and trigonal warping effects of twisted trilayer graphene/WSe$_2$ heterostructures. Moreover, a current flowing in a particular direction breaks the threefold degeneracy and favors a particular FF pairing domain. We therefore propose that the incipient superconducting state is naturally understood as a multidomain state where the interdomain supercurrent is difficult to flow due to the tiny Josephson coupling caused by the mismatch of Cooper-pair momenta between different FF domains. Nevertheless, a sufficiently large current in a particular direction can selectively populate a certain FF state and create monodomain pathways with zero resistance. Crucially, due to the threefold symmetry of the system, a current flowing in the opposite direction can fail to generate the zero-resistance pathways, thus giving rise to the observed nonreciprocity. Finally, we suggest that the long-sought-after triangular finite-momentum state can also be realized in valley-polarized superconductors. △ Less

Submitted 1 December, 2025; v1 submitted 21 March, 2025; originally announced March 2025.

Comments: 11 pages, 6 figures

Journal ref: Phys. Rev. Lett. 135, 236001 (2025)

Kramers nodal lines in intercalated TaS$_2$ superconductors

Authors: Yichen Zhang, Yuxiang Gao, Aki Pulkkinen, Xingyao Guo, Jianwei Huang, Yucheng Guo, Ziqin Yue, Ji Seop Oh, Alex Moon, Mohamed Oudah, Xue-Jian Gao, Alberto Marmodoro, Alexei Fedorov, Sung-Kwan Mo, Makoto Hashimoto, Donghui Lu, Anil Rajapitamahuni, Elio Vescovo, Junichiro Kono, Alannah M. Hallas, Robert J. Birgeneau, Luis Balicas, Ján Minár, Pavan Hosur, Kam Tuen Law , et al. (2 additional authors not shown)

Abstract: Kramers degeneracy is one fundamental embodiment of the quantum mechanical nature of particles with half-integer spin under time reversal symmetry. Under the chiral and noncentrosymmetric achiral crystalline symmetries, Kramers degeneracy emerges respectively as topological quasiparticles of Weyl fermions and Kramers nodal lines (KNLs), anchoring the Berry phase-related physics of electrons. Howev… ▽ More Kramers degeneracy is one fundamental embodiment of the quantum mechanical nature of particles with half-integer spin under time reversal symmetry. Under the chiral and noncentrosymmetric achiral crystalline symmetries, Kramers degeneracy emerges respectively as topological quasiparticles of Weyl fermions and Kramers nodal lines (KNLs), anchoring the Berry phase-related physics of electrons. However, an experimental demonstration for ideal KNLs well isolated at the Fermi level is lacking. Here, we establish a class of noncentrosymmetric achiral intercalated transition metal dichalcogenide superconductors with large Ising-type spin-orbit coupling, represented by In$_x$TaS$_2$, to host an ideal KNL phase. We provide evidence from angle-resolved photoemission spectroscopy with spin resolution, angle-dependent quantum oscillation measurements, and ab-initio calculations. Our work not only provides a realistic platform for realizing and tuning KNLs in layered materials, but also paves the way for exploring the interplay between KNLs and superconductivity, as well as applications pertaining to spintronics, valleytronics, and nonlinear transport. △ Less

Submitted 29 May, 2025; v1 submitted 11 March, 2025; originally announced March 2025.

Comments: 40 pages, 5 figures. Supplementary information PDF included in TeX Source

Journal ref: Nat. Commun. 16, 4984 (2025)

Topological altermagnetic Josephson junctions

Authors: Grant Z. X. Yang, Zi-Ting Sun, Ying-Ming Xie, K. T. Law

Abstract: Planar Josephson junctions are pivotal for engineering topological superconductivity, yet are severely hindered by orbital effects induced by in-plane magnetic fields. In this work, we introduce the generic topological altermagnetic Josephson junctions (TAJJs) by leveraging the intrinsic spin-polarized band splitting and zero net magnetization attributes of altermagnets. Our proposed TAJJs effecti… ▽ More Planar Josephson junctions are pivotal for engineering topological superconductivity, yet are severely hindered by orbital effects induced by in-plane magnetic fields. In this work, we introduce the generic topological altermagnetic Josephson junctions (TAJJs) by leveraging the intrinsic spin-polarized band splitting and zero net magnetization attributes of altermagnets. Our proposed TAJJs effectively mitigate the detrimental orbital effects while robustly hosting Majorana end modes (MEMs) at both ends of the junction. Specifically, we demonstrate that MEMs emerge in $d_{x^2-y^2}$-wave TAJJs but vanish in the $d_{xy}$-wave configuration, thereby establishing the crystallographic orientation angle $θ$ of the altermagnet as a novel control parameter of topology. The distinct spin-polarization of the MEMs provides an unambiguous experimental signature for the spin-resolved measurement. Furthermore, by harnessing the synergy between the $d_{x^2-y^2}$-wave altermagnet and its superconducting counterpart, our proposal extends to high-$T_c$ platforms naturally. Overall, this work establishes altermagnets as a versatile paradigm for realizing topological superconductivity, bridging conceptual innovations with scalable quantum architectures devoid of orbital effects and stray fields. △ Less

Submitted 6 June, 2025; v1 submitted 27 February, 2025; originally announced February 2025.

Comments: 7 pages, 4 figures

Asynchronous mass inversion enriched quantum anomalous Hall states in multilayer graphene

Authors: Xilin Feng, Zi-Ting Sun, K. T. Law

Abstract: Recently, multilayer graphene systems have attracted significant attention due to the discovery of a variety of intriguing phases, particularly quantum anomalous Hall (QAH) states. In rhombohedral pentalayer graphene (RPG), both QAH states with Chern number $C = -5$ and $C = -3$ have been observed. While the $C = -5$ QAH state is well understood, the origin of the $C = -3$ QAH state remains unclea… ▽ More Recently, multilayer graphene systems have attracted significant attention due to the discovery of a variety of intriguing phases, particularly quantum anomalous Hall (QAH) states. In rhombohedral pentalayer graphene (RPG), both QAH states with Chern number $C = -5$ and $C = -3$ have been observed. While the $C = -5$ QAH state is well understood, the origin of the $C = -3$ QAH state remains unclear. In this letter, we propose that the $C = -3$ QAH state, as well as the topological phase transition from $C = -3$ to $C = -5$ state in RPG, arises from an asynchronous mass inversion mechanism driven by the interplay between trigonal warping, staggered layer order, and the displacement field: Trigonal warping splits the low-energy bands of RPG into a central touching point and three satellite Dirac cones. Meanwhile, the coexistence of the staggered layer order and displacement field induces a momentum-dependent effective mass in the low-energy bands. Consequently, mass inversions at the central touching point and the satellite Dirac cones, induced by an increasing displacement field, can occur asynchronously, leading to the formation of the $C = -3$ QAH state and the topological phase transition from QAH state with $C=-3$ to $C=-5$. Additionally, based on this mechanism, we predict the presence of a $C=3$ QAH state in rhombohedral tetralayer graphene (RTG), which can be detected experimentally. Furthermore, this mechanism can also be applied to Bernal tetralayer graphene (BTG), explaining the origin of the observed $C=6$ QAH state. △ Less

Submitted 29 June, 2025; v1 submitted 18 February, 2025; originally announced February 2025.

Probing the flat-band limit of the superconducting proximity effect in Twisted Bilayer Graphene Josephson junctions

Authors: A. Diez-Carlon, J. Diez-Merida, P. Rout, D. Sedov, P. Virtanen, S. Banerjee, R. P. S. Penttila, P. Altpeter, K. Watanabe, T. Taniguchi, S. -Y. Yang, K. T. Law, T. T. Heikkila, P. Torma, M. S. Scheurer, D. K. Efetov

Abstract: While extensively studied in normal metals, semimetals and semiconductors, the superconducting (SC) proximity effect remains elusive in the emerging field of flat-band systems. In this study we probe proximity-induced superconductivity in Josephson junctions (JJs) formed between superconducting NbTiN electrodes and twisted bilayer graphene (TBG) weak links. Here the TBG acts as a highly tunable to… ▽ More While extensively studied in normal metals, semimetals and semiconductors, the superconducting (SC) proximity effect remains elusive in the emerging field of flat-band systems. In this study we probe proximity-induced superconductivity in Josephson junctions (JJs) formed between superconducting NbTiN electrodes and twisted bilayer graphene (TBG) weak links. Here the TBG acts as a highly tunable topological flat-band system, which due to its twist-angle dependent bandwidth, allows to probe the SC proximity effect at the crossover from the dispersive to the flat-band limit. Contrary to our original expectations, we find that the SC remains strong even in the flat-band limit, and gives rise to broad, dome shaped SC regions, in the filling dependent phase diagram. In addition, we find that unlike in conventional JJs, the critical current Ic strongly deviates from a scaling with the normal state conductance GN. We attribute these findings to the onset of strong electron interactions, which can give rise to an excess critical current, and also work out the potential importance of quantum geometric terms as well as multiband pairing mechanisms. Our results present the first detailed study of the SC proximity effect in the flat-band limit and shed new light on the mechanisms that drive the formation of SC domes in flat-band systems. △ Less

Submitted 7 February, 2025; originally announced February 2025.

