Topological quantum chemistry

Abstract

The past decade's apparent success in predicting and experimentally discovering distinct classes of topological insulators (TIs) and semimetals masks a fundamental shortcoming: out of 200,000 stoichiometric compounds extant in material databases, only several hundred of them are topologically nontrivial. Are TIs that esoteric, or does this reflect a fundamental problem with the current piecemeal approach to finding them? To address this, we propose a new and complete electronic band theory that highlights the link between topology and local chemical bonding, and combines this with the conventional band theory of electrons. Topological Quantum Chemistry is a description of the universal global properties of all possible band structures and materials, comprised of a graph theoretical description of momentum space and a dual group theoretical description in real space. We classify the possible band structures for all 230 crystal symmetry groups that arise from local atomic orbitals, and show which are topologically nontrivial. We show how our topological band theory sheds new light on known TIs, and demonstrate the power of our method to predict a plethora of new TIs.

v1: 8 pages + 40 pages supplemenetary material. Previously submitted v2: ~ Published version. 11 pages + 79 pages supplementary material. Descriptions of the data used in this paper can be found in arXiv:1706.08529 and arXiv:1706.09272. All data can be accessed via the Bilbao Crystallographic Server (http://cryst.ehu.es). Two additional papers elaborating on the general theory currently in prep

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• From triple-point materials to multiband nodal links
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• Topological magnons driven by the Dzyaloshinskii-Moriya interaction in the centrosymmetric ferromagnet Mn${}_5$Ge${}_3$
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• Topology invisible to eigenvalues in obstructed atomic insulators
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• Electronic properties, correlated topology and Green's function zeros
• Topological invariants based on generalized position operators and application to the interacting Rice-Mele model
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• Non-Abelian Hopf-Euler insulators
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• The hybrid-order topology of weak topological insulators
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• Double-bowl State in photonic Dirac nodal line semimetal
• Fragile phonon topology on the honeycomb lattice with time-reversal symmetry
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• Symmetry-protected Nodal Points and Nodal Lines in Magnetic Materials
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• Elementary band representations for the single-particle Green's function of interacting topological insulators
• A diagnosis scheme for topological degeneracies at high-symmetry momenta
• Many-Body Invariants for Chern and Chiral Hinge Insulators
• Absence of topological protection of the interface states in ${\mathbb{Z}}_2$ photonic crystals
• Second-order and real Chern topological insulator in twisted bilayer $\alpha$-graphyne
• Glide-symmetric magnetic topological crystalline insulators with inversion symmetry
• Obstructed insulators and flat bands in topological phase-change materials
• Non-Compact Atomic Insulators
• "Quantum Geometric Nesting" and Solvable Model Flat-Band Systems
• Lecture Notes on Berry Phases and Topology
• Geometry and Topology Tango in Ordered and Amorphous Chiral Matter
• Symmetry constraints and spectral crossing in a Mott insulator with Green's function zeros
• Wannier Function Methods for Topological Modes in 1D Photonic Crystals
• Topological edge and corner states and fractional corner charges in blue phosphorene
• Interacting Topological Quantum Chemistry in 2D: Many-body Real Space Invariants
• Projected Topological Branes
• Theory of polarization textures in crystal supercells
• Nodal higher-order topological superconductivity from a ${\mathcal{C}}_4$-symmetric Dirac semimetal
• Tutorial: Classifying Photonic Topology Using the Spectral Localizer and Numerical $K$-Theory
• Spectral and optical properties of Ag${}_3$Au(Se${}_2$,Te${}_2$) and dark matter detection
• Instantaneous response and quantum geometry of insulators
• Dirac cones in Two-dimensional Borane
• Interacting second-order topological insulators in one-dimensional fermions with correlated hopping
• Identifying Higher Order Topology and Fractional Corner Charge Using Entanglement Spectra
• From Dirac semimetals to topological phases in three dimensions: a coupled wire construction
• Universal higher-order bulk-boundary correspondence of triple nodal points
• Multiorbital edge and corner states in black phosphorene
• Advances in Complex Oxide Quantum Materials Through New Approaches to Molecular Beam Epitaxy
