Computing topological invariants without inversion symmetry

Alexey A. Soluyanov; David Vanderbilt

doi:10.1103/PhysRevB.83.235401

paper

Computing topological invariants without inversion symmetry

arXiv:1102.5600 · doi:10.1103/PhysRevB.83.235401

Abstract

We consider the problem of calculating the weak and strong topological indices in noncentrosymmetric time-reversal (T) invariant insulators. In 2D we use a gauge corresponding to hybrid Wannier functions that are maximally localized in one dimension. Although this gauge is not smoothly defined on the two-torus, it respects the T symmetry of the system and allows for a definition of the Z_2 invariant in terms of time-reversal polarization. In 3D we apply the 2D approach to T-invariant planes. We illustrate the method with first-principles calculations on GeTe and on HgTe under [001] and [111] strain. Our approach differs from ones used previously for noncentrosymmetric materials and should be easier to implement in ab initio code packages.

revised version, accepted to PRB

References in corpus (27)

Topological Insulators
Quantum Spin Hall Effect in Graphene
Separable Dual Space Gaussian Pseudo-potentials
Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells
$Z_{2}$ Topological Order and the Quantum Spin Hall Effect
Quantum Spin Hall Insulator State in HgTe Quantum Wells
Maximally-localized generalized Wannier functions for composite energy bands
Topological Insulators in Three Dimensions
Relativistic separable dual-space Gaussian Pseudopotentials from H to Rn
Topological Insulators with Inversion Symmetry
Discovery (theoretical prediction and experimental observation) of a large-gap topological-insulator class with spin-polarized single-Dirac-cone on the surface
A topological Dirac insulator in a quantum spin Hall phase : Experimental observation of first strong topological insulator
Classification of topological insulators and superconductors in three spatial dimensions
Topological invariants of time-reversal-invariant band structures
Periodic table for topological insulators and superconductors
First direct observation of Spin-textures in Topological Insulators : Spin-resolved ARPES as a probe of topological quantum spin Hall effect and Berry's phase
The quantum spin Hall effect and topological insulators
Three dimensional topological invariants for time reversal invariant Hamiltonians and the three dimensional quantum spin Hall effect
Tunable Multifunctional Topological Insulators in Ternary Heusler Compounds
Time Reversal Polarization and a Z_2 Adiabatic Spin Pump
Wannier representation of Z_2 topological insulators
Well-localized edge states in two-dimensional topological insulators: ultrathin Bi films
Half-Heusler Compounds as a New Class of Three-Dimensional Topological Insulators
On the $Z_{2}$ classification of Quantum Spin Hall Models
Quantum spin Hall effect in three dimensional materials: Lattice computation of Z $_{2}$ topological invariants and its application to Bi and Sb
Helical edge and surface states in HgTe quantum wells and bulk insulators
Three-Dimensional Topological Insulators in I-III-VI $_{2}$ and II-IV-V $_{2}$ Chalcopyrite Semiconductors

Cited by in corpus (239)