Odd-parity topological superconductivity in kagome metal RbV$_3$Sb$_5$

Authors: Xilin Feng, Zi-Ting Sun, Ben-Chuan Lin, K. T. Law

Abstract: Kagome superconductors AV$_3$Sb$_5$ (A=K, Rb, Cs) have sparked considerable interest due to the presence of several intertwined symmetry-breaking phases within a single material. Recently, hysteresis and reentrant superconductivity were observed experimentally through magnetoresistance measurements in RbV$_{3}$Sb$_{5}$, providing strong evidence of a spontaneous time-reversal symmetry breaking sup… ▽ More Kagome superconductors AV$_3$Sb$_5$ (A=K, Rb, Cs) have sparked considerable interest due to the presence of several intertwined symmetry-breaking phases within a single material. Recently, hysteresis and reentrant superconductivity were observed experimentally through magnetoresistance measurements in RbV$_{3}$Sb$_{5}$, providing strong evidence of a spontaneous time-reversal symmetry breaking superconducting state. The unconventional magnetic responses, combined with crystalline symmetry, impose strong constraints on the possible pairing symmetries of the superconducting state. In this work, we propose that RbV$_3$Sb$_5$ is an odd-parity superconductor characterized by spin-polarized Cooper pairs. The hysteresis in magnetoresistance and the reentrant superconductivity can both be explained by the formation and evolution of superconducting domains composed of non-unitary pairing. Considering the nodal properties of the kagome superconductor RbV$_{3}$Sb$_{5}$, it is topological and characterized by Majorana zero modes at its boundary, which can be detected through tunneling experiments. △ Less

Submitted 19 January, 2025; originally announced January 2025.

Pseudo-Ising superconductivity induced by $p$-wave magnetism

Authors: Zi-Ting Sun, Xilin Feng, Ying-Ming Xie, Benjamin T. Zhou, Jin-Xin Hu, K. T. Law

Abstract: Unconventional magnetic orders usually interplay with superconductivity in intriguing ways. Here we propose that a conventional superconductor in proximity to a compensated $p$-wave magnet exhibits behaviors analogous to those of Ising superconductivity found in transition-metal dichalcogenides, which we refer to as pseudo-Ising superconductivity. The pseudo-Ising superconductivity is characterize… ▽ More Unconventional magnetic orders usually interplay with superconductivity in intriguing ways. Here we propose that a conventional superconductor in proximity to a compensated $p$-wave magnet exhibits behaviors analogous to those of Ising superconductivity found in transition-metal dichalcogenides, which we refer to as pseudo-Ising superconductivity. The pseudo-Ising superconductivity is characterized by several distinctive features: (i) it stays much more robust under strong $p$-wave magnetism than usual ferromagnetism or $d$-wave altermagnetism, thanks to the apparent time-reversal symmetry in $p$-wave spin splitting; (ii) in the low-temperature regime, a second-order superconducting phase transition occurs at a significantly enhanced in-plane upper critical magnetic field $B_{c2}$; (iii) the supercurrent-carrying state establishes non-vanishing out-of-plane spin magnetization, which is forbidden by symmetry in Rahsba and Ising superconductors. We further propose a spin-orbit-free scheme to realize Majorana zero modes by placing superconducting quantum wires on a $p$-wave magnet. Our work establishes a new form of unconventional superconductivity generated by $p$-wave magnetism. △ Less

Submitted 3 May, 2025; v1 submitted 19 January, 2025; originally announced January 2025.

Comments: 6 pages, 4 figures, plus Supplemental Material

Journal ref: Phys. Rev. B 112, 214504 (2025)

Electric field tunable coupling strength and quantum metric hot spots in a moiré flatband superconductor

Authors: Le Liu, Yu Hong, Chengping Zhang, Jundong Zhu, Jingwei Dong, Kenji Watanabe, Takashi Taniguchi, Luojun Du, Dongxia Shi, Kam Tuen Law, Guangyu Zhang, Wei Yang

Abstract: Superconductivity in flatband systems has attracted tremendous attention in condensed matter physics. Alternating twisted multilayer graphene presents a compelling multiband system, with a coexistence of Dirac bands and flat bands, for exploring superconductivity. However, the roles of flat bands and dispersive bands played in determining the superconductivity remain elusive. Here, we focus on the… ▽ More Superconductivity in flatband systems has attracted tremendous attention in condensed matter physics. Alternating twisted multilayer graphene presents a compelling multiband system, with a coexistence of Dirac bands and flat bands, for exploring superconductivity. However, the roles of flat bands and dispersive bands played in determining the superconductivity remain elusive. Here, we focus on the alternating twisted quadralayer graphene to reveal unconventional superconducting behaviors by systematically quantifying individual contributions for both the dispersive bands and the flat bands. The superconductivity is robust, with a strong electrical field tunability, a maximum BKT transition temperature of 1.6 K, and high critical magnetic fields beyond the Pauli limit. By analyzing the Landau fan diagram at zero electric displacement fields, we disentangle Dirac bands and flat bands, revealing a Coulomb interaction-induced band broadening effect. We further quantify the electric-field-dependent evolution of the critical temperature and coherence length, and estimate the flat-band Fermi velocity and superfluid stiffness via critical current measurements. Our results demonstrate an electric field tunable coupling strength within the superconducting phase, revealing unconventional properties with vanishing Fermi velocity and large superfluid stiffness. These phenomena, attributed to substantial quantum metric contributions mediated by Dirac band hybridization, offer new insights into the mechanisms underlying unconventional flatband superconductivity in moiré systems. △ Less

Submitted 24 November, 2025; v1 submitted 11 January, 2025; originally announced January 2025.

Disorder-induced diffusion transport in flat-band systems with quantum metric

Authors: Chun Wang Chau, Tian Xiang, Shuai A. Chen, K. T. Law

Abstract: Our previous understanding of transport in disordered system depends on the assumption that there is a well-defined Fermi velocity. The Fermi velocity determines important length scales in the system such as the diffusion length and localization length. However, nearly flat band materials with vanishing Fermi velocity, it is uncertain how to understand the disorder effects and what quantities dete… ▽ More Our previous understanding of transport in disordered system depends on the assumption that there is a well-defined Fermi velocity. The Fermi velocity determines important length scales in the system such as the diffusion length and localization length. However, nearly flat band materials with vanishing Fermi velocity, it is uncertain how to understand the disorder effects and what quantities determine the characteristic length scales in the system. In the clean limit, it is expected that the bulk transport is absent. In this work, we demonstrate, with a diamond lattice, that disorder can induce diffusion transport in a flat-band system with finite quantum metric. As disorder increases, the bulk transmission channels are activated, and the conductance reaches a maximum before decays inversely with disorder strength. Importantly, via the calculation of the wave-packet dynamics numerically, we show that the quantum metric determines the diffusion length of the system. Analytically, we show that the interplay between the disorder and quantum geometry gives rise to an effective Fermi velocity, as captured by the self-consistent Born approximation. The diffusion coefficient is identified from the Bethe-Salpeter equation under the ladder approximation. Our results reveal a disorder-driven delocalization mechanism in flat-band systems with finite quantum metric which cannot be understood by well-established theories of quantum diffusion. Our theory is important for understanding the disorder effects and transport properties of flat band materials such as twisted bilayer graphene which are current under intense investigation. △ Less

Submitted 26 September, 2025; v1 submitted 25 December, 2024; originally announced December 2024.

Comments: 4.5 pages and comments are welcome; previously appeared as arXiv:2503.09709v2 which was uploaded in error

Second Harmonic Hall Response in Insulators: Inter-band Quantum Geometry and Breakdown of Kleinman's Conjecture

Authors: Wen-Yu He, K. T. Law

Abstract: The nonlinear Hall effect has recently garnered significant attention as a powerful probe of Fermi surface quantum geometry in metals. While current studies mainly focus on the nonlinear Hall response driven by quasi-static electric fields of low frequencies, the extension of the response to higher frequencies is another promising frontier, which introduces quantum geometry into inter-band transit… ▽ More The nonlinear Hall effect has recently garnered significant attention as a powerful probe of Fermi surface quantum geometry in metals. While current studies mainly focus on the nonlinear Hall response driven by quasi-static electric fields of low frequencies, the extension of the response to higher frequencies is another promising frontier, which introduces quantum geometry into inter-band transitions. Here, we demonstrate that a specific nonlinear Hall response, namely the second harmonic Hall (SHH) response, can arise from inter-band transitions. We establish the quantum geometric origin of the SHH response and show that inter-band quantum geometry dominates the SHH response when driven near inter-band resonance. Crucially, we find that the inter-band SHH response in insulators exhibits strong frequecy dispersion, manifesting the breakdown of Kleinman's conjecture in nonlinear optics. This connects the SHH response to the breakdown of Kleinman's conjecture and reveals that frequency dispersive insulators generally allow the SHH response. Furthermore, we predict a giant SHH susceptibility in gated strained bilayer graphene and propose that one can apply the polarization resolved second harmonic microscopy to detect the SHH response there. △ Less

Submitted 11 December, 2025; v1 submitted 11 November, 2024; originally announced November 2024.

Comments: 7 pages, 3 figures. Comments are welcome

Flat-band Fulde-Ferrell-Larkin-Ovchinnikov State from Quantum Geometric Discrepancy

Authors: Zi-Ting Sun, Ruo-Peng Yu, Shuai A. Chen, Jin-Xin Hu, K. T. Law

Abstract: We propose a new scheme for realizing Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) Cooper pairing states within flat bands, in contrast to the conventional paradigm such as the Zeeman effect. Central to our scheme is the concept of ``quantum geometric discrepancy'' (QGD) that measures differences in the quantum geometry of paired electrons and drives the flat-band FFLO instability. Remarkably, we find… ▽ More We propose a new scheme for realizing Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) Cooper pairing states within flat bands, in contrast to the conventional paradigm such as the Zeeman effect. Central to our scheme is the concept of ``quantum geometric discrepancy'' (QGD) that measures differences in the quantum geometry of paired electrons and drives the flat-band FFLO instability. Remarkably, we find that this instability is directly related to a quantum geometric quantity known as ``anomalous quantum distance'', which formally captures QGD. To model both QGD and the anomalous quantum distance, we examine a flat-band electronic Hamiltonian with tunable spin-dependent quantum metrics. Utilizing the band-projection method, we analyze the QGD-induced FFLO instability from pairing susceptibility. Furthermore, we perform mean-field numerical simulations to obtain the phase diagram of the BCS-FFLO transition, which aligns well with our analytical results. Our work demonstrates that QGD offers a general and distinctive mechanism for stabilizing the flat-band FFLO phase. △ Less

Submitted 28 September, 2025; v1 submitted 1 August, 2024; originally announced August 2024.