• Topological insulators in the NaCaBi family with large SOC gaps
• Topological Superconductivity from Unconventional Band Degeneracy with Conventional Pairing
• Universal Relation among Many-Body Chern Number, Rotation Symmetry, and Filling
• Identifying, and constructing, complex magnon band topology
• Influence of point defects on the electronic and topological properties of monolayer WTe${}_2$
• Impurity bound states as detectors of topological band structures revisited
• Landau quantization of nearly degenerate bands, and full symmetry classification of avoided Landau-level crossings
• Dynamical conductivity in multiply-degenerate point-nodal semimetal CoSi
• Hierarchy of quasi-symmetries and degeneracies in chiral crystal materials CoSi
• MSGCorep: A package for corepresentations of magnetic space groups
• Large shift current, $\pi$ Zak phase and unconventional nature in Se and Te
• The interplay between structural, magnetic and electronic states in the pyrochlore iridate Eu2Ir2O7
• Topological Aspect of Graphene Patchwork with Regular Arrays of Nano Holes
• Discovering two-dimensional magnetic topological insulators by machine learning
• Topological Signatures in Quantum Transport in Anomalous Floquet-Anderson Insulators
• Benchmarking van der Waals-treated DFT: The case of hexagonal boron nitride and graphene on Ir(111)
• Multiplicative topological phases
• Structural disorder-driven topological phase transition in noncentrosymmetric BiTeI
• Anisotropic phonon-mediated electronic transport in chiral Weyl semimetals
• Response to polarization and weak topology in Chern insulators
• Second-Order Topological Insulator in Two-Dimensional C2N and Its Derivatives
• Microscopic probe of magnetic polarons in antiferromagnetic Eu${}_5$In${}_2$Sb${}_6$
• Two-dimensional weak-type topological insulators in inversion symmetric crystals
• Colossal negative magnetoresistance in the complex charge density wave regime of an antiferromagnetic Dirac semimetal
• Geometric superfluid weight of composite bands in multiorbital superconductors
• Intrinsically Interacting Higher-Order Topological Superconductors
• Symmetry-protected metallic and topological phases in penta-materials
• Variants of the symmetry-based indicator
• Unconventional spin textures emerging from a universal symmetry theory of spin-momentum locking
• Three-dimensional $\mathcal{P}\mathcal{T}$-symmetric topological phases with Pontryagin index
• Interferometry of non-Abelian band singularities and Euler class topology
• Correlated Fragile Topology: a Parton Approach
• Complete crystalline topological invariants from partial rotations in (2+1)D invertible fermionic states and Hofstadter's butterfly
• Superconducting properties of the non-centrosymmetric Superconductors TaXSi (X= Re, Ru)
• Unsupervised learning of topological phase diagram using topological data analysis
• FeGe as a building block for the kagome 1:1, 1:6:6, and 1:3:5 families: hidden d-orbital decoupling of flat band sectors, effective models and interaction Hamiltonians
• Topological surface states in thick partially relaxed HgTe film
• Dynamics of self-dual kagome metamaterials and the emergence of fragile topology
• Diversity of Radial Spin Textures in Chiral Materials
• From Atomic Semimetal to Topological Nontrivial Insulator
• Magnetic molecular orbitals in MnSi
• Direct measurement of a beta function and an indirect check of the Schwinger effect near the boundary in Dirac-Weyl semimetals
• Large spin Hall conductivity and excellent hydrogen evolution reaction activity in unconventional PtTe1.75 monolayer
• Magnetic moiré surface states and flat chern band in topological insulators
• Fragility of surface states in non-Wigner Dyson topological insulators
• Superconductivity in unconventional metals
• Disorder-induced topological quantum phase transitions in multi-gap Euler semimetals
• Abundant surface-semimetal phases in three-dimensional obstructed atomic insulators
• Real Hopf Insulator
• Weyl Semimetals with $S_4$ symmetry
• Efficient Design of Helical Higher-Order Topological Insulators in 3D Elastic Medium
• Characterization and classification of interacting (2+1)D topological crystalline insulators with orientation-preserving wallpaper groups
• Anomalous Floquet topological crystalline insulators
• Large-Gap Quantum Anomalous Hall Insulators in $A$Ti$X$ Class
• Kondo effect and its destruction in hetero-bilayer transition metal dichalcogenides
• Topological Quasi-2D Semimetal Co${}_3$Sn${}_2$S${}_2$: Insights To Electronic Structure From NEXAFS and Resonant Photoelectron Spectroscopy
• Finite-Frequency Topological Maxwell Modes in Mechanical Self-Dual Kagome Lattices
• Optical $N$-insulators: topological obstructions in the atomistic susceptibility tensor
• Mirror real Chern insulator in two and three dimensions
• Embedded Topological Semimetals
• Topological phases of the dimerized Hofstadter butterfly
• Monopole Charge Density Wave States in Weyl Semimetals