Maximally localized Wannier functions: Theory and applications
WannierTools: An open-source software package for novel topological materials
Type-II Weyl Semimetals
Two-dimensional materials from high-throughput computational exfoliation of experimentally known compounds
Unique thickness-dependent properties of the van der Waals interlayer antiferromagnet $MnB i_{2} T e_{4}$ films
Prediction of the Weyl semimetal in the orthorhombic MoTe2
Structure-driven intercalated architecture of septuple-atomic-layer $M A_{2} Z_{4}$ family with diverse properties from semiconductor to topological insulator to Ising superconductor
Z2Pack: Numerical Implementation of Hybrid Wannier Centers for Identifying Topological Materials
MoTe2: A Type-II Weyl Topological Metal
Double-Weyl phonons in transition-metal monosilicides
Triple Point Topological Metals
Type-II Dirac fermions in the PtSe $_{2}$ class of transition metal dichalcogenides
A van der Waals antiferromagnetic topological insulator with weak interlayer magnetic coupling
Emergence of non-centrosymmetric topological insulating phase in BiTeI under pressure
Non-Abelian band topology in noninteracting metals
Highly-ordered wide bandgap materials for quantized anomalous Hall and magnetoelectric effects
Weyl semimetals from noncentrosymmetric topological insulators
Generic Wavefunction Description of Fractional Quantum Anomalous Hall States and Fractional Topological Insulators
Topological nodal-line semimetals in alkaline-earth stannides, germanides and silicides
Wannier Center Sheets in Topological Insulators
Topological Materials Discovery from Crystal Symmetry
Robust Type-II Weyl Semimetal Phase in Transition Metal Diphosphides XP $_{2}$ (X = Mo, W)
Topological Quadrupolar Semimetals
Observation of topological states residing at step edges of WTe2
Surfaces of Axion Insulators
Dirac nodal lines and induced spin Hall effect in metallic rutile oxides
High performance Wannier interpolation of Berry curvature and related quantities: WannierBerri code
Wallpaper Fermions and the Nonsymmorphic Dirac Insulator
Computation and data driven discovery of topological phononic materials
Electrically tuneable nonlinear anomalous Hall effect in two-dimensional transition-metal dichalcogenides WTe2 and MoTe2
Large-gap magnetic topological heterostructure formed by subsurface incorporation of a ferromagnetic layer
Topological rainbow trapping for elastic energy harvesting in graded SSH systems
Topological nodal line states and a potential catalyst of hydrogen evolution in the TiSi family
Experimental characterization of fragile topology in an acoustic metamaterial
Possibility of Combining Ferroelectricity and Rashba-like spin splitting in Monolayers of 1T-type Transition-Metal Dichalcogenides MX2
Prediction of a large-gap and switchable Kane-Mele quantum spin Hall insulator
Strain Induced Ferroelectric Topological Insulator
Theory of spin Bott index for quantum spin Hall states in non-periodic systems
Unified bulk-boundary correspondence for band insulators
Black Hole Horizon in a Type-III Dirac Semimetal Zn $_{2}$ In $_{2}$ S $_{5}$
Three-component bosons in TiS, ZrSe and HfTe
Coexisted Three-component Bosons and Two-component Weyl Bosons in TiS, ZrSe and HfTe
Smooth gauge for topological insulators
Topological Dirac States and Pairing Correlations in the Non-Centrosymmetric Superconductor PbTaSe2
Topological Phases in InAs $_{1 - x}$ Sb $_{x}$ : From Novel Topological Semimetal to Majorana Wire
Transition between strong and weak topological insulator in ZrTe $_{5}$ and HfTe $_{5}$
Universal stability of two-dimensional traditional semiconductors
Twofold quadruple Weyl nodes in chiral cubic crystals
Intrinsic axion insulating behavior in antiferromagnetic MnBi $_{6}$ Te $_{10}$
Band structure and unconventional electronic topology of CoSi
Abundance of $Z_{2}$ topological order in exfoliable two-dimensional insulators
Symmetry-Enforced Weyl Phonons
Thickness and electric field dependent polarizability and dielectric constant in phosphorene
Phonons as a platform for non-Abelian braiding and its manifestation in layered silicates
Topological Phases in Cove-Edged and Chevron Graphene Nanoribbons: Geometric Structures, Z2 Invariants, and Junction States
Berry-phase description of Topological Crystalline Insulators
Non-abelian topology of nodal-line rings in $P T$ -symmetric systems
Braiding Majorana corner modes in a second-order topological superconductor
Direct measurement of topological invariants in optical lattices
The Dirac-Weyl semimetal: Coexistence of Dirac and Weyl fermions in polar hexagonal $A B C$ crystals
Topological phonons in oxide perovskites controlled by light
A new paradigm for the quantum spin Hall effect at high temperatures
Four allotropes of semiconducting layered Arsenic which switch into a topological insulator via an electric field: A computational study
Hyperbolic Topological Band Insulators
Machine learning for materials discovery: two-dimensional topological insulators
