Topological Crystalline Insulators

Abstract

The recent discovery of topological insulators has revived interest in the topological properties of insulating band structures. In this work, we extend the topological classification of insulating band structures to include certain point group symmetry of crystals. We find a class of three-dimensional "topological crystalline insulators" which have metallic surface states on certain high symmetry crystal surfaces. These topological crystalline insulators can be viewed as the counterpart of topological insulators in materials without spin-orbit coupling. Their surface states have quadratic band degeneracy instead of linear Dirac dispersion. Their band structures are characterized by new Z2 invariants. We hope this work will enlarge the family of topological phases in band insulators and stimulate the search for them in real materials.

published version, added an appendix on the stability of surface states

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• Observation of nonlinear fractal higher-order topological insulator
• Smooth gauge and Wannier functions for topological band structures in arbitrary dimensions
• Emergence of Topologically Non-trivial Spin-polarized States in a Segmented Linear Chain
• Discovery of Higher-Order Topological Insulators using the Spin Hall Conductivity as a Topology Signature
• Dyakonov-Perel-like Orbital and Spin Relaxations in Centrosymmetric Systems
• Topological crystalline insulator states in the Ca${}_2$As family
• Surface electronic state of superconducting topological crystalline insulator
• Topological spin excitations in Harper-Heisenberg spin chains
• Gapless surface states in a lattice of coupled cavities: a photonic analog of topological crystalline insulators
• Quasiparticle scattering from topological crystalline insulator SnTe (001) surface states
• Bulk characterization of topological crystalline insulators: stability under interactions and relations to symmetry enriched U(1) quantum spin liquids
• Topological Superconductivity in an s-wave Superconductor and Its Implication to Iron-based Superconductors
• Bulk Signatures of Pressure-Induced Band Inversion and Topological Phase Transitions in Pb${}_{1-x}$Sn${}_x$Se
• Delocalization Transition of Disordered Axion Insulator
• Interaction effects on the classification of crystalline topological insulators and superconductors
• Symmetry indicator in non-Hermitian systems
• Observation of Open-Orbit Fermi Surface Topology in Extremely Large Magnetoresistance Semimetal MoAs${}_2$
• Second-Order Bulk-Boundary Correspondence in Rotationally Symmetric Topological Superconductors from Stacked Dirac Hamiltonians
• Topological Insulators and Quantum Spin Liquids
• Temperature dependent conductivity mechanisms observed in Pr2NiTiO6
• Winding number and Zak phase in multi-band SSH models
• Superconductivity induced by In substitution into the topological crystalline insulator Pb(0.5)Sn(0.5)Te
• Synthesis and characterisation of nanomaterials of the topological crystalline insulator SnTe
• Weak-link Josephson Junctions Made from Topological Crystalline Insulators
• Light-induced quantum anomalous Hall effect on the 2D surfaces of 3D topological insulators
• Majorana Flat Bands in s-Wave Gapless Topological Superconductors
• Topological crystalline insulator phase in graphene multilayers
• Tunable Dirac interface states in topological superlattices
• Giant Photonic Response of Mexican-hat Topological Semiconductors for Mid-infrared to THz Applications
• Antiferromagnetic topological insulator state in the correlated Bernevig-Hughes-Zhang model
• Distinct topological crystalline phases in models for the strongly correlated topological insulator SmB6
• Quantum Monte Carlo study of strange correlator in interacting topological insulators
• Saddle-point von Hove singularity and dual topological insulator state in Pt${}_2$HgSe${}_3$
• Statistical Analysis of the Chern Number in the Interacting Haldane-Hubbard Model
• Designer Topological Insulators in Superlattices
• Classification of crystalline insulators without symmetry indicators: atomic and fragile topological phases in twofold rotation symmetric systems
• Construction and classification of point group symmetry protected topological phases in 2D interacting fermionic systems
• Layered Topological Crystalline Insulators
• Amorphous topological phases protected by continuous rotation symmetry
• Rotation Symmetry-Protected Topological Phases of Fermions
• Application of the induction procedure and the Smith Decomposition in the calculation and topological classification of electronic band structures in the 230 space groups
• Indium substitution effect on the topological crystalline insulator family (Pb${}_{1-x}$Sn${}_x$)${}_{1-y}$In${}_y$Te: Topological and superconducting properties
• Studies of the superconducting properties of Sn1-xInxTe (x=0.38 to 0.45) using muon-spin spectroscopy
• Flux-fusion anomaly test and bosonic topological crystalline insulators
• Doubled Quantum Spin Hall Effect with High-Spin Chern Number in $\alpha$-Antimonene and $\alpha$-Bismuthene
• Second harmonic generation as a probe of broken mirror symmetry
• Inducing Lifshitz transition by extrinsic doping of surface bands in topological crystalline insulator Pb${}_{1-x}$Sn${}_x$Se
• Semirelativity in Semiconductors: a Review
• General Theory of Momentum-Space Nonsymmorphic Symmetry
• $N$-band Hopf insulator
• Disclination classes, fractional excitations, and the melting of quantum liquid crystals
• Spin-orbit coupling and topological phases for ultracold atoms
• Wannier functions and Z_2 invariants in time-reversal symmetric topological insulators
• Growth and Magnetotransport in Thin Film α-Sn on CdTe
• Higher-order topological insulators in a magnetic field
• Topological continuum charges of acoustic phonons in 2D
• Floquet engineering of individual band gaps in an optical lattice using a two-tone drive
• Higher-Order Entanglement and Many-Body Invariants for Higher-Order Topological Phases
• Extended topological group structure due to average reflection symmetry
• Topological Crystalline Phases in a Disordered Inversion-Symmetric Chain
• Classification of spin liquids on the square lattice with strong spin-orbit coupling
• Demonstrating Lattice-Symmetry-Protection in Topological Crystalline Superconductors
• Topological Superconductivity Induced by Magnetic Texture Crystals
• Efficient algorithm to compute the second Chern number in four dimensional systems
• Phonon-Induced Topological Transition to a Type-II Weyl Semimetal
• Gapped Surface States in a Strong-Topological-Semimetal
• Sliding Ferroelectrics Induced Hybrid-Order Topological Phase Transitions
• Non-Hermitian spatial symmetries and their stabilized normal and exceptional topological semimetals