• Majorana multipole response: General theory and application to wallpaper groups
• Kagome metals
• Spin-momentum locking from topological quantum chemistry: applications to multifold fermions
• Single-point spin Chern number in a supercell framework
• Interaction-induced crystalline topology of excitons
• Multiple Dirac Nodes and Symmetry Protected Dirac Nodal Line in Orthorhombic $\alpha$-RhSi
• Topology of SmB${}_6$ determined by dynamical mean field theory
• Symmetry indicators in commensurate magnetic flux
• Highly Tunable Band Inversion in AB2X4 (A=Ge, Sn, Pb; B=As, Sb, Bi; X=Se, Te) Compounds
• Origin of Charge Density Wave in Topological Semimetals SrAl4 and EuAl4
• Excitonic topology and quantum geometry in organic semiconductors
• Altermagnetic Instabilities from Quantum Geometry
• Effective field theories of topological crystalline insulators and topological crystals
• Twisted nodal wires and three-dimensional quantum spin Hall effect in distorted square-net compounds
• Chemical-Strain Induced Tilted Dirac Nodes in (BEDT-TTF)${}_2$X${}_3$ (X = I, Cl, Br, F) Based Charge-Transfer Salts
• Twistronics of Kekulé Graphene: Honeycomb and Kagome Flat Bands
• Glide-symmetric topological crystalline insulator phase in a nonprimitive lattice
• Colossal anomalous Hall and Nernst effect from the breaking of nodal-line symmetry in Cu2CoSn Weyl semimetal: A first-principles study
• ${\mathbb{Z}}_2$-Nontrivial Moiré Minibands and Interaction-Driven Quantum Anomalous Hall Insulators in Topological Insulator Based Moiré Heterostructures
• Topology in time-reversal symmetric crystals
• Fractional hinge and corner charges in various crystal shapes with cubic symmetry
• Rational boundary charge in one-dimensional systems with interaction and disorder
• Line-graph-lattice crystal structures of stoichiometric materials
• Pyramids and cootie catchers: new massless fermions in 2D materials
• A New Moiré Platform Based on M-Point Twisting
• Existence and computation of generalized Wannier functions for non-periodic systems in two dimensions and higher
• Magnetic band representations, Fu-Kane-like symmetry indicators and magnetic topological materials
• Universality of moiré physics in collapsed chiral carbon nanotubes
• Topological phonon analysis of the 2D buckled honeycomb lattice: an application to real materials
• Interlayer Coupling Induced Topological Phase Transition to Higher Order
• Orbital shift-induced boundary obstructed topological materials with a large energy gap
• Large anomalous Hall, Nernst effect and topological phases in the 3d-4d/5d based oxide double perovskites
• Effective action approach to the filling anomaly in crystalline topological matter
• Topological Dipole Conserving Insulators and Multipolar Responses
• Multipole groups and fracton phenomena on arbitrary crystalline lattices
• Wave packet dynamics and edge transport in anomalous Floquet topological phases
• Hund nodal line semimetals: The case of twisted magnetic phase in the double-exchange model
• Topological Edge and Corner States in Biphenylene Network
• High-pressure lithium as an elemental topological semimetal
• Quantum-Hall physics and three dimensions
• Topologically distinct atomic insulators
• Corner Charge Fluctuation as an Observable for Quantum Geometry and Entanglement in Two-dimensional Insulators
• Higher angular momentum band inversions in two dimensions
• Zeros of Green Functions in Topological Insulators
• Topological bands in two-dimensional orbital-active bipartite lattices
• Topological insulators and higher-order topological insulators from gauge-invariant 1D lines
• Efficient prediction of superlattice and anomalous miniband topology from quantum geometry
• Prediction of topological phases in metastable ferromagnetic MPX${}_3$ monolayers
• Functional control of network dynamics using designed Laplacian spectra
• Projected spin texture as a bulk indicator of fragile topology
• Coalescence of multiple topological orders in quasi-one-dimensional bismuth halide chains
• Real-space Obstruction in Quantum Spin Hall Insulators
• Enhanced quantum metric due to vacancies in graphene
• The effect of interorbital scattering on superconductivity in doped Dirac materials
• Linear Response in Topological Materials
• Quasi-2D magnetism and origin of the Dirac semimetallic behavior in nonstoichiometric Sr${}_{1-y}$Mn${}_{1-z}$Sb${}_2$ (y, z~$<$0.1)
• Glide Symmetry Protected Higher-Order Topological Insulators from Semimetals with butterfly-like Nodal Lines
• Intrinsic triple degeneracy point bounded by nodal surfaces in chiral photonic crystal
• Magnetic hourglass fermions: from exhaustive symmetry conditions to high-throughput materials predictions
• Good Wannier bases in Hilbert modules associated to topological insulators
• Dynamical polarization, optical conductivity and plasmon mode of a linear triple component fermionic system
• Topological invariants beyond symmetry indicators: Boundary diagnostics for twofold rotationally symmetric superconductors
