Three dimensional topological invariants for time reversal invariant Hamiltonians and the three dimensional quantum spin Hall effect

Abstract

The $Z_2$ invariant for filled bands in the ground states of systems with time reversal invariance characterizes the number of stable pairs of edge states. Here we study the $Z_2$ invariant using band touching methods discussed in a recent previous work \cite{roy2006zcq} and extend the study to three dimensions. Band collisions preserve the $Z_2$ invariant both in two and three dimensions, but there are crucial differences in the two cases. In three dimensions,we find a novel fourth $Z_2$ invariant which is characterized by a "trapped monopole" in momentum space. If the monopole charge in half the Brillouin zone is odd, then atleast one of the monopoles cannot recombine with another monopole and vanish unlike the case when the monopole charge is even. We also point out the possibility of a three dimensional quantum spin Hall effect and discuss the connection of various topological invariants to such an effect.

References in corpus (6)

• Quantum Spin Hall Effect in Graphene
• $Z_2$ Topological Order and the Quantum Spin Hall Effect
• Topological Insulators in Three Dimensions
• Topological invariants of time-reversal-invariant band structures
• Quantum Spin Hall Effect
• Berry Curvature on the Fermi Surface: Anomalous Hall Effect as a Topological Fermi-Liquid Property

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• Interaction-enhanced magnetically ordered insulating state at the edge of a two-dimensional topological insulator
• Line defects in Three dimensional Symmetry Protected Topological Phases
• Dynamical characterization of Weyl nodes in Floquet Weyl semimetal phases
• Z${}_2$ nontrivial topology of rare-earth binary oxide superconductor
• Embedded Topological Semimetals
• Dynamic bulk-boundary correspondence for anomalous Floquet topology
• Modification of transition radiation by three-dimensional topological insulators
• Spatially resolved Landau level spectroscopy of the topological Dirac cone of bulk-type Sb2Te3(0001): potential fluctuations and quasiparticle lifetime
• Variational Monte Carlo Method in the Presence of Spin-Orbit Interaction and Its Application to the Kitaev and Kitaev-Heisenberg Model
• Topology in time-reversal symmetric crystals
• Impact of high-frequency pumping on anomalous finite-size effects in three-dimensional topological insulators
• Josephson effect in normal and ferromagnetic topological insulator planar, step and edge junctions
• Symmetry protected weak topological phases in a superlattice
• Abelian and non-abelian anyons in integer quantum anomalous Hall effect and topological phase transitions via superconducting proximity effect
• Majorana edge magnetization in the Kitaev honeycomb model
• Electronic Structure Examination on the Topological Properties of CaMnSb${}_2$ by Angle-Resolved Photoemission Spectroscopy
• Anomalous localization at the boundary of an interacting topological insulator
• Interaction effects on almost flat surface bands in topological insulators
• Stability of Unconventional Superconductivity on Surfaces of Topological Insulators
• Interlayer Coupling Induced Topological Phase Transition to Higher Order
• Spin polarized STM spectra of Dirac Fermions on the surface of a topological insulator
• Searching for two-dimensional Weyl superconductors in heterostructures
• Transmission through a potential barrier in Luttinger liquids with a topological spin gap
• Coalescence of multiple topological orders in quasi-one-dimensional bismuth halide chains
• Momentum-Space Electromagnetic Induction in Weyl Semimetals
• Bifurcation of the Edge-State Width in the Two-Dimensional Topological Insulator
• Structural versus electronic distortions of symmetry-broken IrTe${}_2$
• Skyrmion spin texture in ferromagnetic semiconductor-superconductor heterostructures
• Topologically distinct atomic insulators
• Tailoring phase transition from topological superconductor to trivial superconductor induced by magnetic textures of a spin-chain on a $p$-wave superconductor
• Spontaneous breaking of time-reversal symmetry in topological insulators
• Bulk superconductivity and non-trivial band topology analysis of Pb2Pd
• Model Hamiltonian for strongly-correlated systems: Systematic, self-consistent, and unique construction
• Interacting Floquet topological phases in three dimensions
• First-principles prediction of a new family of layered topological insulators
• Momentum-Dependent Mass and AC Hall Conductivity of Quantum Anomalous Hall Insulators and Their Relation to the Parity Anomaly
• Higgs-Confinement Transitions in QCD from Symmetry Protected Topological Phases
• Translation symmetry-enriched toric code insulator
