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Liang Fu

Liang Fu contributes to research discovery and scholarly infrastructure.

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cond-mat.mes-hall cond-mat.str-el cond-mat.supr-con cond-mat.mtrl-sci cond-mat.quant-gas Artificial Intelligence cond-mat.stat-mech hep-th Machine Learning physics.app-ph physics.optics

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preprint2026arXiv

QERNEL: a Scalable Large Electron Model

We introduce QERNEL, a foundational neural wavefunction that variationally solves families of parameterized many-electron Hamiltonians and captures their ground states throughout parameter space within a single model. QERNEL combines FiLM-based parameter conditioning with scale-efficient architectural elements -- mixture of experts and grouped-query attention, substantially improving expressivity at low computational cost. We apply QERNEL to interacting electrons in semiconductor moiré heterobilayers, training a single weight-shared model for systems of up to 150 electrons. By solving the many-electron Schrödinger equation conditioned on moiré potential depth, QERNEL captures both quantum liquid and crystal states and discovers the sharp phase transition between them, marked by abrupt changes in interaction energy and charge density. Our work establishes a foundation model for moiré quantum materials and a scalable architecture toward a Large Electron Model for solids.

preprint2022arXiv

Dirac electron under periodic magnetic field: Platform for fractional Chern insulator and generalized Wigner crystal

We propose a platform for flat Chern band by subjecting two-dimensional Dirac materials -- such as graphene and topological insulator thin films -- to a periodic magnetic field, which can be created by the vortex lattice of a type-II superconductor. As a generalization of the $n=0$ Landau level, the flat band of Dirac fermion under a nonuniform magnetic field remains at zero energy, exactly dispersionless and topologically protected, while its local density of states is spatially modulated due to the magnetic field variation. In the presence of short-range repulsion, we find fractional Chern insulators emerge at filling factors $ν=1/m$, whose ground states are generalized Laughlin wavefunctions. We further argue that generalized Wigner crystals may emerge at certain commensurate fillings under a highly nonuniform magnetic field in the form of a flux line lattice.

preprint2022arXiv

Moiré Landau fans and magic zeros

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

preprint2022arXiv

Non-Abelian nonsymmorphic chiral symmetries

The Hofstadter model exemplifies a large class of physical systems characterized by particles hopping on a lattice immersed in a gauge field. Recent advancements on various synthetic platforms have enabled highly-controllable simulations of such systems with tailored gauge fields featuring complex spatial textures. These synthetic gauge fields could introduce synthetic symmetries that do not appear in electronic materials. Here, in an SU(2) non-Abelian Hofstadter model, we theoretically show the emergence of multiple nonsymmorphic chiral symmetries, which combine an internal unitary anti-symmetry with fractional spatial translation. Depending on the values of the gauge fields, the nonsymmorphic chiral symmetries can exhibit non-Abelian algebra and protect Kramer quartet states in the bulk band structure, creating general four-fold degeneracy at all momenta. These nonsymmorphic chiral symmetries protect double Dirac semimetals at zero energy, which become gapped into quantum confined insulating phases upon introducing a boundary. Moreover, the parity of the system size can determine whether the resulting insulating phase is trivial or topological. Our work indicates a pathway for creating topology via synthetic symmetries emergent from synthetic gauge fields.

preprint2022arXiv

Pseudogap metal and magnetization plateau from doping moiré Mott insulator

The problem of doping Mott insulators is of fundamental importance and long-standing interest in the study of strongly correlated electron systems. The advent of semiconductor based moiré materials opens a new ground for simulating the Hubbard model on the triangular lattice and exploring the rich phase diagram of doped Mott insulators as a function of doping and external magnetic field. Based on our recent identification of spin polaron quasiparticle in Mott insulator, in this work we predict a new metallic state emerges at small doping and intermediate field range, a pseudogap metal that exhibits a single-particle gap and a doping-dependent magnetization plateau.