Comments: 7 pages, 5 figures plus supplementary information

Journal ref: Quantum Front 4, 20 (2025)

Nematic Ising superconductivity with hidden magnetism in few-layer 6R-TaS2

Authors: Shao-Bo Liu, Congkuan Tian, Yuqiang Fang, Hongtao Rong, Lu Cao, Xinjian Wei, Hang Cui, Mantang Chen, Di Chen, Yuanjun Song, Jian Cui, Jiankun Li, Shuyue Guan, Shuang Jia, Chaoyu Chen, Wenyu He, Fuqiang Huang, Yuhang Jiang, Jinhai Mao, X. C. Xie, K. T. Law, Jian-Hao Chen

Abstract: In van der Waals heterostructures (vdWHs), the manipulation of interlayer stacking/coupling allows for the construction of customizable quantum systems exhibiting exotic physics. An illustrative example is the diverse range of states of matter achieved through varying the proximity coupling between two-dimensional (2D) quantum spin liquid (QSL) and superconductors within the TaS2 family. This stud… ▽ More In van der Waals heterostructures (vdWHs), the manipulation of interlayer stacking/coupling allows for the construction of customizable quantum systems exhibiting exotic physics. An illustrative example is the diverse range of states of matter achieved through varying the proximity coupling between two-dimensional (2D) quantum spin liquid (QSL) and superconductors within the TaS2 family. This study presents a demonstration of the intertwined physics of spontaneous rotational symmetry breaking, hidden magnetism, and Ising superconductivity in the three-fold rotationally symmetric, non-magnetic natural vdWHs 6R-TaS2. A distinctive phase emerges in 6R-TaS2 below a characteristic temperature (T*) of approximately 30 K, which is characterized by a remarkable set of features, including a giant extrinsic anomalous Hall effect (AHE), Kondo screening, magnetic field-tunable thermal hysteresis, and nematic magneto-resistance. At lower temperatures, a coexistence of nematicity and Kondo screening with Ising superconductivity is observed, providing compelling evidence of hidden magnetism within a superconductor. This research not only sheds light on unexpected emergent physics resulting from the coupling of itinerant electrons and localized/correlated electrons in natural vdWHs but also emphasizes the potential for tailoring exotic quantum states through the manipulation of interlayer interactions. △ Less

Submitted 17 July, 2024; originally announced July 2024.

Comments: 16 pages, 4 figures

Flat band excitons and quantum metric

Authors: Xuzhe Ying, K. T. Law

Abstract: We discuss the excitons in flat band systems. Quantum metric plays a central role in determining the properties of single exciton excitation as well as the exciton condensate. While the electrons and holes are extremely heavy in flat bands, the excitons (boundstate of an electron-hole pair) could be light and mobile. In particular, we show that the inverse of exciton's effective mass tensor is pro… ▽ More We discuss the excitons in flat band systems. Quantum metric plays a central role in determining the properties of single exciton excitation as well as the exciton condensate. While the electrons and holes are extremely heavy in flat bands, the excitons (boundstate of an electron-hole pair) could be light and mobile. In particular, we show that the inverse of exciton's effective mass tensor is proportional to the quantum metric tensor. Meanwhile, the flat band excitons have a finite size, lower bounded by the trace of the quantum metric tensor. Given the properties of single exciton excitation, one can argue for the formation of exciton condensate. Because of the quantum metric, the exciton condensate can support dissipationless counterflow supercurrent, implying the stability of exciton condensate. △ Less

Submitted 29 June, 2024; originally announced July 2024.

Comments: 13 pages, 6 figures

Majorana Zero Modes in the Lieb-Kitaev Model with Tunable Quantum Metric

Authors: Xingyao Guo, Xinglei Ma, Xuzhe Ying, K. T. Law

Abstract: The relation between band topology and Majorana zero energy modes (MZMs) in topological superconductors had been well studied in the past decades. However, the relation between the quantum metric and MZMs has yet to be understood. In this work, we first construct a three band Lieb-like lattice model with an isolated flat band and tunable quantum metric. By introducing nearest neighbor equal spin p… ▽ More The relation between band topology and Majorana zero energy modes (MZMs) in topological superconductors had been well studied in the past decades. However, the relation between the quantum metric and MZMs has yet to be understood. In this work, we first construct a three band Lieb-like lattice model with an isolated flat band and tunable quantum metric. By introducing nearest neighbor equal spin pairing, we obtain the Lieb-Kitaev model which supports MZMs. When the Fermi energy is set within the flat band energy, the MZMs appear which are supposed to be well-localized at the ends of the 1D superconductor due to the flatness of the band. On the contrary, we show both numerically and analytically that the localization length of the MZMs is controlled by a length scale defined by the quantum metric of the flat band, which we call the quantum metric length (QML). The QML can be several orders of magnitude longer than the conventional BCS superconducting coherence length. When the QML is comparable to the length of the superconductor, the two MZMs from the two ends of the superconductor can hybridize and induce ultra long-range crossed Andreev reflections. This work unveils how the quantum metric can greatly influence the properties of MZMs through the QML and the results can be generalized to other topological bound states. △ Less

Submitted 23 November, 2024; v1 submitted 9 June, 2024; originally announced June 2024.

Signatures of spin-polarized p-wave superconductivity in the kagome material RbV$_3$Sb$_5$

Authors: Shuo Wang, Xilin Feng, Jing-Zhi Fang, Jia-Peng Peng, Zi-Ting Sun, Jia-Jie Yang, Jingchao Liu, Jia-Ji Zhao, Jian-Kun Wang, Xin-Jie Liu, Ze-Nan Wu, Shengbiao Sun, Ning Kang, Xiao-Song Wu, Zhensheng Zhang, Xuewen Fu, Kam Tuen Law, Ben-Chuan Lin, Dapeng Yu

Abstract: The study of kagome materials has attracted much attention in the past few years due to the presence of many electron-electron interaction-driven phases in a single material. These include charge density waves, nematic phases, superconducting phases, and pair density waves. In this work, we report the discovery of intrinsic spin-polarized p-wave superconductivity in the thin-flake kagome material… ▽ More The study of kagome materials has attracted much attention in the past few years due to the presence of many electron-electron interaction-driven phases in a single material. These include charge density waves, nematic phases, superconducting phases, and pair density waves. In this work, we report the discovery of intrinsic spin-polarized p-wave superconductivity in the thin-flake kagome material RbV$_3$Sb$_5$. Firstly, when an in-plane magnetic field is swept in opposite directions, we observe a unique form of hysteresis in magnetoresistance which is different from the hysteresis induced by extrinsic mechanisms such as flux-trapping or superheating and supercooling effects. The unconventional hysteresis indicates the emergence of an intrinsic time-reversal symmetry-breaking superconducting phase. Strikingly, at a fixed magnetic field, the finite-resistance state can be transitioned into the superconducting state by applying and subsequently removing a large current. Secondly, at temperatures around 400 mK, the re-entrance of superconductivity occurs during an in-plane field-sweeping process. This kind of re-entrance is asymmetric about the zero field axis and observed in all field directions for a fixed current direction, which is different from the re-entrance observed in conventional superconductors. These findings put very strong constraints on the possible superconducting pairing symmetry of RbV$_3$Sb$_5$. We point out that the pairing symmetry, which is consistent with the crystal symmetry and all the observed novel properties, is possibly a time-reversal symmetry-breaking, p-wave pairing with net spin polarization. Importantly, this p-wave pairing gives rise to a nodal topological superconducting state with Majorana flat bands on the sample edges. △ Less

Submitted 8 August, 2025; v1 submitted 21 May, 2024; originally announced May 2024.

Comments: 42 pages, 16 figures

Origin of Superconductivity in Rhombohedral Trilayer Graphene: Quasiparticle Pairing within the Inter-Valley Coherent Phase

Authors: Chun Wang Chau, Shuai A. Chen, K. T. Law

Abstract: Superconductivity (SC) is observed in rhombohedral trilayer graphene (RTG) with an extremely low charge carrier densities, between the normal metal state and a probable inter-valley coherent (IVC) state. The measured coherence length in RTG is roughly two orders of magnitude shorter than the value predicted by a conventional BCS theory. To resolve these discrepancies, we propose that the RTG SC ph… ▽ More Superconductivity (SC) is observed in rhombohedral trilayer graphene (RTG) with an extremely low charge carrier densities, between the normal metal state and a probable inter-valley coherent (IVC) state. The measured coherence length in RTG is roughly two orders of magnitude shorter than the value predicted by a conventional BCS theory. To resolve these discrepancies, we propose that the RTG SC phase arises from the pairing of quasiparticles within the IVC phase. We illustrate the SC behavior using gapped Dirac cones with the chemical potential close to the conduction band's bottom and establish the Ginzburg-Landau theory. Our findings indicate that the mean-field transition temperature, $T_\mathrm{MF}$, is primarily determined by the density of states of quasiparticles within the IVC phase, and is more suppressed in comparison with the BCS relation. Interestingly, we discover that the coherence length behaves according to $ξ\sim 1/\sqrt{T_\mathrm{MF}}$. When the chemical potential lies within the band gap, the conventional coherence length becomes small, while the quantum metric contribution can diverge. Applying our approach to a microscopic model for RTG, our predictions align well with experimental data and effectively capture key measurable features of quantities such as the mean-field transition temperature $T_\mathrm{MF}$ and the coherence length $ξ$. Furthermore, we reveal that the quantum metric contribution, stemming from the multi-band properties of the IVC quasiparticles, plays a significant role in determining the coherence length around the transition regime from superconductivity to IVC. Lastly, experimental predictions are discussed on bebaviors of the upper critical field and coherence length at low temperatures. △ Less

Submitted 29 April, 2024; originally announced April 2024.

