Quantized Response and Topology of Insulators with Inversion Symmetry

Abstract

We study three dimensional insulators with inversion symmetry, in which other point group symmetries, such as time reversal, are generically absent. Their band topology is found to be classified by the parities of occupied states at time reversal invariant momenta (TRIM parities), and by three Chern numbers. The TRIM parities of any insulator must satisfy a constraint: their product must be +1. The TRIM parities also constrain the Chern numbers modulo two. When the Chern numbers vanish, a magneto-electric response parameterized by "theta" is defined and is quantized to theta= 0, 2pi. Its value is entirely determined by the TRIM parities. These results may be useful in the search for magnetic topological insulators with large theta. A classification of inversion symmetric insulators is also given for general dimensions. An alternate geometrical derivation of our results is obtained by using the entanglement spectrum of the ground state wave-function.

12 pages main text; 12 pages appendices; 11 figures. Added new refs. in 2nd version

References in corpus (9)

• Topological insulators and superconductors
• Topological Insulators with Inversion Symmetry
• Classification of topological insulators and superconductors in three spatial dimensions
• Topological Field Theory of Time-Reversal Invariant Insulators
• Phase transition between the quantum spin Hall and insulator phases in 3D: emergence of a topological gapless phase
• Antiferromagnetic topological insulators
• Topological surface states in three-dimensional magnetic insulators
• Topological phases and phase transitions on the square-octagon lattice
• Relativistic analysis of magnetoelectric crystals: extracting a new 4-dimensional P odd and T odd pseudoscalar from Cr_2 O_3 data

Cited by in corpus (203)