• Broken mirror symmetry tuned topological transport in PbTe/SnTe heterostructures
• Correlation effects on topological crystalline insulators
• Noncollinear twisted RKKY interaction on the optically driven SnTe(001) surface
• Strain engineering of topological properties in lead-salt semiconductors
• Interaction Enabled Topological Crystalline Phases
• Multiple magnetism controlled topological states in EuAgAs
• The Wannier Function Software Ecosystem for Materials Simulations
• Magnetoterahertz Response and Faraday Rotation from Massive Dirac Fermions in the Topological Crystalline Insulator Pb${}_{0.5}$Sn${}_{0.5}$Te
• Noncrystalline topological superconductors
• Topological effects of phonons in GaN and AlxGa1-xN: A potential perspective for tuning phonon transport
• Seeing bulk topological properties of band insulators in small photonic lattices
• Lattice symmetries and the topological protected transport of colloidal particles
• Interacting Dirac fermions under spatially alternating pseudo-magnetic field: Realization of spontaneous quantum Hall effect
• Fractional chiral superconductors
• Spin-orbit interaction and Dirac cones in d orbital noble metal surface states
• Electronic properties of SnTe-class topological crystalline insulator materials
• Topogivity: A Machine-Learned Chemical Rule for Discovering Topological Materials
• Mirror Majorana zero modes in spinful superconductors/superfluids -Non-Abelian braiding of integer quantum vortices-
• Unexpected superconductivity at nanoscale junctions made on the topological crystalline insulator Pb${}_{0.6}$Sn${}_{0.4}$Te
• Topology invisible to eigenvalues in obstructed atomic insulators
• Field Theory of Nematicity in the Spontaneous Quantum Anomalous Hall effect
• No-go theorem for topological insulators and sure-fire recipe for Chern insulators
• Surface States of a System of Dirac Fermions: A Minimal Model
• Symmetry-enforced Band Nodes in 230 Space Groups
• Towards the manipulation of topological states of matter: A perspective from electron transport
• Phase transitions of non-Abelian charged nodal links in a spring-mass system
• Thin film growth of a topological crystal insulator SnTe on the CdTe (111) surface by molecular beam epitaxy
• Trigger of the ubiquitous surface band bending in 3D topological insulators
• Topological edge states of Kekulé-type photonic crystals induced by a synchronized rotation of unit cells
• The hybrid-order topology of weak topological insulators
• Higher-order topological spin Hall effect of sound
• Two distinct topological phases in the mixed valence compound YbB6 and its differences from SmB6
• Non-Abelian Hopf-Euler insulators
• Transport discovery of emerging robust helical surface states in $Z_2=0$ systems
• Interacting topological quantum chemistry of Mott atomic limits
• Edge states at nematic domain walls in FeSe films
• Twist-resilient and robust ferroelectric quantum spin Hall insulators driven by van der Waals interactions
• Topological Crystalline Transition Metals: Strained W, Ta, Mo, and Nb
• Generation of higher-order topological insulators using periodic driving
• Perovskite ThTaN3: a Large Thermopower Topological Crystalline Insulator
• Floquet Engineering Ultracold Polar Molecules to Simulate Topological Insulators
• Experimental search for the origin of low-energy modes in topological materials
• Embedded Topological Insulators
• Phonon-induced topological insulating phases in group IV-VI semiconductors
• Disorder-Induced Weyl Semimetal Phase and Sequential Band Inversions in PbSe-SnSe Alloys
• Landau Levels of the Euler Class Topology
• Adiabatic transformation as a search tool for new topological insulators: distorted ternary Li${}_2$AgSb-class semiconductors and related compounds
• Noncentrosymmetric topological Dirac semimetals in three dimensions
• Converting normal insulators into topological insulators via tuning orbital levels
• Mirror protected Dirac fermions on a Weyl semimetal NbP surface
• Glide-symmetric magnetic topological crystalline insulators with inversion symmetry
• Observation of backscattering induced by magnetism in a topological edge state
• Evidence for bulk nodal loops and universality of Dirac-node arc surface states in ZrGeXc (Xc = S, Se, Te)
• Absence of topological protection of the interface states in ${\mathbb{Z}}_2$ photonic crystals
• Elementary band representations for the single-particle Green's function of interacting topological insulators
• Surface-state-dominated transport in crystals of the topological crystalline insulator In-doped Pb${}_{1-x}$Sn${}_x$Te
• Symmetry-protected entangling boundary zero modes in crystalline topological insulators
• Magnetic states in a three-dimensional topological Kondo insulator
• T-Duality of Topological Insulators
• Entanglement Chern number for an extensive partition of a topological ground state
• Topological properties of multilayers and surface steps in the SnTe material class
• Floquet quadrupole photonic crystals protected by space-time symmetry
• Defect-free SnTe topological crystalline insulator nanowires grown by molecular beam epitaxy on graphene
• Space group symmetry fractionalization in a family of exactly solvable models with Z2 topological order
• Fully gapped superconductivity in In-doped topological crystalline insulator Pb${}_{0.5}$Sn${}_{0.5}$Te
• Electronic Band Structure and Superconducting Properties of SnAs
• Coexistence of Triple Nodal Points, Nodal Links, and Unusual Flat Bands in intermetallic $\mathcal{A}$Pd${}_3$ ($\mathcal{A}$=Pb, Sn)
• `Gauging' time reversal symmetry in tensor network states
• Theory of polarization textures in crystal supercells
• Higher-Order Topological Insulators via Momentum-Space Nonsymmorphic Symmetries
• Observation of oscillatory relaxation in the Sn-terminated surface of epitaxial rock-salt SnSe $\{111\}$ topological crystalline insulator
• High-Pressure Synthesis and Superconductivity of Ag-doped Topological Crystalline Insulator SnTe (Sn1-xAgxTe with x = 0-0.5)
• Projected Topological Branes
• Dirac surface states in magnonic analogs of topological crystalline insulators
• Dual Topological Insulator Device with Disorder Robustness
• Universal Relation among Many-Body Chern Number, Rotation Symmetry, and Filling
• Multiple Topological Electronic Phases in Superconductor MoC
• Disordered fermionic quantum critical points
• Dynamical bulk boundary correspondence and dynamical quantum phase transitions in higher order topological insulators
• Observation of Ultrahigh Mobility Surface States in a Topological Crystalline Insulator by Infrared Spectroscopy
• Topological states in superlattices of HgTe-class materials for engineering three-dimensional flat bands
• Topological Bootstrap: Fractionalization From Kondo Coupling
