Bulk Topological Invariants in Noninteracting Point Group Symmetric Insulators

Abstract

We survey various quantized bulk physical observables in two- and three-dimensional topological band insulators invariant under translational symmetry and crystallographic point group symmetries (PGS). In two-dimensional insulators, we show that: (i) the Chern number of a $C_n$-invariant insulator can be determined, up to a multiple of $n$, by evaluating the eigenvalues of symmetry operators at high-symmetry points in the Brillouin zone; (ii) the Chern number of a $C_n$-invariant insulator is also determined, up to a multiple of $n$, by the $C_n$ eigenvalue of the Slater determinant of a noninteracting many-body system and (iii) the Chern number vanishes in insulators with dihedral point groups $D_n$, and the quantized electric polarization is a topological invariant for these insulators. In three-dimensional insulators, we show that: (i) only insulators with point groups $C_n$, $C_{nh}$ and $S_n$ PGS can have nonzero 3D quantum Hall coefficient and (ii) only insulators with improper rotation symmetries can have quantized magnetoelectric polarization $P_3$ in the term $P_3\mathbf{E}\cdot \mathbf{B}$, the axion term in the electrodynamics of the insulator (medium).

15 pages for main text, 5 pages for appendices, three figures and three tables

References in corpus (29)

• Topological insulators and superconductors
• Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells
• $Z_2$ Topological Order and the Quantum Spin Hall Effect
• Quantum Spin Hall Insulator State in HgTe Quantum Wells
• Superconducting proximity effect and Majorana fermions at the surface of a topological insulator
• Electronic Structure of Pyrochlore Iridates: From Topological Dirac Metal to Mott Insulator
• Topological Insulators in Three Dimensions
• Topological Insulators with Inversion Symmetry
• A topological Dirac insulator in a quantum spin Hall phase : Experimental observation of first strong topological insulator
• Classification of topological insulators and superconductors in three spatial dimensions
• Topological Field Theory of Time-Reversal Invariant Insulators
• Topological invariants of time-reversal-invariant band structures
• Topological Crystalline Insulators
• First observation of Spin-Momentum Helical Locking in Bi2Se3 and Bi2Te3, demonstration of Topological-Order at 300K and a realization of topological-transport-regime
• Chern semi-metal and Quantized Anomalous Hall Effect in HgCr2Se4
• Topological Crystalline Insulators in the SnTe Material Class
• First direct observation of Spin-textures in Topological Insulators : Spin-resolved ARPES as a probe of topological quantum spin Hall effect and Berry's phase
• Topological orders and Edge excitations in FQH states
• Time Reversal Polarization and a Z_2 Adiabatic Spin Pump
• Topological quantization of the spin Hall effect in two-dimensional paramagnetic semiconductors
• Multi-Weyl Topological Semimetals Stabilized by Point Group Symmetry
• Magnetic impurities on the surface of a topological insulator
• Inversion Symmetric Topological Insulators
• Time-reversal invariant realization of the Weyl semimetal phase
• Quantized Response and Topology of Insulators with Inversion Symmetry
• Topological semimetal in a fermionic optical lattice
• Orbital magnetoelectric coupling in band insulators
• Theory of orbital magnetoelectric response
• Quasiparticle scattering in two dimensional helical liquid

Cited by in corpus (320)

• Classification of topological quantum matter with symmetries
• Colloquium: Topological Band Theory
• Electric Multipole Moments, Topological Multipole Moment Pumping, and Chiral Hinge States in Crystalline Insulators
• $(d-2)$-dimensional edge states of rotation symmetry protected topological states
• Classification of stable three-dimensional Dirac semimetals with nontrivial topology
• Symmetry-based Indicators of Band Topology in the 230 Space Groups
• Quantization of fractional corner charge in $C_n$-symmetric higher-order topological crystalline insulators
• Towards ideal topological materials: Comprehensive database searches using symmetry indicators
• Topological Crystalline Insulators and Topological Superconductors: From Concepts to Materials