• Weyl and Dirac Semimetals in Three Dimensional Solids
• Classification of topological quantum matter with symmetries
• Quantized Electric Multipole Insulators
• Weyl semimetal phase in non-centrosymmetric transition metal monophosphides
• Electric Multipole Moments, Topological Multipole Moment Pumping, and Chiral Hinge States in Crystalline Insulators
• Correlated quantum phenomena in the strong spin-orbit regime
• Symmetry-based Indicators of Band Topology in the 230 Space Groups
• Quantization of fractional corner charge in $C_n$-symmetric higher-order topological crystalline insulators
• The space group classification of topological band insulators
• Topology of crystalline insulators and superconductors
• Quantum anomalous Hall effect and related topological electronic states
• Bulk Topological Invariants in Noninteracting Point Group Symmetric Insulators
• Colloquium: Quantum anomalous Hall effect
• Progress and prospects in magnetic topological materials
• High-throughput calculations of magnetic topological materials
• Second-order topological insulators and superconductors with an order-two crystalline symmetry
• Topological Semimetals Predicted from First-principles Calculations
• Fragile Topology and Wannier Obstructions
• Quantized Faraday and Kerr rotation and axion electrodynamics of a 3D topological insulator
• Higher-order Topology of Axion Insulator EuIn${}_2$As${}_2$
• Classification of topological insulators and superconductors in the presence of reflection symmetry
• Classification of reflection symmetry protected topological semimetals and nodal superconductors
• A classification of symmetry enriched topological phases with exactly solvable models
• Higher-order bulk-boundary correspondence for topological crystalline phases
• Symmetry indicators and anomalous surface states of topological crystalline insulators
• Topological Criticality in the Chiral-Symmetric AIII Class at Strong Disorder
• Building Blocks of Topological Quantum Chemistry: Elementary Band Representations
• Structure and Topology of Band Structures in the 1651 Magnetic Space Groups
• Band Topology and Linking Structure of Nodal Line Semimetals with Z2 Monopole Charges
• Wilson loop approach to fragile topology of split elementary band representations and topological crystalline insulators with time reversal symmetry
• Twisted equivariant matter
• Topological exceptional surfaces in non-Hermitian systems with parity-time and parity-particle-hole symmetries
• Axion Electrodynamics in Topological Materials
• A fractional corner anomaly reveals higher-order topology
• Möbius Insulator and Higher-Order Topology in MnBi${}_{2n}$Te${}_{3n+1}$
• Theory of correlated insulating behaviour and spin-triplet superconductivity in twisted double bilayer graphene
• Efficient Topological Materials Discovery Using Symmetry Indicators
• Topological Materials Discovery from Crystal Symmetry
• Higher-order topological insulators protected by inversion and rotoinversion symmetries
• Classification of Two Dimensional Topological Crystalline Superconductors and Majorana Bound States at Disclinations
• Second-order topological non-Hermitian skin effects
• Realization of an intrinsic, ferromagnetic topological state in MnBi8Te13
• Two-dimensional higher-order topology in monolayer graphdiyne
• Universal Approach to Magnetic Second-Order Topological Insulator
• Surfaces of Axion Insulators
• Twisted bilayer graphene. II. Stable symmetry anomaly
• Symmetry Enforced Chiral Hinge States and Surface Quantum Anomalous Hall Effect in Magnetic Axion Insulator ${\text{Bi}}_{2-x}{\text{Sm}}_x{\text{Se}}_3$
• Geometric approach to fragile topology beyond symmetry indicators
• Many-Body Electric Multipole Operators in Extended Systems
• Boundary-obstructed topological phases
• Correlation effects on 3D topological phases: from bulk to boundary
• Topological Insulators from Group Cohomology
• First Principles Calculations for Topological Quantum Materials
• Band Representations and Topological Quantum Chemistry
• Magnetic orders and topological phases from f-d exchange in pyrochlore iridates
• Symmetry Protected Topological States of Interacting Fermions and Bosons
• Second-order Dirac superconductors and magnetic field induced Majorana hinge modes
• Topological semimetals protected by off-centered symmetries in nonsymmorphic crystals
• Topological Insulators with Commensurate Antiferromagnetism
• Emergent topological phenomena in thin films of pyrochlore iridates
• Metal-insulator transition and topological properties of pyrochlore iridates
• Intrinsic axion insulating behavior in antiferromagnetic MnBi${}_6$Te${}_{10}$
• AIII and BDI Topological Systems at Strong Disorder
• Fragile Topology Protected by Inversion Symmetry: Diagnosis, Bulk-Boundary Correspondence, and Wilson Loop
• Exploration and prediction of topological electronic materials based on first-principles calculations
• Phonons as a platform for non-Abelian braiding and its manifestation in layered silicates
• Magnetic crystalline-symmetry-protected axion electrodynamics and field-tunable unpinned Dirac cones in EuIn2As2
• Berry-phase description of Topological Crystalline Insulators
• Quantum limit transport and destruction of the Weyl nodes in TaAs
• Symmetry representation approach to topological invariants in $C_{2z}T$-symmetric systems
• Magnetic topological insulator MnBi6Te10 with zero-field ferromagnetic state and gapped Dirac surface states
• Non-abelian topology of nodal-line rings in $\mathcal{P}\mathcal{T}$-symmetric systems