Comments: 10+15 pages, 3+1 diagrams, 1+1 tables, supplementary included

Flat Band Josephson Junctions with Quantum Metric

Authors: Zhong C. F. Li, Yuxuan Deng, Shuai A. Chen, Dmitri K. Efetov, K. T. Law

Abstract: In this work, we consider superconductor/flat band material/superconductor (S/FB/S) Josephson junctions (JJs) where the flat band material possesses isolated flat bands with exactly zero Fermi velocity. Contrary to conventional S/N/S JJs where the critical Josephson current vanishes when the Fermi velocity goes to zero, we show in this work that the critical current in the S/FB/S junction is contr… ▽ More In this work, we consider superconductor/flat band material/superconductor (S/FB/S) Josephson junctions (JJs) where the flat band material possesses isolated flat bands with exactly zero Fermi velocity. Contrary to conventional S/N/S JJs where the critical Josephson current vanishes when the Fermi velocity goes to zero, we show in this work that the critical current in the S/FB/S junction is controlled by the quantum metric length $ξ_\mathrm{QM}$ of the flat bands. Microscopically, when $ξ_\mathrm{QM}$ of the flat band is long enough, the interface bound states originally localized at the two S/FB, FB/S interfaces can penetrate deeply into the flat band material and hybridize to form Andreev bound states (ABSs). These ABSs are able to carry long range and sizable supercurrents. Importantly, $ξ_\mathrm{QM}$ also controls how far the proximity effect can penetrate into the flat band material. This stands in sharp contrast to the de Gennes' theory for S/N junctions which predicts that the proximity effect is expected to be zero when the Fermi velocity of the normal metal is zero. We further suggest that the S/FB/S junctions would give rise to a new type of resonant Josephson transistors which can carry sizable and highly gate-tunable supercurrent. △ Less

Submitted 13 June, 2024; v1 submitted 14 April, 2024; originally announced April 2024.

Geometric and conventional contributions of superconducting diode effect: Application to flat-band systems

Authors: Jin-Xin Hu, Shuai A. Chen, K. T. Law

Abstract: Nonreciprocal critical supercurrents give rise to the superconducting diode effect (SDE) in noncentrosymmetric superconductors when time-reversal symmetry is broken. In this paper, we investigate the SDE in superconductors with vanishing spin-orbit coupling but featuring narrow bands near the Fermi energy -- a characteristic particularly relevant to moiré heterostructures, such as twisted bilayer… ▽ More Nonreciprocal critical supercurrents give rise to the superconducting diode effect (SDE) in noncentrosymmetric superconductors when time-reversal symmetry is broken. In this paper, we investigate the SDE in superconductors with vanishing spin-orbit coupling but featuring narrow bands near the Fermi energy -- a characteristic particularly relevant to moiré heterostructures, such as twisted bilayer graphene. Using phenomenological Ginzburg-Landau theory and self-consistent mean-field approaches, we analyze the contributions to the SDE from both conventional band dispersion and quantum geometry. While the conventional SDE arises from the asymmetric Fermi surface, we demonstrate that the quantum metric dipole generates a band quantum-geometric contribution to the SDE, even in systems with symmetric single-particle dispersion. Notably, in the flat-band limit, where the attractive interaction strength significantly exceeds the bandwidth, the contributions from quantum geometry to the supercurrent and diode effect become dominant. Our paper elucidates the conventional and quantum-geometric origins of superconducting nonreciprocity and explores their implications for flat-band superconductors. △ Less

Submitted 21 May, 2025; v1 submitted 1 March, 2024; originally announced March 2024.

Comments: 9 pages, 4 figures

Formation of Mn-rich interfacial phases in Co2FexMn1-xSi thin films

Authors: Ka Ming Law, Arashdeep S. Thind, Mihir Pendharkar, Sahil J. Patel, Joshua J. Phillips, Chris J. Palmstrom, Jaume Gazquez, Albina Borisevich, Rohan Mishra, Adam J. Hauser

Abstract: We report the formation of Mn-rich regions at the interface of Co2FexMn1-xSi thin films grown on GaAs substrates by molecular beam epitaxy (MBE). Scanning transmission electron microscopy (STEM) with electron energy loss (EEL) spectrum imaging reveals that each interfacial region: (1) is 1-2 nm wide, (2) occurs irrespective of the Fe/Mn composition ratio and in both Co-rich and Co-poor films, and… ▽ More We report the formation of Mn-rich regions at the interface of Co2FexMn1-xSi thin films grown on GaAs substrates by molecular beam epitaxy (MBE). Scanning transmission electron microscopy (STEM) with electron energy loss (EEL) spectrum imaging reveals that each interfacial region: (1) is 1-2 nm wide, (2) occurs irrespective of the Fe/Mn composition ratio and in both Co-rich and Co-poor films, and (3) displaces both Co and Fe indiscriminately. We also observe a Mn-depleted region in each film directly above each Mn-rich interfacial layer, roughly 3 nm in width in the x = 0 and x = 0.3 films, and 1 nm in the x = 0.7 (less Mn) film. We posit that growth energetics favor Mn diffusion to the interface even when there is no significant Ga interdiffusion into the epitaxial film. Element-specific X-ray magnetic circular dichroism (XMCD) measurements show larger Co, Fe, and Mn orbital to spin magnetic moment ratios compared to bulk values across the Co2FexMn1-xSi compositional range. The values lie between reported values for pure bulk and nanostructured Co, Fe, and Mn materials, corroborating the non-uniform, layered nature of the material on the nanoscale. Finally, SQUID magnetometry demonstrates that the films deviate from the Slater-Pauling rule for uniform films of both the expected and the measured composition. The results inform a need for care and increased scrutiny when forming Mn-based magnetic thin films on III-V semiconductors like GaAs, particularly when films are on the order of 5 nm or when interface composition is critical to spin transport or other device applications. △ Less

Submitted 24 December, 2023; originally announced December 2023.

Three-Dimensional Quantum Anomalous Hall Effect in Magnetic Topological Insulator Trilayers of Hundred-Nanometer Thickness

Authors: Yi-Fan Zhao, Ruoxi Zhang, Zi-Ting Sun, Ling-Jie Zhou, Deyi Zhuo, Zi-Jie Yan, Hemian Yi, Ke Wang, Moses H. W. Chan, Chao-Xing Liu, K. T. Law, Cui-Zu Chang

Abstract: Magnetic topological states refer to a class of exotic phases in magnetic materials with their non-trivial topological property determined by magnetic spin configurations. An example of such states is the quantum anomalous Hall (QAH) state, which is a zero magnetic field manifestation of the quantum Hall effect. Current research in this direction focuses on QAH insulators with a thickness of less… ▽ More Magnetic topological states refer to a class of exotic phases in magnetic materials with their non-trivial topological property determined by magnetic spin configurations. An example of such states is the quantum anomalous Hall (QAH) state, which is a zero magnetic field manifestation of the quantum Hall effect. Current research in this direction focuses on QAH insulators with a thickness of less than 10nm. The thick QAH insulators in the three-dimensional(3D) regime are limited, largely due to inevitable bulk carriers being introduced in thick magnetic TI samples. Here, we employ molecular beam epitaxy (MBE) to synthesize magnetic TI trilayers with a thickness of up to ~106 nm. We find these samples exhibit well-quantized Hall resistance and vanishing longitudinal resistance at zero magnetic field. By varying magnetic dopants, gate voltages, temperature, and external magnetic fields, we examine the properties of these thick QAH insulators and demonstrate the robustness of the 3D QAH effect. The realization of the well-quantized 3D QAH effect indicates that the nonchiral side surface states of our thick magnetic TI trilayers are gapped and thus do not affect the QAH quantization. The 3D QAH insulators of hundred-nanometer thickness provide a promising platform for the exploration of fundamental physics, including axion physics and image magnetic monopole, and the advancement of electronic and spintronic devices to circumvent Moore's law. △ Less

Submitted 7 December, 2023; v1 submitted 3 December, 2023; originally announced December 2023.