• Free and Interacting Short-Range Entangled Phases of Fermions: Beyond the Ten-Fold Way
• Bosonic Crystalline Symmetry Protected Topological Phases Beyond the Group Cohomology Proposal
• Interacting second-order topological insulators in one-dimensional fermions with correlated hopping
• Disorder and interaction in chiral chains: Majoranas vs complex fermions
• Topological insulators in the NaCaBi family with large SOC gaps
• Tailoring band-structure and band-filling in a simple cubic (IV, III) - VI superconductor
• Topology of the planar phase of superfluid ${}^3$He and bulk-boundary correspondence for three dimensional topological superconductors
• Possible Realization of Topological Crystalline Superconductivity with Time-Reversal Symmetry in UTe2
• Topological phases and fractional excitations of the exciton condensate in a special class of bilayer systems
• Classification of crystalline topological semimetals with an application to Na${}_3$Bi
• Characterizing the weak topological properties: Berry phase point of view
• Thermoelectric effects in topological crystalline insulators
• Superconductivity, pairing symmetry, and disorder in the doped topological insulator Sn${}_{1-x}$In${}_x$Te for x $\ge$ 0.10
• Topological Edge States Induced by Zak's Phase in A3B Monolayers
• Computing observables without eigenstates: applications to Bloch Hamiltonians
• Impurity bound states as detectors of topological band structures revisited
• Signatures of dephasing by mirror-symmetry breaking in weak-antilocalization magnetoresistance across the topological transition in Pb${}_{1-x}$Sn${}_x$Se
• Efficient method to compute ${\mathbb{Z}}_4$-indices with glide symmetry and applications to Möbius materials, $\mathrm{CeNiSn}$ and $\mathrm{UCoGe}$
• Topological surface states on Bi${}_{1-x}$Sb${}_x$: Dependence on surface orientation, surface termination and stability
• Bosonic symmetry protected topological phases with reflection symmetry
• PT invariant Weyl semimetals in gauge symmetric systems
• Quantization of Topological Invariants under Symmetry-Breaking Disorder
• Topological crystalline insulator state with type-II Dirac fermions in transition metal dipnictides
• Robustness of chiral edge modes in fractal-like-lattices below two dimensions: A case study
• Lecture Notes on Topological Crystalline Insulators
• Discovering two-dimensional magnetic topological insulators by machine learning
• Topological Superconducting Vortex From Trivial Electronic Bands
• Quantum thermal Hall effect of Majorana fermions on the surface of superconducting topoloigcal insulators
• Quantum oscillations in the zeroth Landau Level and the serpentine Landau fan
• Topological Aspect of Graphene Patchwork with Regular Arrays of Nano Holes
• Observation of Dirac state in half-Heusler material YPtBi
• Symmetry protected vortex bound state in superfluid ${}^3$He B-phase
• Multiplicative topological phases
• Interaction-enabled topological phases in topological insulator-superconductor heterostructures
• Weak antilocalization in (111) thin films of a topological crystalline insulator SnTe
• Generalized Lieb-Schultz-Mattis theorem on bosonic symmetry protected topological phases
• Topological Crystalline Magnets: Symmetry-Protected Topological Phases of Fermions
• ARPES study of the epitaxially grown topological crystalline insulator SnTe(111)
• Quantum spin Hall effect in rutile-based oxide multilayers
• Intrinsically Interacting Higher-Order Topological Superconductors
• Fractonic Higher-Order Topological Phases in Open Quantum Systems
• Topological two-dimensional Su-Schrieffer-Heeger analogue acoustic networks: Total reflection at corners and corner induced modes
• Three-dimensional $\mathcal{P}\mathcal{T}$-symmetric topological phases with Pontryagin index
• Non-Dirac topological surface states in (SnTe)${}_{n\ge 2}$(Bi${}_2$Te${}_3$)${}_{m=1}$
• Evolution of Magnetism in Magnetic Topological Semimetal NdSb${}_x$Te${}_{2-x+\delta }$
• PYATB: An Efficient Python Package for Electronic Structure Calculations Using Ab Initio Tight-Binding Model
• Interferometry of non-Abelian band singularities and Euler class topology
• Spin textures on general surfaces of the correlated topological insulator SmB6
• Electron and hole contributions to normal-state transport in the superconducting system Sn${}_{1-x}$In${}_x$Te
• Quasicrystalline Weyl points and dense Fermi-Bragg arcs
• Interplay between boundary conditions and Wilson's mass in Dirac-like Hamiltonians
• Anomalous symmetry protected topological states in interacting fermion systems
• Surface Magnetism in Topological Crystalline Insulators
• Bulk and surface electronic structure of Bi${}_4$Te${}_3$ from $GW$ calculations and photoemission experiments
• Large transverse Hall-like signal in topological Dirac semimetal Cd3As2
• Anisotropic conductivity in magnetic topological insulators
• Optical investigation of thermoelectric topological crystalline insulator Pb${}_{0.77}$Sn${}_{0.23}$Se
• Connecting the dots: Time-reversal symmetric Weyl Semimetals with tunable Fermi arcs
• Spin- and angle-resolved photoemission on the topological Kondo Insulator candidate: SmB6
• BaSn${}_2$: A new, wide-gap, strong topological insulator
• $GW$ study of pressure-induced topological insulator transition in group IV-tellurides
• Topological corner modes in a brick lattice with nonsymmorphic symmetry
• Pressure-induced Superconductivity in Zintl Topological Insulator SrIn2As2
• Novel topological insulators from crystalline symmetries
• Superconducting Dome and Crossover to an Insulating State in [Tl4]Tl1-xSnxTe3
• Topological phases in Bi/Sb planar and buckled honeycomb monolayers
• Characterization and classification of interacting (2+1)D topological crystalline insulators with orientation-preserving wallpaper groups
• Optical $N$-insulators: topological obstructions in the atomistic susceptibility tensor
• Correlation-induced Fermi surface evolution and topological crystalline superconductivity in CeRh2As2
• Computational search for Dirac and Weyl nodes in $f$-electon antiperovskites
• Pressure-induced superconductivity in weak topological insulator BiSe
• Dynamically characterizing topological phases by high-order topological charges
• Surface field theories of point group symmetry protected topological phases
• Dislocation Majorana zero modes in perovskite oxide 2DEG
• Ferromagnetic phase transition in topological crystalline insulator thin films: interplay of anomalous Hall angle and magnetic anisotropy
• NMR study of native defects in PbSe
• Embedded Topological Semimetals
• Anomalous Floquet topological crystalline insulators
• Dynamic bulk-boundary correspondence for anomalous Floquet topology
• Crystalline spin-orbit interaction and the Zeeman splitting in Pb${}_{1-x}$Sn${}_x$Te