• Topological classification of non-Hermitian bands
• Unified understanding of symmetry indicators for all internal symmetry classes
• Topological phase transition in layered magnetic compound MnSb2Te4: Spin-orbit coupling and interlayer coupling dependeces
• Boundary-locality and perturbative structure of entanglement spectra in gapped systems
• Multipolar Topological Field Theories: Bridging Higher Order Topological Insulators and Fractons
• Torsion, Parity-odd Response and Anomalies in Topological States
• Entanglement Spectrum Classification of $C_n$-invariant Noninteracting Topological Insulators in Two Dimensions
• Band Connectivity for Topological Quantum Chemistry: Band Structures As A Graph Theory Problem
• Modern semiclassical theory of magnetic transport and breakdown
• Shift insulators: rotation-protected two-dimensional topological crystalline insulators
• Symmetry-based indicators for topological Bogoliubov-de Gennes Hamiltonians
• Bicircular light tuning of magnetic symmetry and topology in Dirac semimetal Cd${}_3$As${}_2$
• Topological indices, defects and Majorana fermion in chiral superconductors
• Symmetry indicators of band topology
• Dynamical Majorana Edge Modes in a Broad Class of Topological Mechanical Systems
• Patterns of Electro-magnetic Response in Topological Semi-metals
• Large dynamical axion field in topological antiferromagnetic insulator Mn${}_2$Bi${}_2$Te${}_5$
• Higher-order topological band structures
• Tunable interlayer magnetism and band topology in van der Waals heterostructures of MnBi2Te4-family materials
• Topological Weyl and Node-Line Semimetals in Ferromagnetic Vanadium-Phosphorous-Oxide $\beta$-V${}_2$OPO${}_4$ Compound
• Symmetry-protected Topological Phases, Generalized Laughlin Argument and Orientifolds
• On the matter of topological insulators as magnetoelectrics
• Topological semimetals studied by ab initio calculations
• ${\mathbb{Z}}_2$-enriched symmetry indicators for topological superconductors in the 1651 magnetic space groups
• Three-dimensional superconductors with hybrid higher order topology
• Temperature Dependent Electronic Structure in a Higher Order Topological Insulator Candidate EuIn${}_2$As${}_2$
• Bulk invariants and topological response in insulators and superconductors with nonsymmorphic symmetries
• Topological classification and diagnosis in magnetically ordered electronic materials
• Anyon condensation and a generic tensor-network construction for symmetry protected topological phases
• Symmetric tensor networks and practical simulation algorithms to sharply identify classes of quantum phases distinguishable by short-range physics
• Non-Hermitian band topology with generalized inversion symmetry
• Bound states at partial dislocation defects in multipole higher-order topological insulators
• Multiple magnetic topological phases in bulk van der Waals crystal MnSb4Te7
• Atiyah-Hirzebruch Spectral Sequence in Band Topology: General Formalism and Topological Invariants for 230 Space Groups
• Symmetry indicators for topological superconductors
• Tuning the magnetism and band topology through antisite defects in Sb doped MnBi4Te7
• Multi-gap topology and non-Abelian braiding of phonons from first principles
• Dynamical axion state with hidden pseudospin Chern numbers in MnBi${}_2$Te${}_4$-based heterostructures
• Z2 topological invariants in two dimensions from quantum Monte Carlo
• Theory of optical axion electrodynamics and application to the Kerr effect in topological antiferromagnets
• Anomalous Hall Crystals in Rhombohedral Multilayer Graphene II: General Mechanism and a Minimal Model
• CPT theorem and classification of topological insulators and superconductors
• Chiral Hinge Magnons in Second-Order Topological Magnon Insulators
• Quantum anomalous Hall effect in two-dimensional magnetic insulator heterojunctions
• Homotopy Theory of Strong and Weak Topological Insulators
• Fractional charge bound to a vortex in two dimensional topological crystalline insulators
• Electronic structures and topological properties in nickelates $L{n}_{n+1}$Ni${}_n$O${}_{2n+2}$
• Theory of quasiparticle interference in mirror symmetric 2D systems and its application to surface states of topological crystalline insulators
• Teleportation of Berry curvature on the surface of a Hopf insulator
• Axionic Band Topology in Inversion-Symmetric Weyl-Charge-Density Waves
• Anisotropic topological magnetoelectric effect in axion insulators
• Axion coupling in the hybrid Wannier representation
• Entanglement Spectroscopy using Quantum Monte Carlo
• Symmetry-protected line nodes and Majorana flat bands in nodal crystalline superconductors
• Smooth gauge and Wannier functions for topological band structures in arbitrary dimensions
• Tunable dynamical magnetoelectric effect in antiferromagnetic topological insulator MnBi${}_2$Te${}_4$ films
• Bulk-edge and bulk-hinge correspondence in inversion-symmetric insulators
• Delocalization Transition of Disordered Axion Insulator
• Entanglement spectrum of the Heisenberg XXZ chain near the ferromagnetic point
• $N$-band Hopf insulator
• Doubled Quantum Spin Hall Effect with High-Spin Chern Number in $\alpha$-Antimonene and $\alpha$-Bismuthene
• Bott periodicity for the topological classification of gapped states of matter with reflection symmetry
• Topological Crystalline Phases in a Disordered Inversion-Symmetric Chain
• Persistence of chirality in the Su-Schrieffer-Heeger model in the presence of on-site disorder