• Kramers nodal lines in intercalated TaS${}_2$ superconductors
• Flat bands with fragile topology through superlattice engineering on single-layer graphene
• Homotopic classification of band structures: Stable, fragile, delicate, and stable representation-protected topology
• Localization of generalized Wannier bases implies Chern triviality in non-periodic insulators
• Revealing intrinsic superconductivity of the Nb/BiSbTe${}_2$Se interface
• $\pi$-fluxes, semi-metals and flat bands in artificial materials
• Sparse Sampling for Fast Quasiparticle Interference Mapping
• Revisiting (higher order and crystalline) topology in old models of lead telluride
• Novel Family of Topological Semimetals with Butterfly-like Nodal Lines
• Magnetic field filtering of the hinge supercurrent in unconventional metal NiTe${}_2$-based Josephson junctions
• Dynamical Fragile Topology in Floquet Crystals
• Quasiparticle excitations in a one-dimensional interacting topological insulator: Application for dopant-based quantum simulation
• Selection rules for quasiparticle interference with internal nonsymmorphic symmetries
• Planar Hall Plateau in Magnetic Weyl Semimetals
• From local spin nematicity to altermagnets: Footprints of band topology
• Filling-enforced Dirac loops and their evolutions under various perturbations
• Symmetric Wannier states and tight-binding model for quantum spin Hall bands in AB-stacked MoTe${}_2$/WSe${}_2$
• Ring-Exchange Interaction Effects on Magnons in Dirac Magnet CoTiO${}_3$
• Topological electronic structure and Weyl points in nonsymmorphic hexagonal materials
• Electron correlations in the kagome flat band metal $\mathrm{CsC}{\mathrm{r}}_3\mathrm{S}{\mathrm{b}}_5$
• Hybrid nodal surface and nodal line phonons in solids
• Simulating Floquet topological phases in static systems
• Catalogue of Flat-Band Stoichiometric Materials
• Selective Control of Surface Spin Current in Topological Materials based on Pyrite-type OsX2 (X = Se, Te) Crystals
• Anomalous geometric transport signatures of topological Euler class
• Tuning Dirac nodes with correlated d-electrons in BaCo_{1-x}Ni_{x}S_{2}
• Thin films as practical quantum materials: a status quo and beyond
• Dual topological nodal line and nonsymmorphic Dirac semimetal in three dimensions
• Quasi-One-Dimensional Higher-Order Topological Insulators
• Wannier band transitions in disordered $\pi$-flux ladders
• Discovery of Ĉ${}_2$ rotation anomaly in topological crystalline insulator SrPb
• Topological obstructed atomic limit by annihilating Dirac fermions
• Superconducting ground state of nonsymmorphic superconducting compound Zr${}_2$Ir
• Constructions and Applications of Irreducible Representations of Spin-Space Groups
• The Streda Formula for Floquet Systems: Topological Invariants and Quantized Anomalies from Cesaro Summation
• Topological phases of the interacting Su-Schrieffer-Heeger model: An analytical study
• Exact projected entangled pair ground states with topological Euler invariant
• Orbital doublet driven even-spin Chern insulators
• Materials Expert-Artificial Intelligence for Materials Discovery
• Anderson Critical Metal Phase in Trivial States Protected by Average Magnetic Crystalline Symmetry
• Andreev reflection in Euler materials
• Higher-order topological superconductivity in a topological metal 1T${}^{\prime }$-MoTe${}_2$
• Magnetic wallpaper Dirac fermions and topological magnetic Dirac insulators
• Supersymmetry on the lattice: Geometry, Topology, and Flat Bands
• Protected Gapless Edge States In Trivial Topology
• Green's Function Approach to Interacting Higher-order Topological Insulators
• Energy density as a probe of band representations in photonic crystals
• Rotoinversion-symmetric bulk-hinge correspondence and its applications to higher-order Weyl semimetals
• A diagnosis of explicit symmetry breaking in the tight-binding constructions for symmetry-protected topological systems
• $n$-Hourglass Weyl fermions in nonsymmorphic materials
• Online Search Tool for Graphical Patterns in Electronic Band Structures
• Topological phase diagrams of in-plane field polarized Kitaev magnets
• On the possibility of magnetic Weyl fermions in non-symmorphic compound PtFeSb
• Gapping fragile topological bands by interactions
• Higher-order topological insulators in a crisscross antiferromagnetic model
• Implementation and characterization of the dice lattice in the electron quantum simulator
• Pressure Effect on Band Inversion in AECd2As2
• Crystallographic bulk-edge correspondence: glide reflections and twisted mod 2 indices
• Crystalline-electromagnetic responses of higher order topological semimetals
• Threes Company
• Kagome and honeycomb flat bands in moiré graphene
• Correlated phases and topological phase transition in twisted bilayer graphene at one quantum of magnetic flux
• Structural and electronic properties of $\alpha ,\beta$-(BEDT-TTF)${}_2$I${}_3$ and $\kappa$-(BEDT-TTF)${}_2$X${}_3$ (X=I,F,Br,Cl) organic charge transfer salts