preprint2022arXiv

Quantum anomalous Hall effect from inverted charge transfer gap

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

preprint2022arXiv

Supercurrent diode effect and finite momentum superconductivity

When both inversion and time-reversal symmetries are broken, the critical current of a superconductor can be nonreciprocal. In this work we show that in certain classes of two-dimensional superconductors with antisymmetric spin-orbit coupling, Cooper pairs acquire a finite momentum upon the application of an in-plane magnetic field, and as a result, critical currents in the direction parallel and antiparallel to the Cooper pair momentum become unequal. This supercurrent diode effect is also manifested in the polarity-dependence of in-plane critical fields induced by a supercurrent. These nonreciprocal effects may be found in polar SrTiO$_3$ film, few-layer MoTe$_2$ in the $T_d$ phase, and twisted bilayer graphene in which the valley degrees of freedom plays the role analogous to spin.

preprint2022arXiv

Supercurrent induced resonant optical response

The optical conductivity encodes the current response to a time dependent electric field. We develop a theory of the optical conductivity $σ(ω)$ in presence of a dc supercurrent. Current induced optical response is prohibited by Galilean invariance from occurring in systems with a single parabolic band. However, we show that lattice effects give rise to a pronounced current dependent peak in $σ(ω)$ at the gap edge $ω= 2 Δ$, which diverges in the clean limit. We demonstrate this in a model of a multi-band superconductor. Our theory explains the recent observation of a current induced peak in the optical conductivity in NbN by Nakamura et al. (2019), and provides a new mechanism for direct activation of the Higgs mode with light.

preprint2021arXiv

Ferromagnetic helical nodal line and Kane-Mele spin-orbit coupling in kagome metal Fe3Sn2

The two-dimensional kagome lattice hosts Dirac fermions at its Brillouin zone corners K and K', analogous to the honeycomb lattice. In the density functional theory electronic structure of ferromagnetic kagome metal Fe$_3$Sn$_2$, without spin-orbit coupling we identify two energetically split helical nodal lines winding along $z$ in the vicinity of K and K' resulting from the trigonal stacking of the kagome layers. We find that hopping across A-A stacking introduces a layer splitting in energy while that across A-B stacking controls the momentum space amplitude of the helical nodal lines. The effect of spin-orbit coupling is found to resemble that of a Kane-Mele term, where the nodal lines can either be fully gapped to quasi-two-dimensional massive Dirac fermions, or remain gapless at discrete Weyl points depending on the ferromagnetic moment orientation. Aside from numerically establishing Fe$_3$Sn$_2$ as a model Dirac kagome metal, our results provide insights into materials design of topological phases from the lattice point of view, where paradigmatic low dimensional lattice models often find realizations in crystalline materials with three-dimensional stacking.

preprint2021arXiv

Interfacial ferroelectricity in rhombohedral-stacked bilayer transition metal dichalcogenides

Van der Waals (vdW) materials have greatly expanded our design space of heterostructures by allowing individual layers to be stacked at non-equilibrium configurations, for example via control of the twist angle. Such heterostructures not only combine characteristics of the individual building blocks, but can also exhibit emergent physical properties absent in the parent compounds through interlayer interactions. Here we report on a new family of emergent, nanometer-thick, semiconductor 2D ferroelectrics, where the individual constituents are well-studied non-ferroelectric monolayer transition metal dichalcogenides (TMDs), namely WSe2, MoSe2, WS2, and MoS2. By stacking two identical monolayer TMDs in parallel, we obtain electrically switchable rhombohedral-stacking configurations, with out-of-plane polarization that is flipped by in-plane sliding motion. Fabricating nearly-parallel stacked bilayers enables the visualization of moiré ferroelectric domains as well as electric-field-induced domain wall motion with piezoelectric force microscopy (PFM). Furthermore, by using a nearby graphene electronic sensor in a ferroelectric field transistor geometry, we quantify the ferroelectric built-in interlayer potential, in good agreement with first-principles calculations. The novel semiconducting ferroelectric properties of these four new TMDs opens up the possibility of studying the interplay between ferroelectricity and their rich electric and optical properties.

preprint2021arXiv

New mechanism and exact theory of superconductivity from strong repulsive interaction