Topological Bloch oscillations
Prediction of Weyl semimetal, AFM topological insulator, nodal line semimetal, and Chern insulator phases in Bi2MnSe4
First-principles calculation of topological invariants Z2 within the FP-LAPW formalism
Two-Dimensional Inversion Asymmetric Topological Insulators in Functionalized III-Bi Bilayers
Topological magnetic materials of the (MnSb $_{2}$ Te $_{4}$ ) $\cdot$ (Sb $_{2}$ Te $_{3}$ ) $_{n}$ van der Waals compounds family
Real space mapping of topological invariants using artificial neural networks
Crystallographic splitting theorem for band representations and fragile topological photonic crystals
Two Dimensional Antiferromagnetic Chern Insulator NiRuCl6
Modification of electronic, magnetic structure and topological phase of bismuthene by point defects
Intertwined Rashba, Dirac and Weyl Fermions in Hexagonal Hyperferroelectrics
Bulk invariants and topological response in insulators and superconductors with nonsymmorphic symmetries
Strain induced topological phase transitions in monolayer honeycomb structures of group-V binary compounds
Topological phase transitions in (Bi $_{1 - x}$ In $_{x})_{2}$ Se $_{3}$ and (Bi $_{1 - x}$ Sb $_{x})_{2}$ Se $_{3}$
Spin texture on the Fermi surface of tensile strained HgTe
Multiple magnetic topological phases in bulk van der Waals crystal MnSb4Te7
Surface theorem for the Chern-Simons axion coupling
Wannier representation of Floquet topological states
Symmetry Conserving Maximally Projected Wannier Functions
Topological Insulator to Dirac Semimetal Transition Driven by Sign Change of Spin-Orbit Coupling in Thallium Nitride
Electric Field Tunable Topological Phases in Graphene Nanoribbons
Quantum anomalous Hall effect in stable 1T-YN $_{2}$ monolayer with a large nontrivial band gap and high Chern number
Topological flat band, Dirac fermions and quantum spin Hall phase in 2D Archimedean lattices
Group theoretical and topological analysis of the quantum spin Hall effect in silicene
Two-dimensional Topological Ferroelectric Metal with Giant Shift Current
Raman anomalies as signatures of pressure induced electronic topological and structural transitions in black phosphorus: Experiments and Theory
Adiabatic Pumping of Chern-Simons Axion Coupling
Coexistence of New Fermions in Topological Semimetal TaS
Antiferroelectric topological insulators in orthorhombic $A$ MgBi compounds ( $A =$ Li, Na, K)
Prediction of Ideal Topological Semimetals with Triply Degenerate Points in NaCu $_{3}$ Te $_{2}$ Family
Design and realization of topological Dirac fermions on a triangular lattice
The magnetic, electronic, and light-induced topological properties in two-dimensional hexagonal FeX2 (X = Cl, Br, I) monolayers
Alloy engineering of topological semimetal phase transition in MgTa $_{2 - x}$ Nb $_{x}$ N $_{3}$
Pressure-induced topological phase transition in polar semiconductor BiTeBr
Modern theory of magnetic breakdown
Effect of Strong Disorder in a 3-Dimensional Topological Insulator: Phase Diagram and Maps of the Z2 Invariant
Phonon-induced renormalization of electron wave functions
$Z_{2}$ invariants of topological insulators as geometric obstructions
High-throughput Discovery of Topologically Non-trivial Materials using Spin-orbit Spillage
Cubic 3D Chern photonic insulators with orientable large Chern vectors
Dirac semimetal phase in the hexagonal LiZnBi
Surface polarization and edge charges
Smooth gauge and Wannier functions for topological band structures in arbitrary dimensions
Domain wall induced spin-polarized flat bands in antiferromagnetic topological insulators
Recipe for single-pair-Weyl-points phonons carrying the same chiral charges
Quantum electronic transport of topological surface states in beta-Ag2Se nanowire
Temperature dependence of the bulk Rashba splitting in the bismuth tellurohalides
Topological fate of edge states of Bi single bilayer on Bi(111)
Unconventional spin texture in a non-centrosymmetric quantum spin Hall insulator
Designing 3D topological insulators by 2D-Xene (X = Ge, Sn) sheet functionalization in the GaGeTe-type structures
Transforming common III-V and II-VI semiconductor compounds into topological heterostructures: The case of CdTe/InSb superlattices
Three-dimensional topological insulators: A review on host materials
Construction of real-valued localized composite Wannier functions for insulators
Structural and electronic properties of realistic two-dimensional amorphous topological insulators
Semi-Dirac and Weyl Fermions in Transition Metal Oxides
The Wannier Function Software Ecosystem for Materials Simulations
Two different topological insulator phases in NaBaBi
Towards Topological Quasi-Freestanding Stanene via Substrate Engineering
Accurate high-throughput screening of I-II-V 8-electron Half-Heusler compounds for renewable-energy applications
First-principles study of electric-field-induced topological phase transition in one-bilayer Bi(111)
Observation of possible excitonic charge density waves and metal-insulator transitions in atomically thin semimetals