• Glide Symmetry Protected Higher-Order Topological Insulators from Semimetals with butterfly-like Nodal Lines
• Homotopic classification of band structures: Stable, fragile, delicate, and stable representation-protected topology
• Interacting weak topological insulators and their transition to Dirac semimetal phases
• Ferromagnetism and glassiness on the surface of topological insulators
• Approximate formula for the macroscopic polarization including quantum fluctuations
• Dyon condensation in topological Mott insulators
• Non-local order parameters for states with topological electromagnetic response
• Magnetoelectric effect of a conducting sphere near a planar topological insulator
• Superconducting proximity effect on a two-dimensional Dirac electron system
• On exotic sphere fibrations, topological phases, and edge states in physical systems
• Stability of zero energy Dirac touchings in the honeycomb Hofstadter problem
• Conductivity of a two-dimensional HgTe layer near the critical width: The role of developed edge states network and random mixture of $p$- and $n$-domains
• Fermion-fermion interaction driven instability and criticality of quadratic band crossing systems with the breaking of time-reversal symmetry
• Confining electrons on a topological insulator surface using potentials and a magnetic field
• On the relation of the entanglement spectrum to the bulk polarization
• Gapless interface states at the junction between two topological insulators
• Wannier Topology and Quadrupole Moments for a generalized Benalcazar-Bernevig-Hughes Model
• Experimental signatures of 3d fractional topological insulators
• Disorder effects on thermal transport on the surface of topological superconductors by the self-consistent Born approximation
• Effects of short-ranged interactions on the Kane-Mele model without discrete particle-hole symmetry
• Hybridization of topological surface states with a flat band
• Structure of surface electronic states in strained mercury telluride
• Chiral Gravitomagnetic Effect in Topological Superconductors and Superfluids
• Quantum engineering of Majorana quasiparticles in one-dimensional optical lattices
• Partial Charge Transfer and Absence of Induced Magnetization in EuS(111)/Bi${}_2$Se${}_3$ Heterostructures
• Quasi-One-Dimensional Higher-Order Topological Insulators
• Driving Topological Phases by Spatially Inhomogeneous Pairing Centers
• Delocalization of surface Dirac electrons in disordered weak topological insulators
• Emergent topological fields and relativistic phonons within the thermoelectricity in topological insulators
• Transport properties of band engineered p-n heterostructures of epitaxial Bi${}_2$Se${}_3$/(Bi${}_{1-x}$Sb${}_x$)${}_2$(Te${}_{1-y}$Se${}_y$)${}_3$ topological insulators
• Single-Dirac-cone Z2 topological insulator phases in distorted Li2AgSb-class and related quantum critical Li-based spin-orbit compounds
• Cooper instability generated by attractive fermion-fermion interaction in the two-dimensional semi-Dirac semimetals
• An ab-initio study of topological and transport properties of YAuPb
• Quantization of non-Abelian Berry phase for time reversal invariant systems
• Protection of the surface states in topological insulators: Berry phase perspective
• Textured Exciton Insulators
• Effective model for massless Dirac electrons on a surface of weak topological insulators
• Signature of Anomalous Andreev bound states in magnetic Josephson junction of noncentrosymmetric superconductor on a topological insulator
• Revealing topological Dirac fermions at the surface of strained HgTe thin films via Quantum Hall transport spectroscopy
• Impurity Effects on Superconductivity on Surfaces of Topological Insulators
• The search for strong topological insulators
• The tenfold way redux: Fermionic systems with $N$-body interactions
• Dirac Fermions and Topological Phases in Magnetic Topological Insulator Films
• Hidden-symmetry-protected Z_2 topological insulator in a cubic lattice
• Geometric Approach to 3D Interfaces at Strong Coupling
• Entanglement Chern number for three-dimensional topological insulators: Characterization by Weyl points of entanglement Hamiltonians
• Majorana Zero-modes and Topological Phases of Multi-flavored Jackiw-Rebbi model
• Topological crystalline protection in a photonic system
• Fractionalized Metals and Superconductors in Three Dimensions
• Topological electronic bands in crystalline solids
• The weak side of strong topological insulators
• Surfaces and Slabs of Fractional Topological Insulator Heterostructures
• Tight-Binding Model and Electronic Property of Dirac Nodal Line in Single-Component Molecular Conductor [Pt(dmdt)${}_2$]
• Proximity induced ferromagnetism, superconductivity, and finite-size effects on the surface and edge states of topological insulator nanostructures