• Textured Exciton Insulators
• Effective Dynamics of 2D Bloch Electrons in External Fields Derived From Symmetry
• Topologically localized insulators
• Optimally Localized Wannier Functions for 2D Chern Insulators
• Majorana corner modes in unconventional monolayers of the 1T-PtSe2 family
• Quantum Spin Hall Effect and Su-Schrieffer-Heeger Model Implementation in Novel C3N-based Dumbbell Morphologies
• Topological Wannier cycles for the bulk and edges
• Classification of Classical Spin Liquids: Topological Quantum Chemistry and Crystalline Symmetry
• Theory of Anomalous Floquet Higher-Order Topology: Classification, Characterization, and Bulk-Boundary Correspondence
• Microwave hinge states in a simple-cubic-lattice photonic crystal insulator
• Protection of Correlation-Induced Phase Instabilities by Exceptional Susceptibilities
• Universal Wilson Loop Bound of Quantum Geometry
• Influence of magnetism, strain and pressure on the band topology of EuCd${}_2$As${}_2$
• Observation of floating surface state in obstructed atomic insulator candidate NiP${}_2$
• Topological modes in radiofrequency resonator arrays
• Nodal lines and mapping to mirror Chern numbers in Ca${}_2$As family
• Anomalous Crystal Shapes of Topological Crystalline Insulators
• Fully-gapped superconductivity and topological aspects of the noncentrosymmetric TaReSi superconductor
• Database Construction for Two-Dimensional Material-Substrate Interfaces
• Stacking-Induced Symmetry-Protected Topological Phase Transitions
• Electric polarization and its quantization in one-dimensional non-Hermitian chains
• Topological gapless points in superconductors: From the viewpoint of symmetry
• A mono-atomic orbital-based 1D topological crystalline insulator
• Pfaffian invariant identifies magnetic obstructed atomic insulators
• Multiple superconducting phases driven by pressure in the topological insulator GeSb4Te7
• Topology in abundance
• Band alignment effect in the topological photonic alloy
• 4D beyond-cohomology topological phase protected by $C_2$ symmetry and its boundary theories
• Simulating Higher-Order Topological Insulators in Density Wave Insulators
• Phase diagram and topology of the XXZ chain with alternating bonds and staggered magnetic field
• Diagnosis of topological nodal lines with nontrivial monopole charge in the presence of rotation symmetries
• Multi-type Dirac fermions protected by orthogonal glide symmetries in a noncentrosymmetric system
• A Recipe for Flat Bands in Pyrochlore Materials: A Chemist's Perspective
• Nonlinear breathers with crystalline symmetries
• Classification of symmetry-enriched topological quantum spin liquids
• Predicting topological materials: symmetry-based indicator theories and beyond
• Understanding the magnetic response of the Quantum spin liquid compound 1T-TaS2
• Optical signatures of Euler superconductors
• Distinct Floquet topological classifications from color-decorated frequency lattices with space-time symmetries
• Chern dartboard insulator: sub-Brillouin zone topology and skyrmion multipoles
• Altermagnetic Weyl node-network semimetals protected by spin symmetry
• Wannier center spectroscopy to identify boundary-obstructed topological insulators
• Upper bound of a band complex
• Topological metals constructed by sliding quantum wire arrays
• Discovery of topological metamaterials by symmetry relaxation and smooth topological indicators
• Gapless Criterion for Crystals from Effective Axion Field
• Fractional corner charges in threefold-symmetric two-dimensional materials with fragile topology
• Interaction Driven Topological Phase Transition in Monolayer CrCl${}_2$(pyrazine)${}_2$
• Kramers-Weyl fermions in the chiral charge density wave material (TaSe${}_4$)${}_2$I
• Fermionic tensor networks for higher order topological insulators from charge pumping
• Computing the ${\mathbb{Z}}_2$ Invariant in Two-Dimensional Strongly-Correlated Systems
• Universal Metallic Surface States in Electride
• Scattering theory of delicate topological insulators
• All hourglass bosonic excitations in the 1651 magnetic space groups and 528 magnetic layer groups
• STM observation of the hinge-states of bismuth nanocrystals
• IrF4: From Tetrahedral Compass Model to Topological Semimetal
• A topological classification of molecules and chemical reactions with a perplectic structure
• Materials discovery acceleration by using condition generative methodology
• XFe4Ge2 (X = Y, Lu) and Mn3Pt: Filling-enforced magnetic topological metals
• Kitaev Building-block Construction for Inversion-Protected Higher-order Topological Superconductors
• Probing fragile topology with a screw dislocation
• $Z_2$ Dirac points with topologically protected multihelicoid surface states
• Fragile topological phase on the triangular kagome lattice and its bulk-boundary correspondence
• Nonsymmorphic bosonization in one-dimensional generalized Kitaev spin-1/2 models