• Topological classification of crystalline insulators through band structure combinatorics
• Topology of crystalline insulators and superconductors
• All "Magic Angles" Are "Stable" Topological
• Novel Topological Phase with Zero Berry Curvature
• High-throughput calculations of magnetic topological materials
• Field Induced Positional Shift of Bloch Electrons and its Dynamical Implications
• Second-order topological insulators and superconductors with an order-two crystalline symmetry
• Fragile Topology and Wannier Obstructions
• Magic in twisted transition metal dichalcogenide bilayers
• Classification of topological insulators and superconductors in the presence of reflection symmetry
• Classification of reflection symmetry protected topological semimetals and nodal superconductors
• Gapless surface Dirac cone in antiferromagnetic topological insulator MnBi${}_2$Te${}_4$
• Quantitative mappings between symmetry and topology in solids
• Triple Point Topological Metals
• Higher-order bulk-boundary correspondence for topological crystalline phases
• Ground State and Hidden Symmetry of Magic Angle Graphene at Even Integer Filling
• Symmetry indicators and anomalous surface states of topological crystalline insulators
• Building Blocks of Topological Quantum Chemistry: Elementary Band Representations
• Structure and Topology of Band Structures in the 1651 Magnetic Space Groups
• Wilson loop approach to fragile topology of split elementary band representations and topological crystalline insulators with time reversal symmetry
• New classes of topological crystalline insulators with unpinned surface Dirac cones
• Tunable topological phononic crystals
• Surface States of Topological Crystalline Insulators in IV-VI Semiconductors
• Topological Mirror Superconductivity
• All Topological Bands of All Nonmagnetic Stoichiometric Materials
• Theory of correlated insulating behaviour and spin-triplet superconductivity in twisted double bilayer graphene
• Efficient Topological Materials Discovery Using Symmetry Indicators
• Helical Topological Edge States in a Quadrupole Phase
• Topological Materials Discovery from Crystal Symmetry
• Higher-order topological insulators protected by inversion and rotoinversion symmetries
• Classification of Two Dimensional Topological Crystalline Superconductors and Majorana Bound States at Disclinations
• Charged Skyrmions and Topological Origin of Superconductivity in Magic Angle Graphene
• Topological Euler class as a dynamical observable in optical lattices
• Majorana Fermions and Disclinations in Topological Crystalline Superconductors
• Topological superconductivity in Dirac semimetals
• Gauging spatial symmetries and the classification of topological crystalline phases
• Surfaces of Axion Insulators
• Higher-order Weyl Semimetals
• Topology of nonsymmorphic crystalline insulators and superconductors
• Fractional disclination charge in two-dimensional $C_n-$symmetric topological crystalline insulators
• Dirac nodal lines and induced spin Hall effect in metallic rutile oxides
• Topological non-symmorphic crystalline insulators
• Real Space Invariants: Twisted Bulk-Boundary Correspondence of Fragile Topology
• Dimensional Crossover of Topological Edge States in Su-Schrieffer-Heeger Model
• Observation of non-Abelian topological semimetals and their phase transitions
• Twisted bilayer graphene. II. Stable symmetry anomaly
• Rotation Anomaly and Topological Crystalline Insulators
• Fractional quantum anomalous Hall states in twisted bilayer MoTe${}_2$ and WSe${}_2$
• In-plane Magnetization Induced Quantum Anomalous Hall Effect
• Geometric approach to fragile topology beyond symmetry indicators
• Topological Classification of Crystalline Insulators with Point Group Symmetry
• Disconnected Elementary Band Representations, Fragile Topology, and Wilson Loops as Topological Indices: An Example on the Triangular Lattice
• Topological Crystalline Materials - General Formulation, Module Structure, and Wallpaper Groups -
• Twisted bilayer graphene.VI. An Exact Diagonalization Study of Twisted Bilayer Graphene at Non-Zero Integer Fillings
• Band Representations and Topological Quantum Chemistry
• Realization of the square-root higher-order topological insulator in electric circuits