Twist-resilient and robust ferroelectric quantum spin Hall insulators driven by van der Waals interactions
Perovskite ThTaN3: a Large Thermopower Topological Crystalline Insulator
Spin-orbit spillage as a measure of band inversion in insulators
Triple point semimetal and topological phase transitions in NaCu $_{3}$ Te $_{2}$
Noncentrosymmetric topological Dirac semimetals in three dimensions
Realization of the Chern insulator and Axion insulator phases in antiferromagnetic $M n T e$ - $B i_{2} (S e, T e)_{3}$ - $M n T e$ heterostructures
Wannier Function Methods for Topological Modes in 1D Photonic Crystals
Pressure-Induced Topological Phase Transitions in CdGeSb $_{2}$ and CdSnSb $_{2}$
Gauge-discontinuity contributions to Chern-Simons orbital magnetoelectric coupling
Topologically-protected metallic states induced by a one-dimensional extended defect in a 2D topological insulator
Coexistence of Triple Nodal Points, Nodal Links, and Unusual Flat Bands in intermetallic $A$ Pd $_{3}$ ( $A$ =Pb, Sn)
Electrically switchable giant Berry curvature dipole in silicene, germanene and stanene
New Group V Elemental Bilayers: A Tunable Structure Model with 4,6,8-atom Rings
Universal higher-order bulk-boundary correspondence of triple nodal points
Compactly Supported Wannier Functions and Strictly Local Projectors
Dual Topological Insulator Device with Disorder Robustness
Gallium Bismuth Halides GaBi-X2 (X= I, Br, Cl) Monolayers with Distorted Hexagonal Framework: Novel Room-Temperature Quantum Spin Hall Insulators
Temperature dependence of the topological phase transition of BiTeI from first principles
Organizing symmetry-protected topological phases by layering and symmetry reduction: a minimalist perspective
Detection of topological phase transitions through entropy measurements: the case of germanene
Efficient method to compute $Z_{4}$ -indices with glide symmetry and applications to Möbius materials, $CeNiSn$ and $UCoGe$
Electronic properties of topological insulator candidate CaAgAs
Structural disorder-driven topological phase transition in noncentrosymmetric BiTeI
The interplay between structural, magnetic and electronic states in the pyrochlore iridate Eu2Ir2O7
Emergence of topological electronic phases in elemental lithium under pressure
Quantum spin Hall effect in rutile-based oxide multilayers
Symmetry-protected metallic and topological phases in penta-materials
Switchable large-gap quantum spin Hall state in two-dimensional MSi $_{2}$ Z $_{4}$ materials class
Superconductivity in PtPb $_{4}$ with Possible Nontrivial Band Topology
Impurity induced topological phase transitions in Cd $_{3}$ As $_{2}$ and Na $_{3}$ Bi Dirac semimetals
Two-dimensional Janus Si dichalcogenides: A first-principles study
Tunable Topology and Berry Curvature Dipole in Transition Metal Dichalcogenide Janus Monolayers
2D and 3D topological phases in BiTe $X$ compounds
Honeycomb-Lattice Mott insulator on Tantalum Disulphide
Emergent topological quantum orbits in the charge density wave phase of kagome metal CsV $_{3}$ Sb $_{5}$
Ferroelectric tuning of superconductivity and band topology in a two-dimensional heterobilayer
Noncentrosymmetric compensated half-metal hosting pure spin Weyl nodes, triple nodal points, nodal loops, and nexus fermions
Interlayer Exchange Interaction Driven Topological Phase Transition in Antiferromagnetic Electride Gd $_{2}$ O
Topological Properties of Bulk and Bilayer 2M WS $_{2}$ : A First-Principles Study
Single-point spin Chern number in a supercell framework
Topological phonon analysis of the 2D buckled honeycomb lattice: an application to real materials
Existence and computation of generalized Wannier functions for non-periodic systems in two dimensions and higher
Multiple topological Dirac cones in a mixed-valent Kondo semimetal: g-SmS
Intertwined non-trivial band topology and giant Rashba spin splitting
Weak Antilocalization and topological edge states in PdSn $_{4}$
Real-space Obstruction in Quantum Spin Hall Insulators
Topologically distinct atomic insulators
Large Magnetoresistance in Topological Insulator Candidate TaSe3
The Iterated Projected Position Algorithm for Constructing Exponentially Localized Generalized Wannier Functions for Periodic and Non-Periodic Insulators in Two Dimensions and Higher
A real-space many-body marker for correlated $Z_{2}$ topological insulators
Theory of local $Z_{2}$ topological markers for finite and periodic two-dimensional systems
Tunable topological edge modes in Su-Schrieffer-Heeger arrays
Structural phase transition in monolayer gold(I) telluride: From a room-temperature topologicalinsulator to an auxetic semiconductor
High-throughput screening of Weyl semimetals
Topological phase in non-centrosymmetric material NaSnBi
Topological Phase Transition Coupled with Spin-Valley Physics in Ferroelectric Oxide Heterostructures
Strain-induced topological phase transition at (111) SrTiO $_{3}$ -based heterostructures