Comments: 24 pages, 5 figures. Comments are welcome

Anomalous Hall effect in the antiferromagnetic Weyl semimetal SmAlSi

Authors: Yuxiang Gao, Shiming Lei, Eleanor M. Clements, Yichen Zhang, Xue-Jian Gao, Songxue Chi, Kam Tuen Law, Ming Yi, Jeffrey W. Lynn, Emilia Morosan

Abstract: The intrinsic anomalous Hall effect (AHE) has been reported in numerous ferromagnetic (FM) Weyl semimetals. However, AHE in the antiferromagnetic (AFM) or paramagnetic (PM) state of Weyl semimetals has been rarely observed experimentally, and only in centrosymmetric materials. Different mechanisms have been proposed to establish the connection between the AHE and the type of magnetic order. In thi… ▽ More The intrinsic anomalous Hall effect (AHE) has been reported in numerous ferromagnetic (FM) Weyl semimetals. However, AHE in the antiferromagnetic (AFM) or paramagnetic (PM) state of Weyl semimetals has been rarely observed experimentally, and only in centrosymmetric materials. Different mechanisms have been proposed to establish the connection between the AHE and the type of magnetic order. In this paper, we report AHE in both the AFM and PM states of non-centrosymmetric compound SmAlSi. To account for the AHE in non-centrosymmetric Weyl semimetals without FM, we introduce a new mechanism based on magnetic field-induced Weyl nodes evolution. Angle-dependent quantum oscillations in SmAlSi provide evidence for the Weyl points and large AHE in both the PM and the AFM states. The proposed mechanism qualitatively explains the temperature dependence of the anomalous Hall conductivity (AHC), which displays unconventional power law behavior of the AHC in both AFM and PM states of SmAlSi. △ Less

Submitted 24 August, 2024; v1 submitted 13 October, 2023; originally announced October 2023.

Journal ref: Phys. Rev. Materials 9, L061201 (2025)

Visualizing the Localized Electrons of a Kagome Flat Band

Authors: Caiyun Chen, Jiangchang Zheng, Ruopeng Yu, Soumya Sankar, Hoi Chun Po, Kam Tuen Law, Berthold Jäck

Abstract: Destructive interference between electron wavefunctions on the two-dimensional (2D) kagome lattice induces an electronic flat band, which could host a variety of interesting many-body quantum states. Key to realize these proposals is to demonstrate the real space localization of kagome flat band electrons. In particular, the extent to which the often more complex lattice structure and orbital comp… ▽ More Destructive interference between electron wavefunctions on the two-dimensional (2D) kagome lattice induces an electronic flat band, which could host a variety of interesting many-body quantum states. Key to realize these proposals is to demonstrate the real space localization of kagome flat band electrons. In particular, the extent to which the often more complex lattice structure and orbital composition of realistic materials counteract the localizing effect of destructive interference, described by the 2D kagome lattice model, is hitherto unknown. We used scanning tunneling microscopy (STM) to visualize the non-trivial Wannier states of a kagome flat band at the surface of CoSn, a kagome metal. We find that the local density of states associated with the flat bands of CoSn is localized at the center of the kagome lattice, consistent with theoretical expectations for their corresponding Wannier states. Our results show that these states exhibit an extremely small localization length of two to three angstroms concomitant with a strongly renormalized quasiparticle velocity, which is comparable to that of moiré superlattices. Hence, interaction effects in the flat bands of CoSn could be much more significant than previously thought. Our findings provide fundamental insight into the electronic properties of kagome metals and are a key step for future research on emergent many-body states in transition metal based kagome materials. △ Less

Submitted 17 August, 2023; originally announced August 2023.

Valley-polarized Josephson Junctions as gate-tunable $0$-$π$ qubit platforms

Authors: Zhong-Chang-Fei Li, Yu-Xuan Deng, Zi-Ting Sun, Jin-Xin Hu, K. T. Law

Abstract: Recently, gate-defined Josephson junctions based on magic-angle twisted bilayer graphene (MATBG) have been fabricated. In such a junction, local electrostatic gating can create two superconducting regions connected by an interaction-driven valley-polarized state as the weak link. Due to the spontaneous time-reversal and inversion symmetry breaking of the valley-polarized state, novel phenomena suc… ▽ More Recently, gate-defined Josephson junctions based on magic-angle twisted bilayer graphene (MATBG) have been fabricated. In such a junction, local electrostatic gating can create two superconducting regions connected by an interaction-driven valley-polarized state as the weak link. Due to the spontaneous time-reversal and inversion symmetry breaking of the valley-polarized state, novel phenomena such as the Josephson diode effect have been observed without applying external fields. Importantly, when the so-called nonreciprocity efficiency (which measures the sign and strength of the Josephson effect) changes sign, the energy-phase relation of the junction is approximate $F(φ) \approx \cos(2φ)$ where $F$ is the free energy and $φ$ is the phase difference of the two superconductors. In this work, we show that such a MATBG-based Josephson junction, when shunted by a capacitor, can be used to realize the long-sought-after $0$-$π$ qubits which are protected from local perturbation-induced decoherence. Interestingly, by changing the junction parameters, transmon-like qubits with large anharmonicity can also be realized. In short, by utilizing the novel interaction-driven valley-polarized state in MATBG, a single gate-defined Josephson junction can be used to replace complicated superconducting circuits for realizing qubits that are protected from local perturbations. △ Less

Submitted 15 August, 2023; originally announced August 2023.

Anomalous Coherence Length in Superconductors with Quantum Metric

Authors: Jin-Xin Hu, Shuai A. Chen, K. T. Law

Abstract: The coherence length $ξ$ is the fundamental length scale of superconductors which governs the sizes of Cooper pairs, vortices, Andreev bound states, and more. In BCS theory, the coherence length is $ξ_\mathrm{BCS} = \hbar v_{F}/Δ$, where $v_{F}$ is the Fermi velocity and $Δ$ is the pairing gap. It is clear that increasing $Δ$ will shorten $ξ_\mathrm{BCS}$. In this work, we show that the quantum me… ▽ More The coherence length $ξ$ is the fundamental length scale of superconductors which governs the sizes of Cooper pairs, vortices, Andreev bound states, and more. In BCS theory, the coherence length is $ξ_\mathrm{BCS} = \hbar v_{F}/Δ$, where $v_{F}$ is the Fermi velocity and $Δ$ is the pairing gap. It is clear that increasing $Δ$ will shorten $ξ_\mathrm{BCS}$. In this work, we show that the quantum metric, which is the real part of the quantum geometric tensor, gives rise to an anomalous contribution to the coherence length. Specifically, $ξ= \sqrt{ξ_\mathrm{BCS}^2 +\ell_{\mathrm{qm}}^{2}}$ for a superconductor where $\ell_{\mathrm{qm}}$ is the quantum metric contribution. In the flat-band limit, $ξ$ does not vanish but is bound below by $\ell_{\mathrm{qm}}$. We demonstrate that under the uniform pairing condition, $\ell_{\mathrm{qm}}$ is controlled by the quantum metric of minimal trace in the flat-band limit. Physically, the Cooper pair size of a superconductor cannot be squeezed down to a size smaller than $\ell_{\mathrm{qm}}$ which is a fundamental length scale determined by the quantum geometry of the wave functions. Lastly, we compute the quantum metric contributions for the family of superconducting moiré graphene materials, demonstrating the significant role played by quantum metric effects in these narrow-band superconductors. △ Less

Submitted 22 December, 2024; v1 submitted 10 August, 2023; originally announced August 2023.

Comments: 8 pages, 5 figures, plus Supplementary Material

Anomalous $h/2e$ periodicity and Majorana zero modes in chiral Josephson junctions

Authors: Zi-Ting Sun, Jin-Xin Hu, Ying-Ming Xie, K. T. Law

Abstract: Recent experiments reported that quantum Hall chiral edge state-mediated Josephson junctions (chiral Josephson junctions) could exhibit Fraunhofer oscillations with a periodicity of either $h/e$ [Vignaud \textit{et al}.,~Nature~(2023)] or $h/2e$ [Amet \textit{et al}.,~Science~\textbf{352}~966~(2016)]. While the $h/e$-periodic component of the supercurrent had been anticipated theoretically before,… ▽ More Recent experiments reported that quantum Hall chiral edge state-mediated Josephson junctions (chiral Josephson junctions) could exhibit Fraunhofer oscillations with a periodicity of either $h/e$ [Vignaud \textit{et al}.,~Nature~(2023)] or $h/2e$ [Amet \textit{et al}.,~Science~\textbf{352}~966~(2016)]. While the $h/e$-periodic component of the supercurrent had been anticipated theoretically before, the emergence of the $h/2e$-periodicity is still not fully understood. In this work, we show that the chiral edge states coupled to the superconductors become chiral Andreev edge states. In short junctions, the coupling of the chiral Andreev edge states can cause the $h/2e$-magnetic flux periodicity. Our theory resolves the long-standing puzzle concerning the appearance of the $h/2e$-periodicity in chiral Josephson junctions. Furthermore, we explain that when the chiral Andreev edge state couple, a pair of localized Majorana modes appear at the ends of the Josephson junction, which are robust and independent of the phase difference between the two superconductors. As the $h/2e$-periodicity and the Majorana zero modes have the same physical origin, the Fraunhofer oscillation period can be used to identify the regime with Majorana zero modes. △ Less

Submitted 26 December, 2023; v1 submitted 2 August, 2023; originally announced August 2023.