• Metallic states beyond Tomonaga-Luttinger liquids in one dimension
• Surface spectra of Weyl semimetals through self-adjoint extensions
• Hidden-symmetry-protected quantum pseudo-spin Hall effect in optical lattices
• Optical intersubband properties of a core-shell semiconductor-topological insulator quantum dot described by $\theta$-Electrodynamics
• Structure-driven phase transitions in paracrystalline topological insulators
• Interplay between spin-orbit coupling and crystal-field effect in topological insulators
• Topological Orders with Global Gauge Anomalies
• Intrinsic surface dipole in topological insulators
• Quantum transport through three-dimensional topological insulator p-n junction under magnetic field
• Gapped gravitinos, isospin $\frac{1}{2}$ particles and $\mathcal{N}=2$ partial breaking
• Spin Berry phase in a helical edge state: Sz nonconservation and transport signatures
• Topological quantum memory interfacing atomic and superconducting qubits
• Holographic Wilson Loops, Dielectric Interfaces, and Topological Insulators
• Nontrivial gapless electronic states at the stacking faults of weak topological insulators
• $U(1)$ symmetry-enriched toric code
• Phase Diagram Structure of Topological Mott Transition for Zero-gap Semiconductors beyond Conventional Landau-Ginzburg-Wilson Scenario
• Green's Function Method for Line Defects and Gapless Modes in Topological Insulators : Beyond Semiclassical Approach
• Three-dimensional topological insulators in the octahedron-decorated cubic lattice
• Hall and spin Hall viscosity ratio in 2d topological insulators
• Zero-Energy State Localized near an Arbitrary Edge in Quadrupole Topological Insulators
• Vavilov-Cherenkov radiation for parallel motion in three-dimensional topological insulators
• Manipulating quantum channels in weak topological insulator nanoarchitectures
• Landau levels in a topological insulator
• Transport signatures of surface potentials on three-dimensional topological insulators
• Exact correlations in topological quantum chains
• Weakly interacting one-dimensional topological insulators: a bosonization approach
• Electric and thermoelectric transport in graphene and helical metal in finite magnetic fields
• Low temperature thermal transport at the interface of a topological insulator and a d-wave superconductor
• Weak topological insulating phases of hard-core-bosons on the honeycomb lattice
• Transport in a thin topological insulator with potential and magnetic barriers
• Short-ranged interaction effects on $Z_2$ topological phase transitions
• Topological electronic properties of silicon
• Spin-torque resonance due to diffusive dynamics at a surface of topological insulator
• Theory of metal-insulator transitions in graphite under high magnetic field
• Sorting and Routing Topologically Protected Edge States by their Valleys
• Dynamics of impurity in the environment of Dirac fermions
• Fermion-fermion interaction driven phase transitions in rhombohedral trilayer graphene
• Disorder-induced density of states on the surface of a spherical topological insulator
• Emergent Topology in Many-Body Dissipative Quantum Matter
• Spontaneous symmetry breaking and quantum Hall valley ordering on the surface of topological hexaborides
• Unwinding of a one-dimensional topological superconductor
• Probing surface states exposed by crystal terminations at arbitrary orientations of three-dimensional topological insulators
• Model non-Hermitian topological operators without skin effect: A general principle of construction
• Quantized thermal and spin transports of dirty planar topological superconductors
• Correlated Zak insulator in organic antiferromagnets
• Topological insulators on fractal lattices: A general principle of construction
• Quantized electrical, thermal, and spin transports of non-Hermitian clean and dirty two-dimensional topological insulators and superconductors
• Discriminant indicator with generalized rotational symmetry
• Topological semimetals and insulators in three-dimensional honeycomb materials
• Floquet topological phases with time-reversal and space inversion symmetries and dynamical detection of topological charges
• Weyl Semimetal and Nonassociative Nambu Geometry
• Gauge-invariant cutoff for Dirac electron systems with a vector potential
• Boson-fermion duality in four dimensions
• Hall effect of ferro/antiferromagnetic wallpaper fermions
• Topological phases of many-body non-Hermitian systems
• Edge Spin fractionalization in one-dimensional spin-$S$ quantum antiferromagnets
• Bulk--Boundary Correspondence and Boundary Zero Modes in a Non-Hermitian Kitaev Chain Model
• Phase Diagram of a Non-Hermitian Chern Insulator: Destabilization of Chiral Edge States and Bulk-Boundary Correspondence
• Topological Crystalline Metal in Orthorhombic Perovskite Iridates