• Fractional corner charges in spin-orbit coupled crystals
• Nonlinear Hall effect with time-reversal symmetry: Theory and material realizations
• Topological Insulators with Commensurate Antiferromagnetism
• Diagnosis for topological semimetals in the absence of spin-orbital coupling
• Refined symmetry indicators for topological superconductors in all space groups
• Emergence of one-dimensional wires of free carriers in transition-metal-dichalcogenide nanostructures
• Topological correspondence between magnetic space group representations
• Fragile Topology Protected by Inversion Symmetry: Diagnosis, Bulk-Boundary Correspondence, and Wilson Loop
• Phonons as a platform for non-Abelian braiding and its manifestation in layered silicates
• The translational side of topological band insulators
• Polarization-driven band topology evolution in twisted MoTe${}_2$ and WSe${}_2$
• Unified understanding of symmetry indicators for all internal symmetry classes
• Square-root higher-order topological insulator on a decorated honeycomb lattice
• Topological Weaire-Thorpe models of amorphous matter
• Crystalline topological phases as defect networks
• Torsion, Parity-odd Response and Anomalies in Topological States
• New class of topological superconductors protected by magnetic group symmetries
• Maximally Localized Wannier Orbitals, Interaction Models and Fractional Quantum Anomalous Hall Effect in Twisted Bilayer MoTe2
• Band Connectivity for Topological Quantum Chemistry: Band Structures As A Graph Theory Problem
• Modern semiclassical theory of magnetic transport and breakdown
• Many-body topological invariants in fermionic symmetry protected topological phases: Cases of point group symmetries
• Novel magnetic orderings in the kagome Kondo-lattice model
• Shift insulators: rotation-protected two-dimensional topological crystalline insulators
• Symmetry-based indicators for topological Bogoliubov-de Gennes Hamiltonians
• Observation of degenerate zero-energy topological states at disclinations in an acoustic lattice
• Quantum anomalous Hall effect in atomic crystal layers from in-plane magnetization
• Chiral Dirac Superconductors: Second-order and Boundary-obstructed Topology
• Momentum-space structure of surface states in a topological semimetal with a nexus point of Dirac lines
• Symmetry indicators of band topology
• Patterns of Electro-magnetic Response in Topological Semi-metals
• Topological Bloch oscillations
• Topological magnon bands in a room temperature Kagome magnet
• Global band topology of simple and double Dirac-point (semi-)metals
• ${\mathbb{Z}}_2$ Topological Invariant for Magnon Spin Hall Systems
• On the matter of topological insulators as magnetoelectrics
• Symmetry-protected Topological Phases, Generalized Laughlin Argument and Orientifolds
• Topological magnetic crystalline insulators and co-representation theory
• Inverse design of higher-order photonic topological insulators
• Topological Materials Discovery By Large-order symmetry indicators
• Classification of topological crystalline insulators based on representation theory
• Topological Phases of Photonic Crystals under Crystalline Symmetries
• Multi-orbital model reveals second-order topological insulator in 1H-transition metal dichalcogenide
• ${\mathbb{Z}}_2$-enriched symmetry indicators for topological superconductors in the 1651 magnetic space groups
• Three-dimensional superconductors with hybrid higher order topology
• Fractional quantum Hall states for moiré superstructures in the Hofstadter regime
• Bulk invariants and topological response in insulators and superconductors with nonsymmorphic symmetries
• Topological classification and diagnosis in magnetically ordered electronic materials
• Topological invariants, surface states, and interaction-driven phase transitions in correlated Kondo insulators with cubic symmetry
• Interaction-driven topological phase diagram of twisted bilayer MoTe${}_2$
• Non-Hermitian band topology with generalized inversion symmetry
• Monolayer V2MX4: A new family of quantum anomalous Hall insulators
• Engineering polar discontinuities in honeycomb lattices
• Atiyah-Hirzebruch Spectral Sequence in Band Topology: General Formalism and Topological Invariants for 230 Space Groups