• Light-Induced Nonthermal Phase Transition to the Topological Crystalline Insulator State in SnSe
• Metallic Surface States Probed Within the Microwave Skin Depth of the Putative Topological Insulator YBiPt Compound
• Z${}_2$ nontrivial topology of rare-earth binary oxide superconductor
• Spectroscopic evidence for temperature-dependent convergence of light and heavy hole valence bands of PbQ (Q=Te, Se, S)
• Topology in time-reversal symmetric crystals
• Symmetry protected weak topological phases in a superlattice
• Topological Properties of SnSe/EuS and SnTe/CaTe Interfaces
• Classification and construction of interacting fractonic higher-order topological phases
• Excitonic topology and quantum geometry in organic semiconductors
• Prediction of Topological Crystalline Insulator and Topological Phase Transitions in Two-dimensional PbTe Films
• Interaction-induced crystalline topology of excitons
• Topological crystalline insulators from stacked graphene layers
• Effective field theories of topological crystalline insulators and topological crystals
• Spatially resolved Landau level spectroscopy of the topological Dirac cone of bulk-type Sb2Te3(0001): potential fluctuations and quasiparticle lifetime
• Group theory study of the vibrational modes and magnetic order in the topological antiferromagnet MnBi${}_2$Te${}_4$
• Twisted nodal wires and three-dimensional quantum spin Hall effect in distorted square-net compounds
• Scattering theory of topological invariants in nodal superconductors
• Topological crystalline antiferromagnetic state in tetragonal FeS
• Spin-orbit insulating phase in SnTe cubic nanowires: consequences on the topological surface states
• Magnetic-Field Induced Semimetal in Topological Crystalline Insulator Thin Films
• Anyonic Topological Order in Twisted Equivariant Differential (TED) K-Theory
• Topological d-wave superconductivity in two dimensions
• Topological Nonsymmorphic Ribbons out of Symmorphic Bulk
• Kane-Mele-Hubbard model on the $\pi$-flux honeycomb lattice
• Inducing a many-body topological state of matter through Coulomb-engineered local interactions
• Haldane model on the Sierpiński gasket
• Impact of strong correlations on a band topological insulator on the Lieb lattice
• Multiple topological Dirac cones in a mixed-valent Kondo semimetal: g-SmS
• Fermionic criticality of anisotropic nodal point semimetals away from the upper critical dimension: exact $1/N_f$ exponents
• Robust Dirac lines against Ge vacancy and possible spin-orbit Dirac points in nonsymmorphic HfGe0.92Te
• Absence of nonlocal resistance in microstructures of PbTe quantum wells
• Effect of coordination on topological phases on self-similar structures
• A Systematic Investigation of the Coupling between One-Dimensional Edge States of a Topological Crystalline Insulator
• Topological phonon analysis of the 2D buckled honeycomb lattice: an application to real materials
• Magnetic band representations, Fu-Kane-like symmetry indicators and magnetic topological materials
• Strongly correlated crystalline higher-order topological phases in two-dimensional systems: A coupled-wire study
• Fractional hinge and corner charges in various crystal shapes with cubic symmetry
• Topological Floquet states on a Möbius band irradiated by circularly polarised light
• Topological Edge and Corner States in Biphenylene Network
• Third-order topological insulator induced by disorder
• Topologically Protected Wormholes in Type-III Weyl Semimetal Co${}_3$In${}_2$X${}_2$ (X = S, Se)
• Nonsymmorphic symmetry protected node-line semimetal in the trigonal YH3
• Topological Dipole Conserving Insulators and Multipolar Responses
• Adiabatic continuity, wavefunction overlap and topological phase transitions
• Topological classification of intrinsic 3D superconductors using anomalous surface construction
• A General Method to Design Acoustic Higher-Order Topological Insulators
• Transport Induced Dimer State from Topological Corner States
• Observation of Weyl and Dirac fermions at smooth topological Volkov-Pankratov heterojunctions
• Electronic band structure of epitaxial PbTe (111) thin films observed by angle-resolved photoemission spectroscopy
• Site-Specific Contributions to the Band Inversion in a Topological Crystalline Insulator
• Projected spin texture as a bulk indicator of fragile topology
• Anisotropic non-linear optical response of nodal loop materials
• Interacting topological mirror excitonic insulator in one dimension
• Nickel-Titanium double perovskite: A three-dimensional spin-1 Heisenberg antiferromagnet
• Massive fermions with low mobility in antiferromagnet orthorhombic CuMnAs single crystals
• Granular Graphene: direct observation of zigzag and armchair edge waves
• Intertwined Weyl phases emergent from higher-order topology and unconventional Weyl fermions via crystalline symmetry
• Computing edge states without hard truncation
• Landau level spectroscopy of PbSnSe topological crystalline insulator
• Engineering of Chern insulators and circuits of topological edge states
• Unusual phonon density of states and response to the superconducting transition in the In-doped topological crystalline insulator Pb${}_{0.5}$Sn${}_{0.5}$Te
• Quantum transport evidence of the boundary states and Lifshitz transition in Bi${}_4$Br${}_4$
• Shear Viscosity in a Non-Fermi Liquid Phase of a Quadratic Semimetal
• One-dimensional Dirac electrons on the surface of weak topological insulators
• Quantum Criticalities with Infinite Anisotropy in Topological Phase Transitions between Dirac and Weyl Semi-metals
• Topological Crystalline Bose Insulator in Two Dimensions via Entanglement Spectrum
• Topological $Z_2$ invariant in Kitaev spin liquids: Classification of gapped spin liquids beyond projective symmetry group
• Topologically distinct atomic insulators
• Topological invariants beyond symmetry indicators: Boundary diagnostics for twofold rotationally symmetric superconductors
• Glide Symmetry Protected Higher-Order Topological Insulators from Semimetals with butterfly-like Nodal Lines
• Topological Electromagnetic Effects and Higher Second Chern Numbers in Four-Dimensional Gapped Phases
• Non-adiabatic bulk-surface oscillations in driven topological insulators
• Inherited topological superconductivity in two-dimensional Dirac semimetals
• Linear Response in Topological Materials
• Topology of quantum vacuum
• Topological chiral currents in the Gross-Neveu model extension
• Uniaxial Strain Induced Topological Phase Transition in Bismuth-Tellurohalide-Graphene Heterostructures
• $\pi$-fluxes, semi-metals and flat bands in artificial materials
• Generic phase diagram for Weyl superconductivity in mirror-symmetric superconductors
• Temperature-driven band inversion in Pb${}_{0.77}$Sn${}_{0.23}$Se: Optical and Hall-effect studies