Tunable bulk photovoltaic effect in strained $γ$ -GeSe
Topological phase in oxidized zigzag stanene nanoribbons
WloopPHI: A tool for ab initio characterization of Weyl semimetals
Entropy Signatures of Topological Phase Transitions
Topological superconductor candidates PdBi $_{2}$ Te $_{4}$ and PdBi $_{2}$ Te $_{5}$ from a generic ab initio strategy
Quantum computing topological invariants of two-dimensional quantum matter
Strain-Induced Charge Density Waves with Emergent Topological States in Monolayer NbSe2
Quantum Spin Hall Effect and Su-Schrieffer-Heeger Model Implementation in Novel C3N-based Dumbbell Morphologies
BerryEasy: A GPU enabled python package for diagnosis of nth-order and spin-resolved topology in the presence of fields and effects
Entanglement Chern number for three-dimensional topological insulators: Characterization by Weyl points of entanglement Hamiltonians
Gate field effects on the topological insulator BiSbTeSe2 interface
Gate-tunable imbalanced Kane-Mele model in encapsulated bilayer jacutingaite
Atomic-ordering-induced quantum phase transition between topological crystalline insulator and Z2 topological insulator
Effect of the external fields in high Chern number quantum anomalous Hall insulators
Topological insulator on honeycomb lattices and ribbons without inversion symmetry
Superconductivity in a Topological Lattice Model with Strong Repulsion
Epitaxial binding and strain effects of monolayer stanene on the Al $_{2}$ O $_{3}$ (0001) surface
RKKY interactions mediated by topological states in transition metal doped bismuthene
ZrOsSi: A $Z_{2}$ topological metal with a superconducting ground state
A complementary screening for quantum spin Hall insulators in 2D exfoliable materials
Piezoelectric quantum spin Hall insulator VCClBr monolayer with pure out-of-plane piezoelectric response
Topological theory of inversion-breaking charge-density-wave monolayer 1\textit{T}-TiSe $_{2}$
Anion-Anion Bonding and the Topology in Ternary Iridium Seleno-Stannides
Topological insulating phase arising in transition metal dichalcogenide alloy
SrPd, a candidate material with extremely large magnetoresistance
Topological phases in $α$ -Li $_{3}$ N-type crystal structure of light-element compounds
Recipe for higher-order topology on the triangular lattice
Tailoring topological states in silicene using different halogen-passivated Si(111) substrates
Robustness of topological states to lattice instability in non-symmorphic topological insulator KHgSb
Quantized thermal and spin transports of dirty planar topological superconductors
Ideal Spin-Orbit-Free Dirac Semimetal and Diverse Topological Transitions in Pr $_{8}$ CoGa $_{3}$ Family
A phase diagram for band inversion of topological materials as a function of interactions between two involved bands
An anomalous band inversion protected by symmetry in a topological insulator of the Kane-Mele model
The effects of dissipation on topological mechanical systems
Noncentrosymmetric two-dimensional Weyl semimetals in porous Si/Ge structures
Mapping rules from nodal line semimetal to topological crystalline insulator in face centered cubic lattice
Nonlinear bulk photocurrent probe Z2 topological phase transition
On quasi-nodal spheres and the spin Hall effect: the case of YH3 and CaTe
Layer dependent topological phases and transitions in TaRhTe $_{4}$ : From monolayer and bilayer to bulk
Transitions in Xenes between excitonic, topological and trivial insulator phases: influence of screening, band dispersion and external electric field
Surface Reconstructions in Thin-Films of Magnetic Topological Insulator MnBi $_{2}$ Te $_{4}$
Topological insulators and geometry of vector bundles
Topological charge and spin pumping in a semiconductor nanowire
A Unified View of Topological Phase Transition in Band Theory
TopologicalNumbers.jl: A Julia package for topological number computation
Wannier Center Analysis on Possible Three-Dimensional Topological Phases in α-Type Layered Organic Conductors
Pressure-induced Superconductivity in Noncentrosymmetric Weyl Semimetals LaAlX (X = Si and Ge)
Dirac topological insulator in the d $_{z^{2}}$ manifold of a honeycomb oxide
Panoply of Ni-Doping-Induced Reconstructions, Electronic Phases, and Ferroelectricity in 1T-MoS $_{2}$
A first-principles investigation of Topological Phase Transition in face-centred cubic LiMgBi
Kagome edge states under lattice termination, spin-orbit coupling, and magnetic order
Hinge modes of three-dimensional Euler insulators
Shaping Maximally Localized Wannier Functions via Discrete Adiabatic Transport
Quantized Spin Hall Effect in Three-Dimensional Nodal-Ring Semimetal: Geometric Scaling and Symmetry-Engineered Spin Response
Systematic study for two-dimensional $Z_{2}$ topological phase transitions at high-symmetry points in all layer groups
Non-Trivial Topological Phase in the Sn_{1-x}In_xTe Superconductor
Glide-resolved photoemission spectroscopy: Measuring topological invariants in nonsymmorphic space groups