• Non-Hermiticity and topological invariants of magnon Bogoliubov-de Gennes systems
• Topological classification under nonmagnetic and magnetic point group symmetry: Application of real-space Atiyah-Hirzebruch spectral sequence to higher-order topology
• Surface theorem for the Chern-Simons axion coupling
• Weak Topological Insulators in PbTe/SnTe Superlattices
• Symmetry indicators for topological superconductors
• Quantum gyro-electric effect: Photon spin-1 quantization in continuum topological bosonic phases
• Bulk-corner correspondence of time-reversal symmetric insulators: deduplicating real-space invariants
• Multicellularity of delicate topological insulators
• Dislocation charges reveal two-dimensional topological crystalline invariants
• Multi-gap topology and non-Abelian braiding of phonons from first principles
• Reentrant Correlated Insulators in Twisted Bilayer Graphene at 25T ($2\pi$ Flux)
• Topological Invariants in Point Group Symmetric Photonic Topological Insulators
• Stability of Anomalous Hall Crystals in multilayer rhombohedral graphene
• Classification of engineered topological superconductors
• Filling anomaly for general 2D and 3D $C_4$ symmetric lattices
• Excess charges as a probe of one-dimensional topological crystalline insulating phases
• Anomalous Hall Crystals in Rhombohedral Multilayer Graphene II: General Mechanism and a Minimal Model
• CPT theorem and classification of topological insulators and superconductors
• $2^n$-root weak, Chern, and higher-order topological insulators, and $2^n$-root topological semimetals
• Subdimensional topologies, indicators and higher order phases
• Kane-Mele with a twist: Quasicrystalline higher-order topological insulators with fractional mass kinks
• Higher-order topology in monolayer graphene
• Delicate topology protected by rotation symmetry: Crystalline Hopf insulators and beyond
• Pfaffian formalism for higher-order topological insulators
• Diagnosis of interaction-driven topological phase via exact diagonalization
• Coupled-layer description of topological crystalline insulators
• Manipulation and braiding of Weyl nodes using symmetry-constrained phase transitions
• Electronic structures and topological properties in nickelates $L{n}_{n+1}$Ni${}_n$O${}_{2n+2}$
• Crystalline Kitaev spin liquids
• Non-local topological electromagnetic phases of matter
• Theory of quasiparticle interference in mirror symmetric 2D systems and its application to surface states of topological crystalline insulators
• Existence of zero-energy impurity states in different classes of topological insulators and superconductors and their relation to topological phase transitions
• High-throughput Discovery of Topologically Non-trivial Materials using Spin-orbit Spillage
• Axionic Band Topology in Inversion-Symmetric Weyl-Charge-Density Waves
• Giant proximity exchange and flat Chern band in 2D magnet-semiconductor heterostructures
• Symmetry analysis of translational symmetry broken density waves: application to hexagonal lattices in two dimensions
• In-Plane Magnetic-Field-Induced Quantum Anomalous Hall Plateau Transition
• Symmetry and topology of hyperbolic Haldane models
• qeirreps: an open-source program for Quantum ESPRESSO to compute irreducible representations of Bloch wavefunctions
• Two-dimensional type-II Dirac fermions in layered oxides
• Smooth gauge and Wannier functions for topological band structures in arbitrary dimensions
• Corner states of topological fullerenes
• Bulk-edge and bulk-hinge correspondence in inversion-symmetric insulators
• Second-Order Bulk-Boundary Correspondence in Rotationally Symmetric Topological Superconductors from Stacked Dirac Hamiltonians
• Symmetry indicator in non-Hermitian systems
• Massive Dirac fermions in moiré superlattices: a route towards topological flat minibands
• Construction and classification of point group symmetry protected topological phases in 2D interacting fermionic systems
• Layered Topological Crystalline Insulators
• Nematic excitonic insulator in transition metal dichalcogenide moiré heterobilayers
• Disclination classes, fractional excitations, and the melting of quantum liquid crystals
• Bott periodicity for the topological classification of gapped states of matter with reflection symmetry