• Symmetry-driven Phononic Metamaterials
• Second Euler number in four dimensional synthetic matter
• Topological end states in a one-dimensional spatially modulated interaction spinless fermion model
• Effects of first- and second-order topological phases on equilibrium crystal shapes
• Observation of nonlinear higher-order topological insulators with unconventional boundary truncations
• Intrinsic antiferromagnetic topological insulator and axion state in V2WS4
• Nodal phases in non-Hermitian wallpaper crystals
• Coexisting Euler and Stiefel-Whitney Topological Phases in Elastic Metamaterials
• Topological Gap Opening without Symmetry Breaking from Dynamical Quantum Correlations
• Isolated nearly flat higher Chern band in monolayer transition metal trihalides
• Two-dimensional orbital-obstructed insulators with higher-order band topology
• Spin Weyl Topological Insulators
• Theoretical analysis of glide-Z_2 magnetic topological photonic crystals
• Atiyah-Hirzebruch spectral sequence for topological insulators and superconductors: $E_2$ pages for 1651 magnetic space groups
• Projective Representations, Bogomolov Multiplier, and Their Applications in Physics
• Purely anharmonic charge-density wave in the 2D Dirac semimetal SnP
• Axion insulator, Weyl points, quantum anomalous Hall effect and magnetic topological phase transition in Eu3In2As4
• Correlated Zak insulator in organic antiferromagnets
• Electric polarization and discrete shift from boundary and corner charge in crystalline Chern insulators
• Emergent Topological Semimetal
• Enhancing the Hyperpolarizability of Crystals with Quantum Geometry
• Topological Descendants of Multicritical EuTl2
• Topological Signatures in Nodal Semimetals through Neutron Scattering
• Omnidirectional domain wall modes protected by fragile topological states
• Recipe for higher-order topology on the triangular lattice
• Topology of SmB6 revisited by means of topological quantum chemistry
• Polarization textures in crystal supercells with topological bands
• Two-atom-thin topological crystalline insulators lacking out of plane inversion symmetry
• General corner charge formulas in various tetrahedral and cubic space groups
• Second-order topological insulator in Bilayer borophene
• Understanding spin textures in PT-broken systems through universal symmetry-constrained rules
• Quantized electrical, thermal, and spin transports of non-Hermitian clean and dirty two-dimensional topological insulators and superconductors
• Topological insulators on fractal lattices: A general principle of construction
• Quantum geometric bounds in spinful systems with trivial band topology
• Ideal Spin-Orbit-Free Dirac Semimetal and Diverse Topological Transitions in Pr${}_8$CoGa${}_3$ Family
• Visualising the connection between edge states and the mobility edge in adiabatic and non-adiabatic topological charge transport
• Hong-Ou-Mandel Interference in a temporal-average-inversion-symmetric chain
• Nonreciprocal Weyl semimetal waveguide
• Broken time-reversal symmetry in cubic skutterudite-like superconductor Y${}_3$Ru${}_4$Ge${}_{13}$
• Exciton Berryology
• Symmetry-enforced double Weyl points, multiband quantum geometry, and singular flat bands of doping-induced states at the Fermi level
• Quantized thermal and spin transports of dirty planar topological superconductors
• Pumping with Symmetry
• IrRep: symmetry eigenvalues and irreducible representations of ab initio band structures
• Dynamical Phase Error in Interacting Topological Quantum Memories
• Homotopy invariant in time-reversal and twofold rotation symmetric systems
• Fragile topology in nodal-line semimetal superconductors
• Mapping rules from nodal line semimetal to topological crystalline insulator in face centered cubic lattice
• Observation of Dirac Charge Density Waves in Bi${}_2$Te${}_2$Se
• Topological States in Chevrel Phase Materials from First-principle Calculations
• Nonsymmorphic spin-space cubic groups and SU(2)${}_1$ conformal invariance in one-dimensional spin-1/2 models
• Field Theoretic Aspects of Condensed Matter Physics: An Overview
• The destiny of obstructed atomic insulator under correlation
• Unconventional phonon spectra and obstructed edge phonon modes
• Transversality-Enforced Tight-Binding Models for 3D Photonic Crystals aided by Topological Quantum Chemistry
• Hybrid symmetry class topological insulators
• Microscopic Green's function approach for generalized Dirac Hamiltonians
• Symmetry-based classification of exact flat bands in single and bilayer moiré systems
• Fidelity and variability in the interlayer electronic structure of the kagome superconductor CsV3Sb5
• Simple realization of a fragile topological lattice with quasi flat-bands in a microcavity array
• Representation Theory for Massless Quasiparticles in Bogoliubov-de Gennes Systems
• Crystalline invariants of fractional Chern insulators
• Topological Dynamics and Correspondences in Composite Exceptional Rings