We introduce a new and general mechanism for superconductivity in Fermi systems with strong repulsive interaction. Because kinetic terms are small compared to the bare repulsion, the dynamic of charge carriers is constrained by the the presence of other nearby carriers. By treating kinetic terms as a perturbation around the atomic limit, we show that pairing can be induced by correlated multi-particle tunneling processes that favor two itinerant carriers to be close together. Our analytically-controlled theory provides a quantitative formula relating $T_c$ to microscopic parameters, with maximum $T_c$ reaching about 10% of the Fermi temperature. Our work demonstrates a powerful method for studying strong coupling superconductivity with unconventional pairing symmetry. It also offers a realistic new route to realizing finite angular momentum superfluidity of spin-polarized fermions in optical lattice.

preprint2021arXiv

Spin-triplet superconductivity from interband effect in doped insulators

Despite being of fundamental importance and potential interest for topological quantum computing, spin-triplet superconductors remain rare in solid state materials after decades of research. In this work, we present a general mechanism for spin-triplet superconductivity in multi-band systems, where a non-retarded pairing interaction between conduction electrons is produced by their electronic repulsion to a third-electron undergoing a virtual interband transition. Our theory is analytically controlled by an interband hybridization parameter, and explicitly demonstrated in doped band insulators with the example of an extended Hubbard model. In light of this theory, we propose that recently discovered dilute superconductors such as ZrNCl and WTe$_2$ are spin-triplet, and compare the expected consequences of our theory with experimental data.

preprint2021arXiv

Unconventional superconductivity due to interband polarization

We analyze in detail the superconductivity that arises in an extended Hubbard model describing a multiband system with repulsive interactions. We show that virtual interband processes induce an effective attractive interaction for small momentum transfers, a situation not found in most models of superconductivity from repulsion. This attraction can be traced back, in real space, to the presence of correlated hopping terms induced by interband polarization. We reveal this physics with both strong-coupling expansion and many-body perturbation theory, supplemented by numerical calculations. Finally, we point out interesting similarities with the problem of interacting electrons in twisted bilayer graphene, suggesting the importance of interband contribution to superconductivity.

preprint2020arXiv

Charge Transfer Excitations, Pair Density Waves, and Superconductivity in Moiré Materials

Transition metal dichalcogenide (TMD) bilayers are a new class of tunable moiré systems attracting interest as quantum simulators of strongly-interacting electrons in two dimensions. In particular, recent theory predicts that the correlated insulator observed in WSe$_2$/WS$_2$ at half filling is a charge-transfer insulator similar to cuprates and, upon further hole doping, exhibits a transfer of charge from anion-like to cation-like orbitals at different locations in the moiré unit cell. In this work, we demonstrate that in this doped charge-transfer insulator, tightly-bound charge-2e excitations can form to lower the total electrostatic repulsion. This composite excitation, which we dub a trimer, consists of a pair of holes bound to a charge-transfer exciton. When the bandwidth of doped holes is small, trimers crystallize into insulating pair density waves at a sequence of commensurate doping levels. When the bandwidth becomes comparable to the pair binding energy, itinerant holes and charge-2e trimers interact resonantly, leading to unconventional superconductivity similar to superfluidity in an ultracold Fermi gas near Feshbach resonance. Our theory is broadly applicable to strongly-interacting charge-transfer insulators, such as WSe$_2$/WS$_2$ or TMD homobilayers under an applied electric field.

preprint2020arXiv

Density functional approach to correlated moire states: itinerant magnetism

Two-dimensional moire superlattices have recently emerged as a fertile ground for creating novel electronic phases of matter with unprecedented control. Despite intensive efforts, theoretical investigation of correlated moire systems has been challenged by the large number of atoms in a superlattice unit cell and the inherent difficulty of treating electron correlation. The physics of correlated moire systems is governed by low-energy electrons in a coarse-grained long-wavelength potential, unlike the singular Coulomb potential of atomically-spaced ions in natural solids. Motivated by the separation between moire and atomic length scales, in this work we apply density functional theory to study directly the continuum model of interacting electrons in the periodic moire potential. Using this quantitatively accurate method, we predict itinerant spin-valley ferromagnetism in transition metal dichalchogenide heterobilayers, which originates from the constructive interplay between moire potential and Coulomb interaction in a two-dimensional electron system.