• Quantized charge polarization as a many-body invariant in (2+1)D crystalline topological states and Hofstadter butterflies
• Symmetry Analysis of Anomalous Floquet Topological Phases
• Topological Crystalline Phases in a Disordered Inversion-Symmetric Chain
• Unidirectional Maxwellian Spin Waves
• Edge states, corner states, and flat bands in a two-dimensional $\mathcal{P}\mathcal{T}$ symmetric system
• Interaction Enabled Topological Crystalline Phases
• Phase transitions of non-Abelian charged nodal links in a spring-mass system
• Hidden Breathing Kagome Topology in Hexagonal Transition Metal Dichalcogenides
• Theory of inversion-${\mathbb{Z}}_4$ protected topological chiral hinge states and its applications to layered antiferromagnets
• No-go theorem for topological insulators and sure-fire recipe for Chern insulators
• Topology invisible to eigenvalues in obstructed atomic insulators
• Flat bands with band crossings enforced by symmetry representation
• Landau Levels of the Euler Class Topology
• Simulation of higher-order topological phases in 2D spin-phononic crystal networks
• Theory of Correlated Insulators and Superconductor at $\nu =1$ in Twisted WSe${}_2$
• Rapid Exploration of Topological Band Structures using Deep Learning
• Topological flat bands without magic angles in massive twisted bilayer graphenes
• Spin Splitting Nernst Effect in Altermagnet
• Interacting models for twisted bilayer graphene: a quantum chemistry approach
• Glide-symmetric magnetic topological crystalline insulators with inversion symmetry
• Symmetry-protected entangling boundary zero modes in crystalline topological insulators
• Bridging the small and large in twisted transition metal dicalcogenide homobilayers: a tight binding model capturing orbital interference and topology across a wide range of twist angles
• Space group symmetry fractionalization in a family of exactly solvable models with Z2 topological order
• Interacting Topological Quantum Chemistry in 2D: Many-body Real Space Invariants
• Interacting second-order topological insulators in one-dimensional fermions with correlated hopping
• Topological near-field heat flow in a honeycomb lattice
• Universal higher-order bulk-boundary correspondence of triple nodal points
• The Bulk-Hinge Correspondence and Three-Dimensional Quantum Anomalous Hall Effect in Second Order Topological Insulators
• Space group constraints on weak indices in topological insulators
• Identifying, and constructing, complex magnon band topology
• Universal Relation among Many-Body Chern Number, Rotation Symmetry, and Filling
• Polaritonic Chern insulators in monolayer semiconductors
• Interplay of topology and interactions in quantum Hall topological insulators: U(1) symmetry, tunable Luttinger liquid, and interaction-induced phase transitions
• Topological Edge States Induced by Zak's Phase in A3B Monolayers
• Crystal-symmetry preserving Wannier states for fractional chern insulators
• Stable Dirac semi-metal in the allotrope of IV elements
• Discovering two-dimensional magnetic topological insulators by machine learning
• Higher-Order Topological Insulator on a Martini Lattice and Its Square Root Descendant
• Dynamical Piezomagnetic Effect in Time-Reversal Invariant Weyl Semimetals with Axionic Charge-Density Waves
• Quantization of Topological Invariants under Symmetry-Breaking Disorder
• Quantized surface magnetism and higher-order topology: Application to the Hopf insulator
• Two-dimensional weak-type topological insulators in inversion symmetric crystals
• Designing topology and fractionalization in narrow gap semiconductor films via electrostatic engineering
• Topological states in a dimerized system with staggered magnetic fluxes
• Quasiperiodicity and 2D Topology in 1D Charge Ordered Materials
• Three-dimensional $\mathcal{P}\mathcal{T}$-symmetric topological phases with Pontryagin index
• Variants of the symmetry-based indicator
• Detecting Bulk Topology of Quadrupolar Phase from Quench Dynamics
• Characterization and classification of interacting (2+1)D topological crystalline insulators with orientation-preserving wallpaper groups
• Embedded Topological Semimetals
