Model Hamiltonian for Topological Insulators

Abstract

In this paper we give the full microscopic derivation of the model Hamiltonian for the three dimensional topological insulators in the $B{i}_{2}S{e}_3$ family of materials ($B{i}_{2}S{e}_3$, $B{i}_{2}T{e}_3$ and $S{b}_{2}T{e}_3$). We first give a physical picture to understand the electronic structure by analyzing atomic orbitals and applying symmetry principles. Subsequently, we give the full microscopic derivation of the model Hamiltonian introduced by Zhang {\it et al} [\onlinecite{zhang2009}] based both on symmetry principles and the $\mathbf{k}\cdot \mathbf{p}$ perturbation theory. Two different types of $k^3$ terms, which break the in-plane full rotation symmetry down to three fold rotation symmetry, are taken into account. Effective Hamiltonian is derived for the topological surface states. Both the bulk and the surface models are investigated in the presence of an external magnetic field, and the associated Landau level structure is presented. For more quantitative fitting to the first principle calculations, we also present a new model Hamiltonian including eight energy bands.

18 pages, 9 figures, 5 tables

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• Gap Generation in Topological Insulator Surface States by non-Ferromagnetic Magnets
• Strong interband Faraday rotation in 3D topological insulator Bi2Se3
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• Landau level spectroscopy of Bi${}_2$Te${}_3$
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• Controversy over large proximity induced s wave like pairing from a d wave superconductor
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• Topological insulators in random potentials
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• Three-dimensional Topological Insulators and Bosonization
• Spin-orbit torques from topological insulator surface states: Effect of extrinsic spin-orbit scattering on an out-of-plane magnetization
• Geometrically induced electric polarization in conical topological insulators
• Dynamical density and spin response of Fermi arcs and their consequences for Weyl semimetals
• Fulde-Ferrell States in Inverse Proximity Coupled Magnetically-Doped Topological Heterostructures
• Non-linear antidamping spin-orbit torque originating from intra-band transport on the warped surface of a topological insulator
• Manipulating topological-insulator properties using quantum confinement
• Temperature Induced Spin Density Wave in Magnetic Doped Topological Insulators
• Impurity scattering in the bulk of topological insulators
• Ta2NiSe5: a candidate topological excitonic insulator with multiple band inversions
• Spin Conduction in Anisotropic 3-D Topological Insulators
• Surface-state spin textures in strained bulk HgTe: strain-induced topological phase transitions
• Topological Magnetoelectric Response in Ferromagnetic Axion Insulators
• Edelstein and inverse Edelstein effects caused by the pristine surface states of topological insulators
• Current amplification and relaxation in Dirac systems
• Fermiology of possible topological superconductor Tl0.5Bi2Te3 derived from hole-doped topological insulator
• Emergent Momentum-Space Skyrmion Texture on the Surface of Topological Insulators
• Strain-enhanced optical absorbance of topological insulator films
• Interacting weak topological insulators and their transition to Dirac semimetal phases
• Anomalous Magneto Optic Effects from an Antiferromagnet Topological-Insulator Heterostructure
• Quantum Interference Effects in Topological Nanowires In a Longitudinal Magnetic Field
• Crossed Andreev reflection in topological insulator nanowire T-junctions
• Nematic superconductivity in topological insulators induced by hexagonal warping
• Influence of magnetic disorders on Quantum Anomalous Hall Effect in Magnetic Topological Insulator Films beyond the two-dimensional limit
• Intrinsic torque on the orbital angular momentum in an electric field
• Anisotropic magnetotransport in Dirac-Weyl magnetic junctions
• Dirac Electrons on a Sharply Edged Surface of Topological Insulators
• Spin-spin interaction in the bulk of topological insulators
• Effective low energy theory for surface Andreev bound states of superconducting phases in generalized Bernevig-Hughes-Zhang models
• Phonon-induced rotation of the electronic nematic director in superconducting Bi${}_2$Se${}_3$
• Quantum geometrical properties of topological materials
• Superconducting proximity effect on a two-dimensional Dirac electron system
• Hybrid-order topology in unconventional magnets of Eu-based Zintl compounds with surface-dependent quantum geometry
• Finite-size effects in cylindrical topological insulators
• Gapless interface states at the junction between two topological insulators
• Confining electrons on a topological insulator surface using potentials and a magnetic field
• A Dirac-fermion approach and its application to design high Chern numbers in magnetic topological insulator multilayers
• Majorana fermions in topological insulator nanowires: from single superconducting nanowires to Josephson junctions
• Robustness of Gapless Interface State in a Junction of Two Topological Insulators
• DFT2kp: effective kp models from ab-initio data
• Appearance of flat surface bands in three-dimensional topological insulators in a ferromagnetic exchange field
• Spin torque and persistent currents caused by percolation of topological surface states