preprint2020arXiv

Discovery of segmented Fermi surface induced by Cooper pair momentum

Since the early days of Bardeen-Cooper-Schrieffer theory, it has been predicted that a sufficiently large supercurrent can close the energy gap in a superconductor and creates gapless Bogoliubov quasiparticles through the Doppler shift of quasiparticle energy due to the Cooper pair momentum. In this gapless superconducting state, zero-energy quasiparticles reside on a segment of the normal state Fermi surface, while its remaining part is still gapped. The finite density of states of field-induced quasiparticles, known as the Volovik effect, has been observed in tunneling and specific heat measurements on d- and s-wave superconductors. However, the segmented Fermi surface of a finite-momentum state carrying a supercurrent has never been detected directly. Here we use quasiparticle interference (QPI) technique to image field-controlled Fermi surface of Bi$_2$Te$_3$ thin films proximitized by the superconductor NbSe$_2$. By applying a small in-plane magnetic field, a screening supercurrent is induced which leads to finite-momentum pairing on topological surface states of Bi$_2$Te$_3$. Our measurements and analysis reveal the strong impact of finite Cooper pair momentum on the quasiparticle spectrum, and thus pave the way for STM study of pair density wave and FFLO states in unconventional superconductors.

preprint2020arXiv

Enhanced anomalous Nernst effect in disordered Dirac and Weyl materials

We analyze the thermoelectric response of Dirac and Weyl semimetals using the semiclassical approach, focusing on the extrinsic contributions due to skew-scattering and side jump. Our results apply to linear response Nernst effect in ferromagnetic Dirac materials such as Fe$_3$Sn$_2$, Weyl semimetal Co$_3$Sn$_2$S$_2$ and to second order response of monolayer graphene on hBN with trigonal warping. Our analysis indicates that the extrinsic contributions can be a significant component of anomalous Nernst response and used to explain an enhanced thermoelectric response.

preprint2020arXiv

Enhanced Superconductivity in Monolayer $T_d$-MoTe$_2$ with Tilted Ising Spin Texture

Crystalline two-dimensional (2D) superconductors with low carrier density are an exciting new class of materials in which superconductivity coexists with strong interactions, the effects of complex topology are not obscured by disorder, and electronic properties can be strongly tuned by electrostatic gating. Very recently, two such materials, 'magic-angle' twisted bilayer graphene and monolayer $T_d$-WTe$_2$, have been reported to show superconductivity at temperatures near 1 K. Here we report superconductivity in semimetallic monolayer $T_d$-MoTe$_2$. The critical temperature $T_\textrm{c}$ reaches 8 K, a sixty-fold enhancement as compared to the bulk. This anomalous increase in $T_\textrm{c}$ is only observed in monolayers, and may be indicative of electronically mediated pairing. Reflecting the low carrier density, the critical temperature, magnetic field, and current density are all tunable by an applied gate voltage, revealing a superconducting dome that extends across both hole and electron pockets. The temperature dependence of the in-plane upper critical field is distinct from that of $2H$ transition metal dichalcogenides (TMDs), consistent with a tilted spin texture as predicted by \textit{ab initio} theory.

preprint2020arXiv

High-frequency rectification via chiral Bloch electrons

Rectification is a process that converts electromagnetic fields into a direct current. Such a process underlies a wide range of technologies such as wireless communication, wireless charging, energy harvesting, and infrared detection. Existing rectifiers are mostly based on semiconductor diodes, with limited applicability to small voltage or high frequency inputs. Here, we present an alternative approach to current rectification that uses the intrinsic electronic properties of quantum crystals without using semiconductor junctions. We identify a previously unknown mechanism for rectification from skew scattering due to the inherent chirality of itinerant electrons in time-reversal-invariant but inversion-breaking materials. Our calculations reveal large, tunable rectification effects in graphene multilayers and transition metal dichalcogenides. Our work demonstrates the possibility of realizing high-frequency rectifiers by rational material design and quantum wavefunction engineering.