Comments: 6 pages, 3 figures, plus Supplemental Material

Journal ref: Phys. Rev. Lett. 133, 056601 (2024)

Nonlinear optical diode effect in a magnetic Weyl semimetal

Authors: Christian Tzschaschel, Jian-Xiang Qiu, Xue-Jian Gao, Hou-Chen Li, Chunyu Guo, Hung-Yu Yang, Cheng-Ping Zhang, Ying-Ming Xie, Yu-Fei Liu, Anyuan Gao, Damien Bérubé, Thao Dinh, Sheng-Chin Ho, Yuqiang Fang, Fuqiang Huang, Johanna Nordlander, Qiong Ma, Fazel Tafti, Philip J. W. Moll, Kam Tuen Law, Su-Yang Xu

Abstract: Diode effects are of great interest for both fundamental physics and modern technologies. Electrical diode effects (nonreciprocal transport) have been observed in Weyl systems. Optical diode effects arising from the Weyl fermions have been theoretically considered but not probed experimentally. Here, we report the observation of a nonlinear optical diode effect (NODE) in the magnetic Weyl semimeta… ▽ More Diode effects are of great interest for both fundamental physics and modern technologies. Electrical diode effects (nonreciprocal transport) have been observed in Weyl systems. Optical diode effects arising from the Weyl fermions have been theoretically considered but not probed experimentally. Here, we report the observation of a nonlinear optical diode effect (NODE) in the magnetic Weyl semimetal CeAlSi, where the magnetization introduces a pronounced directionality in the nonlinear optical second-harmonic generation (SHG). We show demonstrate a six-fold change of the measured SHG intensity between opposite propagation directions over a bandwidth exceeding 250 meV. Supported by density-functional theory, we establish the linearly dispersive bands emerging from Weyl nodes as the origin of this broadband effect. We further demonstrate current-induced magnetization switching and thus electrical control of the NODE. Our results advance ongoing research to identify novel nonlinear optical/transport phenomena in magnetic topological materials and further opens new pathways for the unidirectional manipulation of light. △ Less

Submitted 8 April, 2024; v1 submitted 28 July, 2023; originally announced July 2023.

Comments: 20 pages, 4 figures, SI included

Journal ref: Nat. Commun 15, 3017 (2024)

Quantum geometry quadrupole-induced third-order nonlinear transport in antiferromagnetic topological insulator MnBi2Te4

Authors: Hui Li, Chengping Zhang, Chengjie Zhou, Chen Ma, Xiao Lei, Zijing Jin, Hongtao He, Baikui Li, Kam Tuen Law, Jiannong Wang

Abstract: The study of quantum geometry effects in materials has been one of the most important research directions in recent decades. The quantum geometry of a material is characterized by the quantum geometry tensor of the Bloch states. The imaginary part of the quantum geometry tensor gives rise to the Berry curvature while the real part gives rise to the quantum metric. While Berry curvature has been we… ▽ More The study of quantum geometry effects in materials has been one of the most important research directions in recent decades. The quantum geometry of a material is characterized by the quantum geometry tensor of the Bloch states. The imaginary part of the quantum geometry tensor gives rise to the Berry curvature while the real part gives rise to the quantum metric. While Berry curvature has been well studied in the past decades, the experimental investigation on the quantum metric effects is only at its infancy stage. In this work, we measure the nonlinear transport of bulk MnBi${_2}$Te${_4}$, which is a topological anti-ferromagnet. We found that the second order nonlinear responses are negligible as required by inversion symmetry, the third-order nonlinear responses are finite. The measured third-harmonic longitudinal ($V_{xx}^{3ω}$) and transverse ($V_{xy}^{3ω}$) voltages with frequency 3w, driven by an a.c. current with frequency w, show an intimate connection with magnetic transitions of MnBi${_2}$Te${_4}$ flakes. Their magnitudes change abruptly as MnBi${_2}$Te${_4}$ flakes go through magnetic transitions from an AFM state to a canted AFM state and to a FM state. In addition, the measured $V_{xx}^{3ω}$ is an even function of the applied magnetic field B while $V_{xy}^{3ω}$ is odd in B. Amazingly, the field dependence of the third-order responses as a function of the magnetic field suggests that $V_{xx}^{3ω}$ is induced by quantum metric quadrupole and $V_{xy}^{3ω}$ is induced by Berry curvature quadrupole. Therefore, the quadrupoles of both the real and the imaginary part of the quantum geometry tensor of bulk MnBi${_2}$Te${_4}$ are revealed through the third order nonlinear transport measurements. This work greatly advanced our understanding on the connections between the higher order moments of quantum geometry and nonlinear transport. △ Less

Submitted 7 November, 2023; v1 submitted 23 July, 2023; originally announced July 2023.

Journal ref: Nat Commun 15, 7779 (2024)

Axion Insulator State in Hundred-Nanometer-Thick Magnetic Topological Insulator Sandwich Heterostructures

Authors: Deyi Zhuo, Zi-Jie Yan, Zi-Ting Sun, Ling-Jie Zhou, Yi-Fan Zhao, Ruoxi Zhang, Ruobing Mei, Hemian Yi, Ke Wang, Moses H. W. Chan, Chao-Xing Liu, K. T. Law, Cui-Zu Chang

Abstract: An axion insulator is a three-dimensional (3D) topological insulator (TI), in which the bulk maintains the time-reversal symmetry or inversion symmetry but the surface states are gapped by surface magnetization. The axion insulator state has been observed in molecular beam epitaxy (MBE)-grown magnetically doped TI sandwiches and exfoliated intrinsic magnetic TI MnBi2Te4 flakes with an even number… ▽ More An axion insulator is a three-dimensional (3D) topological insulator (TI), in which the bulk maintains the time-reversal symmetry or inversion symmetry but the surface states are gapped by surface magnetization. The axion insulator state has been observed in molecular beam epitaxy (MBE)-grown magnetically doped TI sandwiches and exfoliated intrinsic magnetic TI MnBi2Te4 flakes with an even number layer. All these samples have a thickness of ~10 nm, near the 2D-to-3D boundary. The coupling between the top and bottom surface states in thin samples may hinder the observation of quantized topological magnetoelectric response. Here, we employ MBE to synthesize magnetic TI sandwich heterostructures and find that the axion insulator state persists in a 3D sample with a thickness of ~106 nm. Our transport results show that the axion insulator state starts to emerge when the thickness of the middle undoped TI layer is greater than ~3 nm. The 3D hundred-nanometer-thick axion insulator provides a promising platform for the exploration of the topological magnetoelectric effect and other emergent magnetic topological states, such as the high-order TI phase. △ Less

Submitted 3 October, 2023; v1 submitted 22 June, 2023; originally announced June 2023.

Comments: 25 pages, 5 figures. Comments are very much welcome

Heesch Weyl Fermions in inadmissible chiral antiferromagnets

Authors: Xue-Jian Gao, Zi-Ting Sun, Ruo-Peng Yu, Xing-Yao Guo, K. T. Law

Abstract: Symmetry is a crucial factor in determining the topological properties of materials. In nonmagnetic chiral crystals, the existence of the Kramers Weyl fermions reveals the topological nature of the Kramers degeneracy at time-reversal-invariant momenta (TRIMs). However, it is not clear whether Weyl nodes can also be pinned at points of symmetry in magnetic materials where the time-reversal is spont… ▽ More Symmetry is a crucial factor in determining the topological properties of materials. In nonmagnetic chiral crystals, the existence of the Kramers Weyl fermions reveals the topological nature of the Kramers degeneracy at time-reversal-invariant momenta (TRIMs). However, it is not clear whether Weyl nodes can also be pinned at points of symmetry in magnetic materials where the time-reversal is spontaneously broken. In this study, we introduce a new type of Weyl fermions, called Heesch Weyl fermions (HWFs), which are stabilized and pinned at points of symmetry by the Heesch groups in inadmissible chiral antiferromagnets. The emergence of HWFs is fundamentally different from that of Kramers Weyl fermions, as it does not rely on any anti-unitary symmetry $\mathcal{A}$ that satisfies $\mathcal{A}^2=-1$. Importantly, the emergence of HWFs is closely related to the antiferromagnetic order, as they are generally obscured by nodal lines in the parent nonmagnetic state. Using group theory analysis, we classify all the magnetic little co-groups of momenta where Heesch Weyl nodes are enforced and pinned by symmetry. With the guidance of this classification and first-principles calculations, we identify antiferromagnetic (AFM) materials such as YMnO$_3$ and Mn$_3$IrGe as candidate hosts for the AFM-order-induced HWFs.We also explore novel properties of Heesch Weyl antiferromagnets, such as nonlinear anomalous Hall effects and axial movement of Heesch Weyl nodes. Our findings shed new light on the role of symmetry in determining and stabilizing topological properties in magnetic materials, and open up new avenues for the design and exploration of topological materials. △ Less

Submitted 25 May, 2023; originally announced May 2023.

The Ginzburg-Landau theory of flat band superconductors with quantum metric

Authors: Shuai A. Chen, K. T. Law

Abstract: Recent experimental study unveiled highly unconventional phenomena in the superconducting twisted bilayer graphene (TBG) with ultra flat bands, which cannot be described by the conventional BCS theory. For example, given the small Fermi velocity of the flat bands, the superconducting coherence length predicted by BCS theory is more than 20 times shorter than the measured values. A new theory is ne… ▽ More Recent experimental study unveiled highly unconventional phenomena in the superconducting twisted bilayer graphene (TBG) with ultra flat bands, which cannot be described by the conventional BCS theory. For example, given the small Fermi velocity of the flat bands, the superconducting coherence length predicted by BCS theory is more than 20 times shorter than the measured values. A new theory is needed to understand many of the unconventional properties of flat band superconductors. In this work, we establish a Ginzburg-Landau (GL) theory from a microscopic flat band Hamiltonian. The GL theory shows how the properties of the physical quantities such as the critical temperature, the superconducting coherence length, the upper critical field and the superfluid density are governed by the quantum metric of the Bloch states. One key conclusion is that the superconducting coherence length is not determined by the Fermi velocity but by the size of the optimally localized Wannier functions which is limited by quantum metric. Applying the theory to TBG, we calculated the superconducting coherence length and the upper critical fields. The results match the experimental ones well without fine tuning of parameters. The established GL theory provides a new and general theoretical framework for understanding flat band superconductors with quantum metric. △ Less

Submitted 5 October, 2023; v1 submitted 27 March, 2023; originally announced March 2023.