• Persistence of symmetry-protected Dirac points at the surface of the topological crystalline insulator SnTe upon impurity doping
• Magnetization of the Metallic Surface States in Topological Insulators
• Absence of helical surface states in bulk semimetals with broken inversion symmetry
• Shadow surface states in topological Kondo insulators
• Analytical Solutions for the Surface States of Bi${}_{1-x}$Sb${}_x$ ($0\le x\lesssim 0.1$)
• Surface states in Dirac metals and topological crystalline insulators
• Influences of spin-orbit coupling on Fermi surfaces and Dirac cones in ferroelectric-like polar metals
• Thin film of a topological insulator as a spin Hall insulator
• Influence of chirp and carrier-envelope phase on non-integer high-harmonic generation
• Superconductivity in Cu-doped Bi${}_2$Se${}_3$ with potential disorder
• Cherenkov sound on a surface of a topological insulator
• Effective model for massless Dirac electrons on a surface of weak topological insulators
• Phase diagram and phonon-induced backscattering in topological insulator nanowires
• Protection of the surface states in topological insulators: Berry phase perspective
• Unconventional optical selection rules in ZrTe5 under an in-plane magnetic field
• A Numerical Study of the Superconducting Proximity Effect in Topological Surface States
• Exceptional Dirac states in a non-centrosymmetric superconductor, BiPd
• Strong correlations at topological insulator surfaces and the breakdown of the bulk-boundary correspondence
• Disorder-Induced Topological Transitions in a Multilayer Topological Insulator
• High-performance nanoscale topological energy transduction
• Dielectric capping effects on binary and ternary topological insulator surface states
• Metallic Quantized Anomalous Hall Effect without Chiral Edge States
• Low power In Memory Computation with Reciprocal Ferromagnet/Topological Insulator Heterostructures
• Electronic properties of one-dimensional nanostructures of the Bi${}_2$Se${}_3$ topological insulator
• Building topological device through emerging robust helical surface states
• Plasmon modes in the magnetically doped Single Layer and Multilayers of Helical Metals
• Anomalous thermoelectric properties of a Floquet topological insulator with spin momentum non-orthogonality
• Topological Excitonic Superfluids in Three Dimensions
• Ballistic transport in disordered Dirac and Weyl semimetals
• Transport in Selectively Magnetically Doped Topological Insulator Wires
• Impurity Effects on Superconductivity on Surfaces of Topological Insulators
• Universally optimizable strategy for magnetic gaps towards high-temperature quantum anomalous Hall states via magnetic-insulator/topological-insulator building-blocks
• Effective Hamiltonian for surface states of topological insulator nanotubes
• Anomalous Nernst effect on a magnetically-doped topological insulator surface: A Green's function approach
• Ultrahigh magnetic field spectroscopy reveals the band structure of the 3D topological insulator Bi${}_2$Se${}_3$
• Orbit topology analysed from $\pi$ phase shift of magnetic quantum oscillations in three-dimensional Dirac semimetal
• The influence of proximity induced ferromagnetism, superconductivity and Fermi-velocity on evolution of Berry phase in Bi${}_2$Se${}_3$ topological insulator
• Soft Modes and Nonanalyticities in a Clean Dirac Metal
• Tuning topology in thin films of topological insulators by strain gradients
• Designer topological insulator with enhanced gap and suppressed bulk conduction in Bi2Se3/Sb2Te3 ultra-short period superlattices
• Strong magneto-optical effects due to surface states in three-dimensional topological insulators
• Lifshitz transition in dirty nematic superconductor
• Proximity induced ferromagnetism, superconductivity, and finite-size effects on the surface and edge states of topological insulator nanostructures
• Quasiparticle interference in doped topological insulators with nematic superconductivity
• BaHgSn: A Dirac semimetal with surface hourglass fermions
• Topological contribution to magnetism in the Kane-Mele model: An explicit wave function approach
• Effect of the external fields in high Chern number quantum anomalous Hall insulators
• Three-Dimensional Quantum Anomalous Hall Effect in Magnetic Topological Insulator Trilayers of Hundred-Nanometer Thickness
• Symmetry-driven anisotropic coupling effect in antiferromagnetic topological insulator: Mechanism for high-Chern-number quantum anomalous Hall state
• Interplay between spin-orbit coupling and crystal-field effect in topological insulators
• Opacity of graphene independent of light frequency and polarization due to the topological charge of the Dirac points
• Skyrmion nucleation on the surface of a topological insulator
• Giant orbital Hall effect due to the bulk states of 3D topological insulators
• Low-energy modeling of three-dimensional topological insulator nanostructures
• Pseudo-Spin, Real-Spin and Spin Polarization of Photo-emitted Electrons
• Anisotropic Fabry-Pérot resonant states confined within nano-steps on the topological insulator surface
• Phase diagram of a magnetic topological nodal semimetal: Stable nodal line in an easy-plane ferromagnet
• Fabry-Pérot interferometry with gate-tunable 3D topological insulator nanowires
• Probing embedded topological modes in bulk-like GeTe-Sb${}_2$Te${}_3$ heterostructures
• Topological superconductivity in an ultrathin, magnetically-doped topological insulator proximity coupled to a conventional superconductor