• Network model for higher-order topological phases
• Abundance of second order topology in $C_3$ symmetric two-dimensional insulators
• Homotopic classification of band structures: Stable, fragile, delicate, and stable representation-protected topology
• Computing classification of interacting fermionic symmetry-protected topological phases using topological invariants
• Higher Chern numbers in multilayer ($\mathcal{N}\ge 2$) Lieb lattices: Topological transitions and quadratic band crossing lines
• Observation of anisotropic Dirac cones in the topological material Ti2Te2P
• Topologically Protected Edge States in Triangular Lattices
• Topological skyrmion phases of matter
• Interaction effects in a 1D flat band at a topological crystalline step edge
• Face centered cubic SnSe as a ${\mathbb{Z}}_2$ trivial Dirac nodal line material
• Band gap anomaly and topological properties in lead chalcogenides
• Topological electronic structure and Weyl points in nonsymmorphic hexagonal materials
• Atoms to topological electronic materials: A bedtime story for beginners
• Filling-enforced Dirac loops and their evolutions under various perturbations
• Pseudo field effects in type II Weyl semimetals: new probes for over tilted cones
• Prediction of Ideal Triple Degenerate Points in HfIrAs and HfIrBi
• Breaking crystalline symmetry of epitaxial SnTe films by strain
• Symmetry-protected Spinful Magnetic Weyl Nodal Loops and Multi-Weyl Nodes in $5d^n$ Cubic Double Perovskites $(n=1,2)$
• Ab initio study of nontrivial topological phases in corundum structured $($M${}_2$O${}_3)/($Al${}_2$O${}_3{)}_5$ multilayers
• Revisiting (higher order and crystalline) topology in old models of lead telluride
• Exact projected entangled pair ground states with topological Euler invariant
• Driving Topological Phases by Spatially Inhomogeneous Pairing Centers
• Topological obstructed atomic limit by annihilating Dirac fermions
• A semiclassical treatment of spinor topological effects in driven, inhomogeneous insulators under external electromagnetic fields
• A density-wave-like transition in the polycrystalline V3Sb2 sample with bilayer kagome lattice
• Discovery of Ĉ${}_2$ rotation anomaly in topological crystalline insulator SrPb
• Mass Acquisition of Dirac Fermions in Bi4I4 by Spontaneous Symmetry Breaking
• Boundary conditions and anomalies of conformal field theories in 1+1 dimensions
• Wannier band transitions in disordered $\pi$-flux ladders
• Direct observation of a photoinduced topological phase transition in Bi-doped (Pb,Sn)Se
• Electron-phonon coupling and superconductivity in the doped topological-crystalline insulator (Pb${}_{0.5}$Sn${}_{0.5}$)${}_{1-x}$In${}_x$Te
• Protected Gapless Edge States In Trivial Topology
• Quantum transport and mobility spectrum of topological carriers in (001) SnTe/PbTe heterojunctions
• Mechanisms for Magnetic Skyrmion Catalysis and Topological Superconductivity
• Hybridization of topological surface states with a flat band
• $n$-Hourglass Weyl fermions in nonsymmorphic materials
• Twisted crystallograpic T-duality via the Baum--Connes isomorphism
• Magnetic wallpaper Dirac fermions and topological magnetic Dirac insulators
• Topological end states due to inhomogeneous strains in wrinkled semiconducting ribbons
• Experimental observation of edge-dependent quantum pseudospin Hall effect
• Anderson Critical Metal Phase in Trivial States Protected by Average Magnetic Crystalline Symmetry
• Delocalization of edge states in topological phases
• Non-Hermitian skin effect enforced by nonsymmorphic symmetries
• Edge states and topological properties of electrons on the bismuth on silicon surface with giant spin-orbit coupling
• Edge states for topological insulators in two dimensions and their Luttinger-like liquids
• Andreev reflection in Euler materials
• Interaction between interface and massive states in multivalley topological heterostructures
• Spin-polarization of topological crystalline and normal insulator Pb${}_{1-x}$Sn${}_x$Se (111) epilayers probed by photoelectron spectroscopy
• Electromagnetic Response of Three-dimensional Topological Crystalline Insulators
• Higher-order topological insulators in a crisscross antiferromagnetic model
• Edge states in a non-Hermitian topological crystalline insulator
• Conformal QED in two-dimensional topological insulators
• Quantum-confined Stark effect in band-inverted junctions
• Gapping fragile topological bands by interactions
• Higher-order topology protected by latent crystalline symmetries
• Structure of the Entanglement Entropy of (3+1)D Gapped Phases of Matter
• Miniband engineering and topological phase transitions in topological - normal insulator superlattices
• Geometric control of topological dynamics in a singing saw
• Higher-order topological corner states induced solely by onsite potentials with mirror symmetry
• Bulk Pumping in 2D Topological Phases
• Cubic Dirac and quadruple Weyl points in screw-symmetric materials
• Holstein polaron in a pseudospin-$1$ quantum spin Hall system: first and second order topological phase transitions
• Structural Phase Transition and Carrier Density Tuning in SnSexTe1-x Nanoplates for Topological Crystalline Insulators
• Graphene with Rashba spin-orbit interaction and coupling to a magnetic layer: Electron states localized at the domain wall
• Thermodynamics of a Higher-Order Topological Insulator
• 4D beyond-cohomology topological phase protected by $C_2$ symmetry and its boundary theories
• Nodal lines and mapping to mirror Chern numbers in Ca${}_2$As family
• Gate-tunable imbalanced Kane-Mele model in encapsulated bilayer jacutingaite
• Pseudo-time-reversal-symmetry-protected topological Bogoliubov excitations of Bose-Einstein condensates in optical lattices
• Simulating Higher-Order Topological Insulators in Density Wave Insulators
• Diagnosis of topological nodal lines with nontrivial monopole charge in the presence of rotation symmetries
• Topological Classical Systems with Generalized Chiral Symmetry
• Topological gapless points in superconductors: From the viewpoint of symmetry
• Topological phonons in arrays of ultracold dipolar particles
• Anomalous Crystal Shapes of Topological Crystalline Insulators
• Defect bulk-boundary correspondence of topological skyrmion phases of matter
• Suppression of the Spectral Weight of Topological Surface States on the Nanoscale via Local Symmetry Breaking
• Symmetry-Resolved Entanglement of $C_2$-symmetric Topological Insulators
• Extracting unconventional spin texture in two dimensional topological crystalline insulator bismuthene via tuning bulk-edge interactions
• A mono-atomic orbital-based 1D topological crystalline insulator