• Non-trivial topological valence bands of common diamond and zinc-blende semiconductors
• Magneto-optical Conductance of Kane Fermion Gas in Low Frequencies
• Topologically-enhanced exciton transport
• Theory of fractional corner charges in cylindrical crystal shapes
• Intrinsic (Axion) Statistical Topological Insulator
• Topological Anderson insulators by latent symmetry
• Antiferromagnetic Spin Fluctuations and Structural Transition in Cluster Mott Insulator Candidate Nb3Cl8 Revealed by 93Nb- and 35Cl-NMR
• Topological invariants and topological charges in photonic systems
• From quantum geometry to non-linear optics and gerbes: Recent advances in topological band theory
• Multiband superconductivity in the topological Kramers nodal-line semimetals
• Quantum simulation of honeycomb lattice model by high-order moiré pattern
• Projective Spacetime Symmetry of Spacetime Crystals
• Universality of Abelian and non-Abelian Wannier functions in one dimension
• A New Magnetic Topological Quantum Material Candidate by Design
• Selective branching, quenching, and converting of topological modes
• Absence of superconductivity in topological metal ScInAu${}_2$
• Temperature dependence of quantum oscillations from non-parabolic dispersions
• Fermiology and transport properties of the proposed topological crystalline insulator SrAg4Sb2
• Gapless Topological Peierls-like instabilities in more than one dimension
• Real-Space Switching of Local Moments Driven by Quantum Geometry in Correlated Graphene Heterostructures
• Inducing Quantum Phase Transitions in Non-Topological Insulators Via Atomic Control of Sub-Structural Elements
• High-throughput search for topological magnon materials
• Role of effective mass anisotropy in realizing a hybrid nodal-line fermion state
• Symmetry-enforced Fermi degeneracy in topological semimetal RhSb${}_3$
• Perfectly localized Majorana corner modes in fermionic lattices
• Global and Local Topological Crystalline Markers for Rotation-Symmetric Insulators
• Hopf Semimetals
• Topological insulators and geometry of vector bundles
• Local symmetry groups for arbitrary wavevectors
• Topological Spectral Bands with Frieze Groups
• Topological charge excitations and Green's function zeros in paramagnetic Mott insulators
• Cu-doping effects on the ferromagnetic semimetal CeAuGe
• Superfluid stiffness of superconductors with delicate topology
• High-chirality and multiquaternion Weyl nodes in hexagonal ReO${}_3$
• Stacked tree construction for free-fermion projected entangled pair states
• Band structure picture for topology in strongly correlated systems with the ghost Gutzwiller ansatz
• Hilbert band complexes and their applications
• Fermi Surface Topology and Magneto-transport Properties of Superconducting Pd${}_3$Bi${}_2$Se${}_2$
• Anomalous multi-gap topological phases in periodically driven quantum rotors
• Tunable Flux Vortices in 2D Dirac Superconductors
• Interacting Crystalline Topological Insulators in two-dimensions with Time-Reversal Symmetry
• Structural and magnetic properties of CoTeMoO${}_6$ revisited
• Atomically thin obstructed atomic insulators with robust edge modes and quantized spin Hall effect
• Interorbital Antisymmetric Hopping Generated Flat Bands on Kagome and Pyrochlore Lattices
• Arboreal Obstructed Atomic Insulating and Metallic Phases of Fermions
• Reentrant topological phase in half-Heusler compounds
• Topological constraints on the electronic band structure of hexagonal lattice in a magnetic field
• Topological boundary states in engineered quantum-dot molecules on the InAs(111)A surface
• Symmetry-adapted models for multifold fermions with spin-orbit coupling
• Predicted versatile topological nodal magnons in Tb-based icosahedral quasicrystal 1/1 approximants
• Isotropic 3D topological phases with broken time reversal symmetry
• Relativistic spin-momentum locking in ferromagnets
• Crystalline finite-size topology
• Eightfold Degenerate Dirac Nodal Line in Collinear Antiferromagnet Mn${}_5$Si${}_3$
• Spacetime symmetry indicators for two-dimensional Floquet topological insulators
• Hidden topology in flat-band topological insulators: Strong, weak and square-root topological states
• Fragile topological insulators protected by rotation symmetry without spin-orbit coupling
• Frustration-free free fermions
• Frustration-free free fermions and beyond
• Nodal higher-order topological superconductivity from C6-symmetric Dirac semimetals
• Impurity-induced Mott ring states and Mott zeros ring states in the Hubbard operator formalism
• Fragile dislocation modes in obstructed atomic topological phases
• Predicting Many Crystal Properties via an Adaptive Transformer-based Framework
• Interfacial Line Energy of a Topological Phase
• Chiral symmetry and magnetism in a 3D Kagome lattice: RPt${}_2$B (R = La and Nd) prototype crystals
• Disorder-induced delocalization and reentrance in a Chern-Hopf insulator
• Disclinations, dislocations, and emanant flux at Dirac criticality