• Interaction Enabled Topological Crystalline Phases
• Multiple magnetism controlled topological states in EuAgAs
• No-go theorem for topological insulators and sure-fire recipe for Chern insulators
• Topology invisible to eigenvalues in obstructed atomic insulators
• Generation of higher-order topological insulators using periodic driving
• Landau Levels of the Euler Class Topology
• Symmetry-protected entangling boundary zero modes in crystalline topological insulators
• Space group symmetry fractionalization in a family of exactly solvable models with Z2 topological order
• Gauge-discontinuity contributions to Chern-Simons orbital magnetoelectric coupling
• The Bulk-Hinge Correspondence and Three-Dimensional Quantum Anomalous Hall Effect in Second Order Topological Insulators
• A Non-Commutative Formula for the Isotropic Magneto-Electric Response
• Classification of crystalline topological semimetals with an application to Na${}_3$Bi
• Dynamical Piezomagnetic Effect in Time-Reversal Invariant Weyl Semimetals with Axionic Charge-Density Waves
• Quantization of Topological Invariants under Symmetry-Breaking Disorder
• Weyl Phases in Point-Group Symmetric Superconductors
• Dynamic bulk-boundary correspondence for anomalous Floquet topology
• Correlations and entanglement in flat band models with variable Chern numbers
• Antiferromagnetic topological insulator with selectively gapped Dirac cones
• Bulk-edge correspondence of Stiefel-Whitney and Euler insulators through the entanglement spectrum and cutting procedure
• Topological phonon analysis of the 2D buckled honeycomb lattice: an application to real materials
• Topological Crystalline Bose Insulator in Two Dimensions via Entanglement Spectrum
• Topological Magnetoelectric Response in Ferromagnetic Axion Insulators
• Symmetry-breaking pathway towards the unpinned broken helix
• Inherited topological superconductivity in two-dimensional Dirac semimetals
• Intrinsic ferromagnetic axion states and a single pair of Weyl fermions in the stable-state Mn\emph{X}${}_2$\emph{B}${}_2$\emph{T}${}_6$-family materials
• Homotopic classification of band structures: Stable, fragile, delicate, and stable representation-protected topology
• Hybrid-order topology in unconventional magnets of Eu-based Zintl compounds with surface-dependent quantum geometry
• Anderson Critical Metal Phase in Trivial States Protected by Average Magnetic Crystalline Symmetry
• Topological obstructed atomic limit by annihilating Dirac fermions
• Electromagnetic Response of Three-dimensional Topological Crystalline Insulators
• Axion insulators protected by C2T and their K-theory invariants and material realization
• Topological insulators with arbitrarily tunable entanglement
• Intrinsic ferromagnetic and antiferromagnetic axion insulators in van der Waals materials Mn\emph{X}${}_2$\emph{B}${}_2$\emph{T}${}_6$ family
• Simulating Higher-Order Topological Insulators in Density Wave Insulators
• Remote control of spin polarization of topological corner states
• A mono-atomic orbital-based 1D topological crystalline insulator
• Dynamical magnetoelectric coupling in axion insulator thin films
• 5d orbital Induced Room Temperature Quantum Anomalous Hall Effect in TbCl
• Gapless Criterion for Crystals from Effective Axion Field
• Dissipative Edge Transport in Disordered Axion Insulator Films
• Mirror Chern numbers in the hybrid Wannier representation
• Topological Descendants of Multicritical EuTl2
• Orbital Magnetization under an Electric Field and Orbital Magnetoelectric Polarizabilty for a Bilayer Chern System
• Observation of trapped fractional charge and topological states at disclination defects in higher-order topological insulators
• Bulk-entanglement spectrum correspondence in $PT$- and $PC$-symmetric topological insulators and superconductors
• A Bosonic Analog of a Topological Dirac Semi-Metal: Effective Theory, Neighboring Phases, and Wire Construction
• Selective branching, quenching, and converting of topological modes
• Controlling topology through targeted composite symmetry manipulation in magnetic systems
• Electric Field-Induced Skyrmion Crystals via Charged Monopoles in Insulating Helimagets
• Intrinsic (Axion) Statistical Topological Insulator
• Topological States in Chevrel Phase Materials from First-principle Calculations
• Discrete Quantum Geometry and Intrinsic Spin Hall Effect
• $d$-Wave Polarization-Spin Locking in Two-Dimensional Altermagnets
• Anisotropic Penetration Depths of Corner States in a Higher-Order Topological Insulator
• IrRep: symmetry eigenvalues and irreducible representations of ab initio band structures
• Hedgehog spin texture and competing orders associated with strains on the surface of a topological crystalline insulator
• Universal Role of Combined Symmetry for the Protection of the Dirac Cone in Antiferromagnetic Topological Insulators
• Global and Local Topological Crystalline Markers for Rotation-Symmetric Insulators
• Topological insulators and geometry of vector bundles
• Isotropic 3D topological phases with broken time reversal symmetry
• Crystalline finite-size topology
• Critical magnetic flux for Weyl points in the three-dimensional Hofstadter model
• Weak ${\mathbb{Z}}_2$ Supertopology
• Phase Transition of Topological Index driven by Dephasing
• Topological energy pumping in a quasi-periodically driven four-level system
• Dynamical Symmetry Indicators for Floquet Crystals
• Light-element and purely charge-based topological materials