• Atomic-ordering-induced quantum phase transition between topological crystalline insulator and Z2 topological insulator
• Fractal Surface States in Three-Dimensional Topological Quasicrystals
• Topological Insulators with Hybrid-order Boundary States
• The tenfold way redux: Fermionic systems with $N$-body interactions
• Hidden-symmetry-protected quantum pseudo-spin Hall effect in optical lattices
• Topological crystalline protection in a photonic system
• Existence of dual topological phases in Sn-based ternary chalcogenides
• Surface-dependent Majorana vortex phases in topological crystalline insulators
• Spin-Selective Second-Order Topological Insulators Enabling Cornertronics in 2D Altermagnets
• Experimental observation and spin texture of Dirac node arcs in tetradymite topological metals
• Theory of Anomalous Floquet Higher-Order Topology: Classification, Characterization, and Bulk-Boundary Correspondence
• Topological Modes Protected by Chiral and Two-Fold Rotational Symmetry in a Spring-Mass Model with a Lieb Lattice Structure
• Topological spinon bands and vison excitations in spin-orbit coupled quantum spin liquids
• Hidden-symmetry-protected Z_2 topological insulator in a cubic lattice
• Graphene-like conjugated pi-bond system in Pb1-xSnxSe
• Investigating the effect of temperature dependent many-body interactions on bulk electronic structures and the robust nature of (001) surface states of SnTe
• Tip-induced Superconductivity
• Nernst-Ettingshausen effect at the trivial-nontrivial band ordering in topological crystalline insulator Pb1-xSnxSe
• XFe4Ge2 (X = Y, Lu) and Mn3Pt: Filling-enforced magnetic topological metals
• Scattering theory of delicate topological insulators
• Unveiling a crystalline topological insulator in a Weyl semimetal with time-reversal symmetry
• Turning Copper Metal into Weyl Semimetal
• Nontrivial gapless electronic states at the stacking faults of weak topological insulators
• Growth and characterization of high-quality single-crystalline SnTe retaining cubic symmetry down to the lowest temperature studied
• Distinct Floquet topological classifications from color-decorated frequency lattices with space-time symmetries
• Direct probe of ferromagnetic proximity effect at the interface in Fe/SnTe heterostructure by polarized neutron reflectometry
• Topological Critical Materials of Ternary Compounds
• Catalyst-free MBE growth of PbSnTe nanowires with tunable aspect ratio
• IrF4: From Tetrahedral Compass Model to Topological Semimetal
• Topological superconductivity from transverse optical phonons in oxide heterostructures
• STM observation of the hinge-states of bismuth nanocrystals
• Discovery of topological metamaterials by symmetry relaxation and smooth topological indicators
• Specific Heat and Electrical Transport Properties of Sn0.8Ag0.2Te Superconductor
• Systematic analysis for triple points in all magnetic symmorphic systems and symmetry-allowed coexistence of Dirac points and triple points
• Pentagonal nanowires from topological crystalline insulators: a platform for intrinsic core-shell nanowires and higher-order topology
• Magnetic impurities along the edge of a quantum spin Hall insulator: Realizing a one-dimensional AIII insulator
• Topological Field Theories of Three-Dimensional Rotation Symmetric Insulators: Coupling Curvature and Electromagnetism
• Topology in quasicrystals
• Effects of first- and second-order topological phases on equilibrium crystal shapes
• Dual topological insulator with mirror symmetry protected helical edge states
• Topological properties of magnetically ordered heavy-fermion systems in the presence of mirror symmetry
• Kitaev Building-block Construction for Inversion-Protected Higher-order Topological Superconductors
• Observation of nonlinear higher-order topological insulators with unconventional boundary truncations
• Interacting topological phases in thin films of topological mirror Kondo insulators
• Strong and Weak Three-Dimensional Topological Insulators Probed by Surface Science Methods
• Higher-order topological superconductor phases in a multilayer system
• Second Euler number in four dimensional synthetic matter
• Design of spin-orbital-textures in ferromagnetic/topological insulator interfaces
• Entanglement Chern Number of the Kane-Mele Model with Ferromagnetism
• Spin Stiffness and Domain Walls in Dirac-Electron Mediated Magnets
• Topological electronic structure of twin boundaries and twinning superlattices in the SnTe material class
• Topological transition in Pb1-xSnxSe using Meta-GGA
• Low-energy phonons and superconductivity in Sn${}_{0.8}$In${}_{0.2}$Te
• Manipulating quantum channels in weak topological insulator nanoarchitectures
• Additive rule of real and reciprocal space topologies at disclinations
• The Anomalous Hall Effect in Magnetic Topological Insulators
• Nodal phases in non-Hermitian wallpaper crystals
• Non-Hermitian $C_{NH}=2$ Chern insulator protected by generalized rotational symmetry
• Synthesizing Weyl semimetals in weak topological insulator and topological crystalline insulator multilayers
• Theory of Weyl orbital semimetals and predictions of several materials classes
• Three-dimensional symmetry breaking topological matters
• Topological reflection matrix
• Mixed higher-order topology and nodal and nodeless flat band topological phases in a superconducting multiorbital model
• Coexisting Euler and Stiefel-Whitney Topological Phases in Elastic Metamaterials
• A coupled wire description of surface $ADE$ topological orders
• Topological phase diagram of Pb1-xSnxSe1-yTey
• Quantized thermal and spin transports of dirty planar topological superconductors
• Topological phases of amorphous matter
• Tuning topological surface states by cleavage angle in topological crystalline insulators
• Topological surface states in the Kondo insulator YbB${}_{12}$ revealed via planar tunneling spectroscopy
• Model non-Hermitian topological operators without skin effect: A general principle of construction
• Electric polarization and discrete shift from boundary and corner charge in crystalline Chern insulators
• Anomalous in-gap edge states in two-dimensional pseudospin-1 Dirac insulators
• Discriminant indicator with generalized rotational symmetry
• Strain-induced two-dimensional topological crystalline insulator
• Unveiling Symmetry Instability induced by Topological Phase Transitions
• Probing chiral symmetry with a topological domain wall sensor
• Higher-order topology in honeycomb lattice with Y-Kekulé distortions
• Exciton Berryology
• Temperature driven spin-zero effect in TaAs${}_2$
• Stability against contact interactions of a topological superconductor in two-dimensional space protected by time-reversal and reflection symmetries
• Evidence of phase stability, topological phonon and temperature-induced topological phase transition in rocksalt SnS and SnSe