• Color Superconductivity, Fermionic Quasinormal Modes in Reissner-Nordström-anti-de Sitter Spacetimes and Supersymmetry
• Effective field theory of topological insulator and the Foldy-Wouthuysen transformation
• Hopf Semimetals
• Magnon-mediated superconductivity on ferromagnetic wallpaper fermions
• Singular low-energy states of tilted Dirac semimetals induced by the fermion-fermion interactions
• Emergent topological mirror insulator in t2g-orbital systems
• Engineering Dirac electrons emergent on the surface of a topological insulator
• Robust translational invariance in topological bands against lattice potentials and disorders
• Arboreal Obstructed Atomic Insulating and Metallic Phases of Fermions
• Effect of inplane electric field on magnetotransport in helical metal
• Spectroscopic footprints of quantum friction in nonreciprocal and chiral media
• Hybrid Higher-Order Skin Topological Modes in the Two-Dimensional Su-Schrieffer-Heeger Model with Nonreciprocal Hoppings
• Reentrant topological phase in half-Heusler compounds
• Extended Haldane model -- a modern gateway to topological insulators
• Low-energy effective Hamiltonian and end states of an inverted HgTe nanowire
• Parity anomaly with impurities and the Pauli--Villars subtraction
• "Self-Dual" Quantum Critical Point on the surface of $3d$ Topological Insulator
• The magnetoelectric effect due to a semispherical capacitor surrounded by a spherical topologically insulating shell
• Obstructed Atomic Insulators and Superfluids of Fermions Coupled to ${\mathbb{Z}}_2$ Gauge Fields
• Robust nonequilibrium surface currents in the 3D Hofstadter model
• Gapped energy spectra around the Dirac node at the surface of a 3D topological insulator in the presence of the time-reversal symmetry
• Finite-size scaling analysis of the conductivity of Dirac electrons on a surface of disordered topological insulators
• Chiral Bosonic Topological Insulator on the Honeycomb Lattice with Anisotropic Interactions
• Possible Spin-Density Wave on Fermi Arc of Edge State in Single-Component Molecular Conductors [Pt(dmdt)${}_2$] and [Ni(dmdt)${}_2$]
• Weak topological insulators with step edges: Subband engineering and its effect on electron transport
• Short-ranged interaction effects on $Z_2$ topological phase transitions: The perturbative mean-field method
• The evaluation of non-topological components in Berry phase and momentum relaxation time in a gapped 3D topological insulator
• Landau levels on a surface of weak topological insulators
• Scattering states of a vortex in the proximity-induced superconducting state at the interface of a topological insulator and an s-wave superconductor
• Spectrum of the Vortex Bound States of the Dirac and Schrodinger Hamiltonian in the presence of Superconducting Gaps
• Systematic study for two-dimensional $Z_2$ topological phase transitions at high-symmetry points in all layer groups
• Topology behind topological insulators
• Surface states of gapped electron systems and semi-metals
• Critical fates induced by the interaction competition in three-dimensional tilted Dirac semimetals
• Band Topology or Geometry?
• Hydrodynamic theory of surface excitations of three-dimensional topological insulators
• Geometric Approaches to Quantum Fields and Strings at Strong Couplings
• To See a World in a Grain of Sand -- The Scientific Life of Shoucheng Zhang
• Analytical solutions of topological surface states in a series of lattice models
• Mimicing the Kane-Mele type spin orbit interaction by spin-flexual phonon coupling in graphene devices
• Electromagnetic response of the surface states of a topological insulator nanowire embedded within a resonator
• Topological energy pumping in a quasi-periodically driven four-level system
• Hofstadter Butterflies in Topological Insulators
• Sb doping effect on transport behavior in the topological insulator Bi2Se3
• Projected branes as platforms for crystalline, superconducting, and higher-order topological phases
• Quantized Spin Hall Effect in Three-Dimensional Nodal-Ring Semimetal: Geometric Scaling and Symmetry-Engineered Spin Response
• Momentum non-conservation in a scalar quantum field theory with a planar $\theta$ interface
• Out-of-plane spin polarization of edge currents in Chern insulator with Rashba spin-orbit interaction
• Granular topological insulators
• Glide-resolved photoemission spectroscopy: Measuring topological invariants in nonsymmorphic space groups
• Anomaly non-renormalization in interacting Weyl semimetals
• Signatures of Topological Phase Transition in 3d Topological Insulators from Dynamical Axion Response
• Piecewise-terminated spherical topological insulator as a virtual breadboard for Majorana circuitry
• Symmetry-protected topological corner modes in a periodically driven interacting spin lattice