• Quantum anomalous Hall state from spatially decaying interactions on the decorated honeycomb lattice
• Dynamic bulk-boundary correspondence for anomalous Floquet topology
• Topology in time-reversal symmetric crystals
• Glide-symmetric topological crystalline insulator phase in a nonprimitive lattice
• Single-point spin Chern number in a supercell framework
• Symmetry indicators in commensurate magnetic flux
• One-dimensional electronic instabilities at the edges of $Mo{S}_2$
• Prediction of Topological Crystalline Insulator and Topological Phase Transitions in Two-dimensional PbTe Films
• Wave packet dynamics and edge transport in anomalous Floquet topological phases
• Effect of coordination on topological phases on self-similar structures
• Topological flat bands, valley polarization, and interband superconductivity in magic-angle twisted bilayer graphene with proximitized spin-orbit couplings
• Spin-1 Weyl Point and Surface Arc State in a Chiral Phononic Crystal
• Correlation-driven phase transition in a Chern insulator
• Fractional hinge and corner charges in various crystal shapes with cubic symmetry
• Topological phonon analysis of the 2D buckled honeycomb lattice: an application to real materials
• Topological Nonsymmorphic Ribbons out of Symmorphic Bulk
• Hofstadter spectrum of Chern bands in twisted transition metal dichalcogenides
• Topological insulators and higher-order topological insulators from gauge-invariant 1D lines
• Interacting topological mirror excitonic insulator in one dimension
• Nonlocal Moments in the Chern Bands of Twisted Bilayer Graphene
• Fundamental laws of chiral band crossings: local constraints, global constraints, and topological phase diagrams
• Higher angular momentum band inversions in two dimensions
• Efficient prediction of superlattice and anomalous miniband topology from quantum geometry
• Homotopic classification of band structures: Stable, fragile, delicate, and stable representation-protected topology
• Topological invariants beyond symmetry indicators: Boundary diagnostics for twofold rotationally symmetric superconductors
• Hybrid-order topology in unconventional magnets of Eu-based Zintl compounds with surface-dependent quantum geometry
• Topologically Protected Edge States in Triangular Lattices
• Unique surface-state connection between Weyl and nodal ring fermions in ferromagnetic material Cs2MoCl6
• Symmetric Wannier states and tight-binding model for quantum spin Hall bands in AB-stacked MoTe${}_2$/WSe${}_2$
• Generating and detecting topological phases with higher Chern number
• Rotoinversion-symmetric bulk-hinge correspondence and its applications to higher-order Weyl semimetals
• Observation of Multiple Topological Corner States in Thermal Diffusion
• Green's Function Approach to Interacting Higher-order Topological Insulators
• Constructions and Applications of Irreducible Representations of Spin-Space Groups
• Topological obstructed atomic limit by annihilating Dirac fermions
• Observation of Bulk Polarization Transitions and Higher-Order Embedded Topological Eigenstates for Sound
• Correlated phases and topological phase transition in twisted bilayer graphene at one quantum of magnetic flux
• Higher-order topology protected by latent crystalline symmetries
• Electromagnetic Response of Three-dimensional Topological Crystalline Insulators
• Magnetic tilting and emergent Majorana spin connection in topological superconductors
• BaHgSn: A Dirac semimetal with surface hourglass fermions
• Diagnosis of topological nodal lines with nontrivial monopole charge in the presence of rotation symmetries
• Pfaffian invariant identifies magnetic obstructed atomic insulators
• Topological Classical Systems with Generalized Chiral Symmetry
• Topological nodal superconducting phases and topological phase transition in the hyperhoneycomb lattice
• Scattering theory of delicate topological insulators
• Gapless Criterion for Crystals from Effective Axion Field
• Topological Critical Materials of Ternary Compounds
• Computing the ${\mathbb{Z}}_2$ Invariant in Two-Dimensional Strongly-Correlated Systems
• Pressure-Driven Topological Phase Transition in the Yb Chalcogenides YbO and YbS
• Effects of correlations on phase diagrams of the two-dimensional Su-Schrieffer-Heeger model with the longer-range hoppings