Comments: 5 pages, 1 figure, 1 table, and comments are welcome

Experimental evidence for Berry curvature multipoles in antiferromagnets

Authors: Soumya Sankar, Ruizi Liu, Xue-Jian Gao, Qi-Fang Li, Caiyun Chen, Cheng-Ping Zhang, Jiangchang Zheng, Yi-Hsin Lin, Kun Qian, Ruo-Peng Yu, Xu Zhang, Zi Yang Meng, Kam Tuen Law, Qiming Shao, Berthold Jäck

Abstract: Berry curvature multipoles appearing in topological quantum materials have recently attracted much attention. Their presence can manifest in novel phenomena, such as nonlinear anomalous Hall effects (NLAHE). The notion of Berry curvature multipoles extends our understanding of Berry curvature effects on the material properties. Hence, research on this subject is of fundamental importance and may a… ▽ More Berry curvature multipoles appearing in topological quantum materials have recently attracted much attention. Their presence can manifest in novel phenomena, such as nonlinear anomalous Hall effects (NLAHE). The notion of Berry curvature multipoles extends our understanding of Berry curvature effects on the material properties. Hence, research on this subject is of fundamental importance and may also enable future applications in energy harvesting and high-frequency technology. It was shown that a Berry curvature dipole can give rise to a 2nd order NLAHE in materials of low crystalline symmetry. Here, we demonstrate a fundamentally new mechanism for Berry curvature multipoles in antiferromagnets that are supported by the underlying magnetic symmetries. Carrying out electric transport measurements on the kagome antiferromagnet FeSn, we observe a 3rd order NLAHE, which appears as a transverse voltage response at the 3rd harmonic frequency when a longitudinal a.c. current drive is applied. Interestingly, this NLAHE is strongest at and above room temperature. We combine these measurements with a scaling law analysis, a symmetry analysis, model calculations, first-principle calculations, and magnetic Monte-Carlo simulations to show that the observed NLAHE is induced by a Berry curvature quadrupole appearing in the spin-canted state of FeSn. At a practical level, our study establishes NLAHE as a sensitive probe of antiferromagnetic phase transitions in other materials, such as moiré superlattices, two-dimensional van der Waal magnets, and quantum spin liquid candidates, that remain poorly understood to date. More broadly, Berry curvature multipole effects are predicted to exist for 90 magnetic point groups. Hence, our work opens a new research area to study a variety of topological magnetic materials through nonlinear measurement protocols. △ Less

Submitted 8 October, 2023; v1 submitted 6 March, 2023; originally announced March 2023.

Proximity-induced quasi-one-dimensional superconducting quantum anomalous Hall state: a promising scalable top-down approach towards localized Majorana modes

Authors: Omargeldi Atanov, Wai Ting Tai, Ying-Ming Xie, Yat Hei Ng, Molly A. Hammond, Tin Seng Manfred Ho, Tsin Hei Koo, Hui Li, Sui Lun Ho, Jian Lyu, Sukong Chong, Peng Zhang, Lixuan Tai, Jiannong Wang, Kam Tuen Law, Kang L. Wang, Rolf Lortz

Abstract: In this work, ~100 nm wide quantum anomalous Hall insulator (QAHI) nanoribbons are etched from a two-dimensional QAHI film. One part of the nanoribbon is covered with superconducting Nb, while the other part is connected to an Au lead via two-dimensional QAHI regions. Andreev reflection spectroscopy measurements were performed, and multiple in-gap conductance peaks were observed in three different… ▽ More In this work, ~100 nm wide quantum anomalous Hall insulator (QAHI) nanoribbons are etched from a two-dimensional QAHI film. One part of the nanoribbon is covered with superconducting Nb, while the other part is connected to an Au lead via two-dimensional QAHI regions. Andreev reflection spectroscopy measurements were performed, and multiple in-gap conductance peaks were observed in three different devices. In the presence of an increasing magnetic field perpendicular to the QAHI film, the multiple in-gap peak structure evolves into a single zero-bias conductance peak (ZBCP). Theoretical simulations suggest that the measurements are consistent with the scenario that the increasing magnetic field drives the nanoribbons from a multi-channel occupied regime to a single channel occupied regime, and that the ZBCP may be induced by zero energy Majorana modes as previously predicted [24]. Although further experiments are needed to clarify the nature of the ZBCP, we provide initial evidence that quasi-1D QAHI nanoribbon/superconductor heterostructures are new and promising platforms for realizing zero-energy Majorana modes. △ Less

Submitted 13 February, 2023; originally announced February 2023.

Journal ref: Cell Reports Physical Science 5, 101762 (2024)

Josephson Diode Effect Induced by Valley Polarization in Twisted Bilayer Graphene

Authors: Jin-Xin Hu, Zi-Ting Sun, Ying-Ming Xie, K. T. Law

Abstract: Recently, the Josephson diode effect (JDE), in which the superconducting critical current magnitudes differ when the currents flow in opposite directions, has attracted great interest. In particular, it was demonstrated that gate-defined Josephson junctions based on magic-angle twisted bilayer graphene showed a strong nonreciprocal effect when the weak-link region is gated to a correlated insulati… ▽ More Recently, the Josephson diode effect (JDE), in which the superconducting critical current magnitudes differ when the currents flow in opposite directions, has attracted great interest. In particular, it was demonstrated that gate-defined Josephson junctions based on magic-angle twisted bilayer graphene showed a strong nonreciprocal effect when the weak-link region is gated to a correlated insulating state at half-filling (two holes per moiré cell). However, the mechanism behind such a phenomenon is not yet understood. In this work, we show that the interaction-driven valley polarization, together with the trigonal warping of the Fermi surface, induce the JDE. The valley polarization, which lifts the degeneracy of the states in the two valleys, induces a relative phase difference between the first and the second harmonics of supercurrent and results in the JDE. We further show that the nontrivial current phase relation, which is responsible for the JDE, also generates the asymmetric Shapiro steps. △ Less

Submitted 13 December, 2023; v1 submitted 27 November, 2022; originally announced November 2022.

Comments: 6 pages, 4 figures, plus Supplementary Material

Orbital Fulde-Ferrell pairing state in moiré Ising superconductors

Authors: Ying-Ming Xie, K. T. Law

Abstract: In this work, we study superconducting moiré homobilayer transition metal dichalcogenides where the Ising spin-orbit coupling (SOC) is much larger than the moiré bandwidth. We call such noncentrosymmetric superconductors, moiré Ising superconductors. Due to the large Ising SOC, the depairing effect caused by the Zeeman field is negligible and the in-plane upper critical field ($B_{c2}$) is determi… ▽ More In this work, we study superconducting moiré homobilayer transition metal dichalcogenides where the Ising spin-orbit coupling (SOC) is much larger than the moiré bandwidth. We call such noncentrosymmetric superconductors, moiré Ising superconductors. Due to the large Ising SOC, the depairing effect caused by the Zeeman field is negligible and the in-plane upper critical field ($B_{c2}$) is determined by the orbital effects. This allows us to study the effect of large orbital fields. Interestingly, when the applied in-plane field is larger than the conventional orbital $B_{c2}$, a finite-momentum pairing phase would appear which we call the orbital Fulde-Ferrell (FF) state. In this state, the Cooper pairs acquire a net momentum of $2q_B$ where $2q_B=eBd$ is the momentum shift caused by the magnetic field $B$ and $d$ denotes the layer separation. This orbital field-driven FF state is different from the conventional FF state driven by Zeeman effects in Rashba superconductors. Remarkably, we predict that the FF pairing would result in a giant superconducting diode effect under electric gating when layer asymmetry is induced. An upturn of the $B_{c2}$ as the temperature is lowered, coupled with the giant superconducting diode effect, would allow the detection of the orbital FF state. △ Less

Submitted 10 June, 2023; v1 submitted 14 November, 2022; originally announced November 2022.

Comments: 6 pages, 4 figures, plus Supplementary Material

Journal ref: Phys. Rev. Lett. 131, 016001 (2023)

Kramers nodal lines and Weyl fermions in SmAlSi

Authors: Yichen Zhang, Yuxiang Gao, Xue-Jian Gao, Shiming Lei, Zhuoliang Ni, Ji Seop Oh, Jianwei Huang, Ziqin Yue, Marta Zonno, Sergey Gorovikov, Makoto Hashimoto, Donghui Lu, Jonathan D. Denlinger, Robert J. Birgeneau, Junichiro Kono, Liang Wu, Kam Tuen Law, Emilia Morosan, Ming Yi

Abstract: Kramers nodal lines (KNLs) have recently been proposed theoretically as a special type of Weyl line degeneracy connecting time-reversal invariant momenta. KNLs are robust to spin orbit coupling and are inherent to all non-centrosymmetric achiral crystal structures, leading to unusual spin, magneto-electric, and optical properties. However, their existence in in real quantum materials has not been… ▽ More Kramers nodal lines (KNLs) have recently been proposed theoretically as a special type of Weyl line degeneracy connecting time-reversal invariant momenta. KNLs are robust to spin orbit coupling and are inherent to all non-centrosymmetric achiral crystal structures, leading to unusual spin, magneto-electric, and optical properties. However, their existence in in real quantum materials has not been experimentally established. Here we gather the experimental evidence pointing at the presence of KNLs in SmAlSi, a non-centrosymmetric metal that develops incommensurate spin density wave order at low temperature. Using angle-resolved photoemission spectroscopy, density functional theory calculations, and magneto-transport methods, we provide evidence suggesting the presence of KNLs, together with observing Weyl fermions under the broken inversion symmetry in the paramagnetic phase of SmAlSi. We discuss the nesting possibilities regarding the emergent magnetic orders in SmAlSi. Our results provide a solid basis of experimental observations for exploring correlated topology in SmAlSi. △ Less

Submitted 9 June, 2023; v1 submitted 24 October, 2022; originally announced October 2022.