• Topological Descendants of Multicritical EuTl2
• Two-atom-thin topological crystalline insulators lacking out of plane inversion symmetry
• Topological insulators on fractal lattices: A general principle of construction
• Diagnosing the magnetic field-tuned symmetry nature of the topological electrons by conductance fluctuations in bulk-insulating BiSbTeSe2 devices
• Second-order topological insulator in Bilayer borophene
• Quantized electrical, thermal, and spin transports of non-Hermitian clean and dirty two-dimensional topological insulators and superconductors
• Polarization textures in crystal supercells with topological bands
• Magneto-Induced Topological Phase Transition in Inverted InAs/GaSb Bilayers
• Sub-symmetry Protected Topology in Topological Insulators and Superconductors
• General corner charge formulas in various tetrahedral and cubic space groups
• Quantum geometric bounds in spinful systems with trivial band topology
• Enhancing the Hyperpolarizability of Crystals with Quantum Geometry
• Weak localization and Berry flux in topological crystalline insulators with a quadratic surface spectrum
• Coexisting surface states in the weak and crystalline topological insulator Bi_2TeI
• Topological Signatures in Nodal Semimetals through Neutron Scattering
• Observation of trapped fractional charge and topological states at disclination defects in higher-order topological insulators
• Generating Weyl semimetals from alkali metals
• Non-Hermitian ${\mathbb{Z}}_4$ skin effect protected by glide symmetry
• Takagi Topological Insulator on the Honeycomb Lattice
• Non-trivial topological valence bands of common diamond and zinc-blende semiconductors
• Signatures of non-trivial band topology in LaAs/LaBi heterostructure
• Symmetry-Protected Solitons and Bulk-Boundary Correspondence in Generalized Jackiw-Rebbi Models
• Topological Phase Diagram of BiTeX--Graphene Hybrid Structures
• Large surface conductance and two-dimensional superconductivity in microstructured crystalline topological insulators
• Representation-protected topology of spin-singlet $s$-wave superconductors
• Effective field theories for interacting boundaries of 3D topological crystalline insulators through bosonisation
• Boundary states in the chiral symmetric systems with a spatial symmetry
• Kondo-induced hybrid topological insulator in two-dimensional electron system with a quadratic band crossing point
• Edge States with Hidden Topology in Spinner Lattices
• Dynamic melting and condensation of topological dislocation modes
• Topological Crystalline Metal in Orthorhombic Perovskite Iridates
• Role of Hund's splitting in electronic phase competition in ${\mathrm{Pb}}_{1-x}{\mathrm{Sn}}_x\mathrm{Te}$
• Theory of fractional corner charges in cylindrical crystal shapes
• Topological nonsymmorphic insulator versus Dirac semimetal in KZnBi
• Intrinsic (Axion) Statistical Topological Insulator
• Hedgehog spin texture and competing orders associated with strains on the surface of a topological crystalline insulator
• Superconductivity in tin telluride films grown by molecular beam epitaxy
• Dirac edge states as signature of two-dimensional altermagnetic topological crystalline phase
• Selective branching, quenching, and converting of topological modes
• Concurrence of topological electrons and magnons in the Kagome ferromagnet CoCu3(OH)6Cl2
• Saddle point singularity and topological phase diagram in a tunable topological crystalline insulator (TCI)
• IrRep: symmetry eigenvalues and irreducible representations of ab initio band structures
• Dynamical detection of mean-field topological phases in an interacting Chern insulator
• Mapping rules from nodal line semimetal to topological crystalline insulator in face centered cubic lattice
• General response theory of topologically stable Fermi points and its implications for disordered cases
• Projective Spacetime Symmetry of Spacetime Crystals
• Electronic structure in a transition metal dipnictide TaAs2
• Homotopy invariant in time-reversal and twofold rotation symmetric systems
• Phase Diagram of a Non-Hermitian Chern Insulator: Destabilization of Chiral Edge States and Bulk-Boundary Correspondence
• Hybrid symmetry class topological insulators
• From Frustrated to Unfrustrated: Coupling two triangular-lattice itinerant Quantum Magnets
• Topological Spectral Bands with Frieze Groups
• Topology reconstruction for asymmetric systems by isomorphic mapping or perturbation approximation
• High-chirality and multiquaternion Weyl nodes in hexagonal ReO${}_3$
• Topological bosonic Bogoliubov excitations with sublattice symmetry
• Spin-Hall conductivity and optical characteristics of noncentrosymmetric quantum spin Hall insulators: the case of PbBiI
• Anomalous Behaviour in the Magneto-Optics of a Gapped Topological Insulator
• Artificial oxide heterostructures with non-trivial topology
• Global and Local Topological Crystalline Markers for Rotation-Symmetric Insulators
• Fermiology and transport properties of the proposed topological crystalline insulator SrAg4Sb2
• Superconductivity, valence-skipping and topological crystalline metal in AgSnSe${}_2$
• Realizing tunable Fermi level in SnTe by defect control
• Correlated electrons in a Crystalline Topological insulator
• Anomalous multi-gap topological phases in periodically driven quantum rotors
• Interplay between edge states and charge density wave order in the Falicov-Kimball model on a Haldane ribbon
• Topological Aspects of Antiferromagnets
• The Symmetry Principle in Condensed Matter Physics (I)
• Non-equilibrium States and Interactions in the Topological Insulator and Topological Crystalline Insulator Phases of NaCd4As3
• Tunable breakdown of the polaron picture for mobile impurities in a topological semimetal
• Perfectly localized Majorana corner modes in fermionic lattices
• Universal Role of Combined Symmetry for the Protection of the Dirac Cone in Antiferromagnetic Topological Insulators
• Role of effective mass anisotropy in realizing a hybrid nodal-line fermion state
• Exploring temperature dependent electron-electron interaction of topological crystalline insulators (SnS and SnSe) within Matsubara-time domain
• Topological Disclination Pump
• Adiabatic pumping and transport in the Sierpinski-Hofstadter model
• Engineering Dirac electrons emergent on the surface of a topological insulator
• Tunable Flux Vortices in 2D Dirac Superconductors
• Field manipulation of Weyl modes in an ideal Dirac semimetal
• Renormalization group study of systems with quadratic band touching
• Interaction-driven phase transition in one dimensional mirror-symmetry protected topological insulator
• Phase Transition and Field Effect Topological Quantum Transistor made of monolayer MoS2