• Topological Field Theories of Three-Dimensional Rotation Symmetric Insulators: Coupling Curvature and Electromagnetism
• Additive rule of real and reciprocal space topologies at disclinations
• Chern-Textured Exciton Insulators with Valley Spiral Order in Moiré Materials
• Discriminant indicator with generalized rotational symmetry
• Double Majorana Vortex Flat Bands in the Topological Dirac Superconductor
• Duality in topological superconductors and topological ferromagnetic insulators in a honeycomb lattice
• Hong-Ou-Mandel Interference in a temporal-average-inversion-symmetric chain
• Flat-band full localization and symmetry-protected topological phase on bilayer lattice systems
• Observation of trapped fractional charge and topological states at disclination defects in higher-order topological insulators
• Electric polarization and discrete shift from boundary and corner charge in crystalline Chern insulators
• Acoustic semimetal with Weyl points and surface states
• Intrinsic (Axion) Statistical Topological Insulator
• Hedgehog spin texture and competing orders associated with strains on the surface of a topological crystalline insulator
• Electronic Crystal Phases in the Presence of Non-Uniform Berry Curvature and Tunable Berry Flux: The ${\lambda }_N$-Jellium model
• Homotopy invariant in time-reversal and twofold rotation symmetric systems
• Signatures of surface Majorana modes in the magnetic response of topological superconductors
• $d$-Wave Polarization-Spin Locking in Two-Dimensional Altermagnets
• Topological invariants and topological charges in photonic systems
• Stability of the X-Y-phase of the two-dimensional C4 point group insulator
• Global and Local Topological Crystalline Markers for Rotation-Symmetric Insulators
• Topological phases, van Hove singularities, and spin texture in magic-angle twisted bilayer graphene in the presence of proximity-induced spin-orbit couplings
• Realization of chiral whispering gallery mode cavities enabled by photonic Chern insulators
• Topological Higgs Amplitude Modes in Strongly Interacting Superfluids
• Modulating Hamiltonian Approach to Quantum Many-Body Systems and Crystalline Topological Phases Protected by Generalized Magnetic Translations
• High-chirality and multiquaternion Weyl nodes in hexagonal ReO${}_3$
• Wavefunction textures in twisted bilayer graphene from first principles
• Modular Anomalies in (2+1) and (3+1)-D Edge Theories
• Modulation of magnetism via electric field in MgO nanoribbons
• Berry Curvature of Low-Energy Excitons in Rhombohedral Graphene
• Equivariant Parameter Families of Spin Chains: A Discrete MPS Formulation
• Fragile topological insulators protected by rotation symmetry without spin-orbit coupling
• Chern-Selective multi-valley Flat Bands in Twisted Mono-Bilayer and Mono-Trilayer MoTe${}_2$
• Crystalline finite-size topology
• High-root topological edge-state bands
• Fermi-surface diagnosis for topological superconductivity with $s$-wave-like pairing symmetries
• Topological photonics in nanoscaled systems with far field radiation and polarization singularities
• Unconventional Fractional Phases in Multi-Band Vortexable Systems
• Characterization of the 2D Su-Schrieffer-Heeger Model with Second-Nearest-Neighbor Interactions
• Hybrid Higher-Order Skin Topological Modes in the Two-Dimensional Su-Schrieffer-Heeger Model with Nonreciprocal Hoppings
• Spatiotemporal chaos in the interface growth of topological insulators
• Efficient prediction of topological superlattice bands with spin-orbit coupling
• Resonant inelastic X-ray scattering in the topological semimetal FeSi
• Valley-Hall-like second-order photonic topological insulators in Kagome lattice
• Three-dimensional spinless Euler insulators with rotational symmetry
• Topological power pumping in quantum circuits
• Angular momentum-dependent topological transport and its experimental realization using a transmission line network
• Robustness of real-space topology in moiré systems
• Weak ${\mathbb{Z}}_2$ Supertopology
• Quantized Spin Hall Effect in Three-Dimensional Nodal-Ring Semimetal: Geometric Scaling and Symmetry-Engineered Spin Response
• Higher Chern bands in helical homotrilayer transition metal dichalcogenides