Comments: 40 pages, 5 figures, 1 table

Journal ref: Commun. Phys. 6, 134 (2023)

Berry curvature, spin Hall effect and nonlinear optical response in moiré transition metal dichalcogenide heterobilayers

Authors: Jin-Xin Hu, Ying-Ming Xie, K. T. Law

Abstract: Recently, the topological flat bands and spin Hall effect have been experimentally observed in the AB-stacked MoTe$_2$/WSe$_2$ heterostructures. In this work, we systematically study the Berry curvature effects in moiré transition metal dichalcogenide (TMD) heterobilayers. We point out that the moiré potential of the remote conduction bands would induce a sizable periodic pseudo-magnetic field (PM… ▽ More Recently, the topological flat bands and spin Hall effect have been experimentally observed in the AB-stacked MoTe$_2$/WSe$_2$ heterostructures. In this work, we systematically study the Berry curvature effects in moiré transition metal dichalcogenide (TMD) heterobilayers. We point out that the moiré potential of the remote conduction bands would induce a sizable periodic pseudo-magnetic field (PMF) on the valence band. This periodic PMF creates net Berry curvature flux in each valley of the moiré Brillouin zone. The combination of the effect of the Berry curvature and the spin-valley locking can induce the spin Hall effect being observed in the experiment. Interestingly, the valley-contrasting Berry curvature distribution generated by the PMF can be probed through shift currents, which are DC currents induced by linearly polarized lights through nonlinear responses. Our work shed lights on the novel quantum phenomena induced by Berry curvatures in moiré TMD heterobilayers. △ Less

Submitted 17 February, 2023; v1 submitted 3 October, 2022; originally announced October 2022.

Comments: 10 pages, 7 figures

Journal ref: Phys. Rev. B 107, 075424, 2023

Topological $p_x+ip_y$ inter-valley coherent state in Moiré MoTe$_2$/WSe$_2$ heterobilayers

Authors: Ying-Ming Xie, Cheng-Ping Zhang, K. T. Law

Abstract: Recently, a quantum anomalous Hall (QAH) state was observed in AB stacked moiré MoTe$_2$/WSe$_2$ heterobilayers at half-filling. More recent layer-resolved magnetic circular dichroism (MCD) measurements revealed that spin-polarized moiré bands from both the MoTe$_2$ and the WSe$_2$ layers are involved at the formation of the QAH state. This scenario is not expected by existing theories. In this wo… ▽ More Recently, a quantum anomalous Hall (QAH) state was observed in AB stacked moiré MoTe$_2$/WSe$_2$ heterobilayers at half-filling. More recent layer-resolved magnetic circular dichroism (MCD) measurements revealed that spin-polarized moiré bands from both the MoTe$_2$ and the WSe$_2$ layers are involved at the formation of the QAH state. This scenario is not expected by existing theories. In this work, we suggest that the observed QAH state is a new state of matter, namely, a topological $p_x+ip_y$ inter-valley coherent state (TIVC). We point out that the massive Dirac spectrum of the MoTe$_2$ moiré bands, together with the Hund's interaction and the Coulomb interactions give rise to this novel QAH state. Through a self-consistent Hartree-Fock analysis, we find a wide range of interaction strengths and displacement fields that the $p_x+ip_y$-pairing phase is energetically favourable. Besides explaining several key features of the experiments, our theory predicts that the order parameter would involve the pairing of electrons and holes with a definite momentum mismatch such that the pairing would generate a new unit cell which is three times the size of the original moiré unit cell, due to the order parameter modulations. △ Less

Submitted 30 January, 2024; v1 submitted 23 June, 2022; originally announced June 2022.

Comments: 13 pages, 6 figures

Journal ref: Phys. Rev. B 110, 045115 (2024)

Digital Fingerprinting of Microstructures

Authors: Michael D. White, Alexander Tarakanov, Christopher P. Race, Philip J. Withers, Kody J. H. Law

Abstract: Finding efficient means of fingerprinting microstructural information is a critical step towards harnessing data-centric machine learning approaches. A statistical framework is systematically developed for compressed characterisation of a population of images, which includes some classical computer vision methods as special cases. The focus is on materials microstructure. The ultimate purpose is t… ▽ More Finding efficient means of fingerprinting microstructural information is a critical step towards harnessing data-centric machine learning approaches. A statistical framework is systematically developed for compressed characterisation of a population of images, which includes some classical computer vision methods as special cases. The focus is on materials microstructure. The ultimate purpose is to rapidly fingerprint sample images in the context of various high-throughput design/make/test scenarios. This includes, but is not limited to, quantification of the disparity between microstructures for quality control, classifying microstructures, predicting materials properties from image data and identifying potential processing routes to engineer new materials with specific properties. Here, we consider microstructure classification and utilise the resulting features over a range of related machine learning tasks, namely supervised, semi-supervised, and unsupervised learning. The approach is applied to two distinct datasets to illustrate various aspects and some recommendations are made based on the findings. In particular, methods that leverage transfer learning with convolutional neural networks (CNNs), pretrained on the ImageNet dataset, are generally shown to outperform other methods. Additionally, dimensionality reduction of these CNN-based fingerprints is shown to have negligible impact on classification accuracy for the supervised learning approaches considered. In situations where there is a large dataset with only a handful of images labelled, graph-based label propagation to unlabelled data is shown to be favourable over discarding unlabelled data and performing supervised learning. In particular, label propagation by Poisson learning is shown to be highly effective at low label rates. △ Less

Submitted 22 January, 2024; v1 submitted 25 March, 2022; originally announced March 2022.

$\varphi_0$-Josephson junction in twisted bilayer graphene induced by a valley-polarized state

Authors: Ying-Ming Xie, Dmitri K. Efetov, K. T. Law

Abstract: Recently, gate-defined Josephson junctions in magic angle twisted bilayer graphene (MATBG) were studied experimentally and highly unconventional Fraunhofer patterns were observed. In this work, we show that an interaction-driven valley-polarized state connecting two superconducting regions of MATBG would give rise to a long-sought-after purely electric controlled $\varphi_0$-junction in which the… ▽ More Recently, gate-defined Josephson junctions in magic angle twisted bilayer graphene (MATBG) were studied experimentally and highly unconventional Fraunhofer patterns were observed. In this work, we show that an interaction-driven valley-polarized state connecting two superconducting regions of MATBG would give rise to a long-sought-after purely electric controlled $\varphi_0$-junction in which the two superconductors acquire a finite phase difference $\varphi_0$ in the ground state. We point out that the emergence of the $\varphi_0$-junction stems from the valley-polarized state which breaks time-reversal symmetry and trigonal warping effects which break the intravalley inversion symmetry. Importantly, a spatially non-uniform valley polarization order parameter at the junction can explain the highly unconventional Fraunhofer patterns observed in the experiment. Our work explores the novel transport properties of the valley-polarized state and suggests that gate-defined MATBG Josephson junctions could realize the first purely electric controlled $\varphi_0$-junctions with applications in superconducting devices. △ Less

Submitted 28 April, 2023; v1 submitted 11 February, 2022; originally announced February 2022.

Comments: 7 pages, 4 figures, plus Supplementary Material

Journal ref: Phys. Rev. Research 5, 023029 (2023)

Magnetic Josephson Junctions and Superconducting Diodes in Magic Angle Twisted Bilayer Graphene

Authors: J. Diez-Merida, A. Diez-Carlon, S. Y. Yang, Y. -M. Xie, X. -J. Gao, K. Watanabe, T. Taniguchi, X. Lu, K. T. Law, Dmitri K. Efetov

Abstract: The simultaneous co-existence and gate-tuneability of the superconducting (SC), magnetic and topological orders in magic angle twisted bilayer graphene (MATBG) open up entirely new possibilities for the creation of complex hybrid Josephson junctions (JJ). Here we report on the creation of gate-defined, magnetic Josephson junctions in MATBG, where the weak link is gate-tuned close to the correlated… ▽ More The simultaneous co-existence and gate-tuneability of the superconducting (SC), magnetic and topological orders in magic angle twisted bilayer graphene (MATBG) open up entirely new possibilities for the creation of complex hybrid Josephson junctions (JJ). Here we report on the creation of gate-defined, magnetic Josephson junctions in MATBG, where the weak link is gate-tuned close to the correlated state at a moiré filling factor of ν=-2. A highly unconventional Fraunhofer pattern emerges, which is phase-shifted and asymmetric with respect to the current and magnetic field directions, and shows a pronounced magnetic hysteresis. Interestingly, our theoretical calculations of the JJ with a valley polarized ν=-2 with orbital magnetization as the weak link explain most of these unconventional features without fine tuning the parameters. While these unconventional Josephson effects persist up to the critical temperature Tc ~ 3.5K of the superconducting state, at temperatures below T < 800mK, we observed a pronounced magnetic hysteresis possibly due to further spin-polarization of the ν=-2 state. We demonstrate how the combination of magnetization and its current induced magnetization switching in the MATBG JJ allows us to realize a programmable zero field superconducting diode, which represents a major building block for a new generation of superconducting quantum electronics. △ Less

Submitted 3 October, 2021; originally announced October 2021.