preprint2020arXiv

Local Probes for Quantum Hall Ferroelectrics and Nematics

Two-dimensional multi-valley electronic systems in which the dispersion of individual pockets has low symmetry give rise to quantum Hall ferroelectric and nematic states in the presence of strong quantising magnetic fields. We investigate local signatures of these states arising near impurities that can be probed via Scanning Tunnelling Microscopy (STM) spectroscopy. For quantum Hall ferroelectrics, we demonstrate a direct relation between the dipole moment measured at impurity bound states and the ideal bulk dipole moment obtained from the modern theory of polarisation. We also study the many-body problem with a single impurity via exact diagonalization and find that near strong impurities non-trivial excitonic state can form with specific features that can be easily identified via STM spectroscopy.

preprint2020arXiv

Nearly quantized conductance plateau of vortex zero mode in an iron-based superconductor

Majorana zero-modes (MZMs) are spatially-localized zero-energy fractional quasiparticles with non-Abelian braiding statistics that hold a great promise for topological quantum computing. Due to its particle-antiparticle equivalence, an MZM exhibits robust resonant Andreev reflection and 2e2/h quantized conductance at low temperature. By utilizing variable-tunnel-coupled scanning tunneling spectroscopy, we study tunneling conductance of vortex bound states on FeTe0.55Se0.45 superconductors. We report observations of conductance plateaus as a function of tunnel coupling for zero-energy vortex bound states with values close to or even reaching the 2e2/h quantum conductance. In contrast, no such plateau behaviors were observed on either finite energy Caroli-de Genne-Matricon bound states or in the continuum of electronic states outside the superconducting gap. This unique behavior of the zero-mode conductance reaching a plateau strongly supports the existence of MZMs in this iron-based superconductor, which serves as a promising single-material platform for Majorana braiding at a relatively high temperature.

preprint2020arXiv

Observation of a thermoelectric Hall plateau in the extreme quantum limit

The thermoelectric Hall effect is the generation of a transverse heat current upon applying an electric field in the presence of a magnetic field. Here we demonstrate that the thermoelectric Hall conductivity $α_{xy}$ in the three-dimensional Dirac semimetal ZrTe$_5$ acquires a robust plateau in the extreme quantum limit of magnetic field. The plateau value is independent of the field strength, disorder strength, carrier concentration, or carrier sign. We explain this plateau theoretically and show that it is a unique signature of three-dimensional Dirac or Weyl electrons in the extreme quantum limit. We further find that other thermoelectric coefficients, such as the thermopower and Nernst coefficient, are greatly enhanced over their zero-field values even at relatively low fields.

preprint2019arXiv

Classification of Critical Points in Energy Bands Based on Topology, Scaling and Symmetry

A critical point of the energy dispersion is the momentum where electron velocity vanishes. At the corresponding energy, the density of states (DOS) exhibits non-analyticity such as divergence. Critical points can be first classified as ordinary and high-order ones, and the ordinary critical points have been studied thoroughly by Léon van Hove. In this work, we describe and classify high-order critical points based on topology, scaling and symmetry, which are beyond Léon van Hove's framework. We show that high-order critical points can have power-law divergent DOS with particle-hole asymmetry, and can be realized at generic or symmetric momenta by tuning a few parameters such as twist angle, strain, pressure and/or external fields.

preprint2019arXiv

Magic of high order van Hove singularity

We introduce a new type of van Hove singularity in two dimensions, where a saddle point in momentum space is changed from second-order to high-order. Correspondingly, the density of states near such ``high-order van Hove singularity'' is significantly enhanced from logarithmic to power-law divergence, which promises stronger electron correlation effects. High-order van Hove singularity can be generally achieved by tuning the band structure with a single parameter in moiré superlattices, such as twisted bilayer graphene by tuning twist angle or applying pressure, and trilayer graphene by applying vertical electric field.