• Modulating Hamiltonian Approach to Quantum Many-Body Systems and Crystalline Topological Phases Protected by Generalized Magnetic Translations
• Interacting Crystalline Topological Insulators in two-dimensions with Time-Reversal Symmetry
• Stability of the X-Y-phase of the two-dimensional C4 point group insulator
• Competing effects of Hund's splitting and symmetry-breaking perturbations on electronic order in Pb${}_{1-x}$Sn${}_x$Te
• Hybrid Higher-Order Skin Topological Modes in the Two-Dimensional Su-Schrieffer-Heeger Model with Nonreciprocal Hoppings
• Dirac topological insulator in the d${}_{z^2}$ manifold of a honeycomb oxide
• Disorder-induced delocalization and reentrance in a Chern-Hopf insulator
• Hidden topology in flat-band topological insulators: Strong, weak and square-root topological states
• Engineering Majorana Kramers Pairs In Synthetic High Spin Chern Insulators
• Quantum Criticality of Type-I and Critically Tilted Dirac Semimetals
• Higher order topology in a Creutz ladder
• Topological Fermi-arc-like surface states in Kramers nodal line metals
• Coexistence of Rashba and Dirac dispersions on the surface of centrosymmetric topological insulator decorated with transition metals
• Tunable Competing Electronic Orders in Double Quantum Spin Hall Superlattices
• Local expression of fractional corner charges in obstructed atomic insulators and relationship with the fractional disclination charges
• Manipulation of photonic topological edge and corner states via trivial claddings
• Microscopic origin of scalar potential induced topological transition in massive Dirac fermions and scalar Hall effect
• Anomalous gapped boundaries between surface topological orders in higher-order topological insulators and superconductors with inversion symmetry
• Hidden wallpaper fermion and third-order topological insulator
• Tensor network representations of fermionic crystalline topological phases on two-dimensional lattices
• Emergence of a new symmetry class for Bogoliubov-de Gennes (BdG) Hamiltonians: Expanding ten-fold symmetry classes
• Berry curvature generation detected by Nernst responses in ferroelectric Weyl semimetal
• Fragile topological insulators protected by rotation symmetry without spin-orbit coupling
• Generating electromagnetic modes with fine tunable orbital angular momentum by planar topological circuits
• Floquet Gauge Pumps as Sensors for Spectral Degeneracies Protected by Symmetry or Topology
• Topological photocurrent responses from chiral surface Fermi arcs
• Protected Fermionic Zero Modes in Periodic Gauge Fields
• Isotropic 3D topological phases with broken time reversal symmetry
• Possible Topological Superconductivity in a Topological Crystalline Insulator (Pb${}_{1-x}$Sn${}_x$)${}_{1-y}$In${}_y$Te
• Crystalline finite-size topology
• Exact sequence between real and complex bivariant K theories and application to the Z2 pairing
• Pressure-induced superconductivity and topological phase transitions in the topological nodal-line semimetal SrAs3
• Three-nodal surface phonons in solid-state materials: Theory and material realization
• Theory of Superconductivity Mediated by Topological Phonons
• Topological Surface States and Superconductivity in [Tl${}_4$](Tl${}_{1-x}$Sn${}_x$)Te${}_3$ Perovskites
• Analytical solutions of topological surface states in a series of lattice models
• Signature of topological crystalline insulating behavior in new B2X2Zn (X=Ir, Rh, Co) compound from first-principles Computation
• Lithium Niobate Photonic Topological Insulator-based Multi-Wavelength Optical Demultiplexer with Piezoelectric Switch-Off
• Towards a Topological Quantum Chemistry description of correlated systems: the case of the Hubbard diamond chain
• Magnetically tunable Dirac and Weyl fermions in the Zintl materials family
• New mechanisms to engineer magnetic skyrmions and topological superconductors
• Magnetic-Field Tunable Möbius and Higher-Order Topological Insulators in Three-Dimensional Layered Octagonal Quasicrystals
• Topological Charges, Fermi Arcs, and Surface States of $K_4$ Crystal
• Synthetic gauge field and pseudospin-orbit interaction in a stacked two-dimensional ring-network lattice
• Non-Trivial Topological Phase in the Sn_{1-x}In_xTe Superconductor
• Topological property of graphene with triangular array of nanoholes
• Periodic Behavior of Topology in Graphene with Nanohole Array
• Hinge modes of three-dimensional Euler insulators
• Bulk-boundary correspondence in topological two-dimensional non-Hermitian systems: Toeplitz operators and singular values
• Physical Pictures for Quasisymmetry in Crystals
• Orbital magnetization reveals multiband topology
• Proposal for realizing and probing topological crystalline insulators in optical lattices
• Tunable SSH model in ferromagnetic systems
• Wilson loop invariants and bulk-boundary correspondence in higher-order topological insulators with two anticommuting mirror symmetries
• One-dimensional topology and topolectrics of nonsymmorphic Kramers degenerate systems
• Topological energy pumping in a quasi-periodically driven four-level system
• Classification of topological insulators and superconductors with multiple order-two point group symmetries
• Gapped spinful phases obtained via Gutzwiller projections of Euler states
• Projected branes as platforms for crystalline, superconducting, and higher-order topological phases
• Three-dimensional spinless Euler insulators with rotational symmetry
• Topological properties of domain walls in antiferromagnetic topological insulators
• Revealing Spin and Spatial Symmetry Decoupling: New Insights into Magnetic Systems with Dzyaloshinskii-Moriya Interaction
• Crystalline topological states at a topological insulator junction
• Magnetically tuned topological phase in graphene nanoribbon heterojunctions
• Exploiting $\vartheta -$functions for the identification of topological materials
• Band Topology or Geometry?
• Systematic study for two-dimensional $Z_2$ topological phase transitions at high-symmetry points in all layer groups
• Spectral analysis of the magneto-optical response in valley polarized Pb${}_{1-x}$Sn${}_x$Se
• Reflection-Symmetry Protected Antiferromagnetic Topological Insulator in Three-Dimensional Heavy-Fermion Systems
• A study of topological characterization and symmetries for a quantum simulated Kitaev chain
• Higher-order topological quantum paramagnets
• Quantum matter in ultrahigh magnetic fields
• Squeezing Quantum States in Three-Dimensional Twisted Crystals
• Proximity-Induced Superconductivity in a Topological Crystalline Insulator
• Emergence of Type-I and Type-II Dirac line nodes in penta-octa-graphene
• Dynamical Symmetry Indicators for Floquet Crystals
• Robust zero-energy states in two-dimensional Su-Schrieffer-Heeger topological insulators