• Local expression of fractional corner charges in obstructed atomic insulators and relationship with the fractional disclination charges
• Topological invariant and domain connectivity in moiré materials
• Fermi-surface diagnosis for topological superconductivity with $s$-wave-like pairing symmetries
• Higher-order Topological Knots and the classification of non-Hermitian lattices under $C_n$ symmetry
• Topological band insulators without translational symmetry
• Berry Curvature of Low-Energy Excitons in Rhombohedral Graphene
• Laser-induced topological phases in monolayer amorphous carbon
• Anomalous gapped boundaries between surface topological orders in higher-order topological insulators and superconductors with inversion symmetry
• Spin-to-charge conversion in orthorhombic RhSi topological semimetal crystalline thin films
• Emergent chirality and enantiomeric selectivity in layered NbOX${}_2$ crystals
• Topological quantum switch and controllable quasi 1D wires in antimonene
• Self-regulated growth of candidate topological superconducting parkerite by molecular beam epitaxy
• Dynamical Symmetry Indicators for Floquet Crystals
• Design and characterization of all two-dimensional fragile topological bands
• ToMSGKpoint: A user-friendly package for computing symmetry transformation properties of electronic eigenstates of nonmagnetic and magnetic crystalline materials
• Reduced Wannier representation for topological bands
• Symmetry-Based Real-Space Framework for Realizing Flat Bands and Unveiling Nodal-Line Touchings
• Higher-order topological insulator in cubic semiconductor quantum wells
• Anisotropy-driven topological quantum phase transition in magnetic impurities
• Towards a Topological Quantum Chemistry description of correlated systems: the case of the Hubbard diamond chain
• Detection of 2D SPT Order with Partial Symmetries
• Symmetry-protected topological wire in a topological vacuum
• Wavefunction-Free Approach for Predicting Nonlinear Responses in Weyl Semimetals
• Substrate-induced magnetism and topological phase transition in silicene
• Three-dimensional spinless Euler insulators with rotational symmetry
• Projected branes as platforms for crystalline, superconducting, and higher-order topological phases
• Fermi Surface Geometry
• Gapped spinful phases obtained via Gutzwiller projections of Euler states
• Symmetry-breaking-induced topology in FeSe
• Design Principles for Topological Thermoelectrics
• When Wannier centers jump: Critical points between atomic insulating phases
• A Fermi Surface Descriptor Quantifying the Correlations between Anomalous Hall Effect and Fermi Surface Geometry
• Orbital Frontiers: Harnessing Higher Modes in Photonic Simulators
• Colossal magnetoresistance in a nonsymmorphic antiferromagnetic insulator
• Efficient prediction of topological superlattice bands with spin-orbit coupling
• Orbital magnetization reveals multiband topology
• Physical Pictures for Quasisymmetry in Crystals
• Topological Dislocation Response in Elementary Semiconductors
• Periodic Behavior of Topology in Graphene with Nanohole Array
• Topological property of graphene with triangular array of nanoholes
• Topological Lifshitz transition-induced bipolarity of anomalous Nernst effect in kagome magnet YCo3
• Non-self-averaging topological Anderson insulator
• Analysis of the singular band structure occurring in one-dimensional topological normal and superfluid fermionic systems: A pedagogical description
• The mixing-spacetime symmetry in the Floquet-Bloch band theory
• Disorder-mediated linear and nonlinear magnetotransport in the charge-density-wave material $\mathrm{T}{\mathrm{a}}_2\mathrm{NiS}{\mathrm{e}}_7$
• Topological Charges, Fermi Arcs, and Surface States of $K_4$ Crystal
• Symmetry-protected topological polarons
• Dilute Paramagnetism and Non-Trivial Topology in Quasicrystal Approximant Fe${}_4$Al${}_{13}$
• Giant anomalous Hall and Nernst effect in magnetic cubic Heusler compounds
• Systematic study for two-dimensional $Z_2$ topological phase transitions at high-symmetry points in all layer groups
• Crystalline symmetry-protected non-trivial topology in prototype compound BaAl${}_4$
• Magnetically tunable Dirac and Weyl fermions in the Zintl materials family
• Electronic and topological properties of the van der Waals layered superconductor PtTe
• Internal wave crystals
• Monolayer van der Waals kagome lattice for high-temperature flat-band physics
• Topological Invariants of a Filling-Enforced Quantum Band Insulator
• Predication of topological states in the allotropes of group-IV elements
• Magnetization signature of topological surface states in a non-symmorphic superconductor
• Topological power pumping in quantum circuits
• Fractional Wannier Orbitals and Tight-Binding Gauge Fields for Kitaev Honeycomb Superlattices with Flat Majorana Bands
• Glide-resolved photoemission spectroscopy: Measuring topological invariants in nonsymmorphic space groups
• Berry Phase Enforced Spinor Pairing Order