preprint2019arXiv

Supermetal

We study the effect of electron interaction in an electronic system with a high-order Van Hove singularity, where the density of states shows a power-law divergence. Owing to scale invariance, we perform a renormalization group (RG) analysis to find a nontrivial metallic behavior where various divergent susceptibilities coexist but no long-range order appears. We term such a metallic state as a supermetal. Our RG analysis reveals noninteracting and interacting fixed points, which draws an analogy to the $ϕ^4$ theory. We further present a finite anomalous dimension at the interacting fixed point by a controlled RG analysis, thus establishing an interacting supermetal as a non-Fermi liquid.

preprint2019arXiv

Thermoelectric response and entropy of fractional quantum Hall systems

We study thermoelectric transport properties of fractional quantum Hall systems based on exact diagonalization calculation. Based on the relation between thermoelectric response and thermal entropy, we demonstrate that thermoelectric Hall conductivity $α_{xy}$ has powerlaw scaling $α_{xy} \propto T^η$ for gapless composite Fermi-liquid states at filling number $ν=1/2$ and $1/4$ at low temperature ($T$), with exponent $η\sim 0.5$ distinctly different from Fermi liquids. The powerlaw scaling remains unchanged for different forms of interaction including Coulomb and short-range ones, demonstrating the robustness of non-Fermi-liquid behavior at low $T$. In contrast, for $1/3$ fractional quantum Hall state, $α_{xy}$ vanishes at low $T$ with an activation gap associated with neutral collective modes rather than charged quasiparticles. Our results establish a new manifestation of the non-Fermi-liquid nature of quantum Hall fluids at finite temperature.

preprint2017arXiv

Rotation Anomaly and Topological Crystalline Insulators

We show that in the presence of $n$-fold rotation symmetries and time-reversal symmetry, the number of fermion flavors must be a multiple of $2n$ ($n=2,3,4,6$) on two-dimensional lattices, a stronger version of the well-known fermion doubling theorem in the presence of only time-reversal symmetry. The violation of the multiplication theorems indicates anomalies, and may only occur on the surface of new classes of topological crystalline insulators. Put on a cylinder, these states have $n$ Dirac cones on the top and on the bottom surfaces, connected by $n$ helical edge modes on the side surface.

Liang Fu

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27 published item(s)

QERNEL: a Scalable Large Electron Model

Dirac electron under periodic magnetic field: Platform for fractional Chern insulator and generalized Wigner crystal

Moiré Landau fans and magic zeros

Non-Abelian nonsymmorphic chiral symmetries

Pseudogap metal and magnetization plateau from doping moiré Mott insulator

Quantum anomalous Hall effect from inverted charge transfer gap

Supercurrent diode effect and finite momentum superconductivity

Supercurrent induced resonant optical response

Ferromagnetic helical nodal line and Kane-Mele spin-orbit coupling in kagome metal Fe3Sn2

Interfacial ferroelectricity in rhombohedral-stacked bilayer transition metal dichalcogenides

New mechanism and exact theory of superconductivity from strong repulsive interaction

Spin-triplet superconductivity from interband effect in doped insulators

Unconventional superconductivity due to interband polarization

Charge Transfer Excitations, Pair Density Waves, and Superconductivity in Moiré Materials

Density functional approach to correlated moire states: itinerant magnetism

Discovery of segmented Fermi surface induced by Cooper pair momentum

Enhanced anomalous Nernst effect in disordered Dirac and Weyl materials

Enhanced Superconductivity in Monolayer $T_d$-MoTe$_2$ with Tilted Ising Spin Texture

High-frequency rectification via chiral Bloch electrons

Local Probes for Quantum Hall Ferroelectrics and Nematics

Nearly quantized conductance plateau of vortex zero mode in an iron-based superconductor

Observation of a thermoelectric Hall plateau in the extreme quantum limit

Classification of Critical Points in Energy Bands Based on Topology, Scaling and Symmetry

Magic of high order van Hove singularity

Supermetal

Thermoelectric response and entropy of fractional quantum Hall systems

Rotation Anomaly and Topological Crystalline Insulators