• A programmable $k\cdot p$ Hamiltonian method and application to magnetic topological insulator MnBi${}_2$Te${}_4$
• Dissipationless Spin-Charge Conversion in Excitonic Pseudospin Superfluid
• Exotic surface states in hybrid structures of topological insulators and Weyl semimetals
• Pauli paramagnetism of triplet Cooper pairs in a nematic superconductor
• Spin Stiffness and Domain Walls in Dirac-Electron Mediated Magnets
• Transport in a thin topological insulator with potential and magnetic barriers
• Geometric Effect on Quantum Anomalous Hall States in Magnetic Topological Insulators
• Spontaneous Formation of Exceptional Points at the Onset of Magnetism
• Bound states and controllable currents on Topological Insulator surfaces with extended magnetic defects
• Chiral edge state coupling theory of transport in quantum anomalous Hall insulators
• Corner states of two-dimensional second-order topological insulators with a chiral symmetry and broken time reversal and charge conjugation
• Higher-order topological superconductor phases in a multilayer system
• Transport signatures of surface potentials on three-dimensional topological insulators
• Superconducting quantum spin-Hall systems with giant orbital g-factors
• Low temperature thermal transport at the interface of a topological insulator and a d-wave superconductor
• Manipulating quantum channels in weak topological insulator nanoarchitectures
• Dual topological insulator with mirror symmetry protected helical edge states
• Three-dimensional symmetry breaking topological matters
• The Fractional Quantum Hall Effect of Tachyons in a Topological Insulator Junction
• A-geometrical approach to Topological Insulators with defects
• Landau quantization in tilted Weyl semimetals with broken symmetry
• Ab initio k.p theory of spin-momentum locking: Application to topological surface states
• Field induced charge symmetry in topological insulator Bi${}_2$Te${}_3$ revealed by nuclear magnetic resonance
• Collective excitations of a system of coupled relativistic and non-relativistic two-dimensional electron gases
• Magnetic scattering with spin-momentum locking: Single scatterers and diffraction grating
• Topological Descendants of Multicritical EuTl2
• Spontaneous symmetry breaking and quantum Hall valley ordering on the surface of topological hexaborides
• Topological properties of finite-size heterostructures of magnetic topological insulators and superconductors
• Resistively detected NMR as a probe of the topological nature of conducting edge/surface states
• Torque field and skyrmion movement by spin transfer torque in a quasi-2d interface in presence of strong spin-orbit interaction
• In the Pursuit of Majorana Modes in Iron-based High-$T_c$ Superconductors
• Dirac Wire
• Anomalous Decay of Quantum Resistance Oscillations of Two Dimensional Helical Electrons in Magnetic Field
• Visualizing Pairing Symmetry in Nematic Superconductors using spin-polarized spectroscopy of magnetic impurities
• Magnetic Quantum Phase Transitions in a Clean Dirac Metal
• Electrically tunable high-Chern-number quasiflat bands in twisted antiferromagnetic topological insulators
• Berry phases and zero-modes in toroidal topological insulator
• Electric polarization in magnetic topological nodal semimetal thin films
• Magnetoexcitons and optical absorption of bilayer-structured topological insulators
• Topological insulators on fractal lattices: A general principle of construction
• A thermodynamic measure of the Magneto-electric coupling in the 3D topological insulator
• Odd-frequency pairs and anomalous proximity effect in nematic and chiral states of superconducting topological insulators
• Optical Berry Curvature of Hinge State and Its Detection
• Surface Spectral Function of Momentum-dependent Pairing Potentials in a Topological Insulator: Application to Cu${}_x$Bi${}_2$Se${}_3$
• Refined Majorana phase diagram in topological insulator-superconductor hybrid system
• Magnetic Field Induced Quantum Metric Dipole in Dirac Semimetal Cd3As2
• Model non-Hermitian topological operators without skin effect: A general principle of construction
• Disorder-induced density of states on the surface of a spherical topological insulator
• A Green's function approach to Topological Insulator junctions with magnetic and superconducting regions
• Direct topological insulator transitions in three dimensions are destabilized by non-perturbative effects of disorder
• Collective excitations in magnetic topological insulators and axion dark matter search
• Effective Hamiltonian for surface states of \ce{Bi2Te3} nanocylinders with hexagonal warping
• Spin-orbit torques due to topological insulator surface states: an in-plane magnetization as a probe of extrinsic spin-orbit scattering
• Strong-coupling superconductivity near Gross-Neveu quantum criticality in Dirac systems
• Inter-surface interaction via phonon in three-dimensional topological insulator
• Hybrid symmetry class topological insulators
• High-Chern-number Quantum anomalous Hall insulators in mixing-stacked MnBi${}_2$Te${}_4$ thin films
• Spin accumulation in disordered topological insulator thin films
• Conductance asymmetry in proximitized magnetic topological insulator junctions with Majorana modes
• Exact solution of the Schrödinger equation for an hydrogen atom at the interface between the vacuum and a topologically insulating surface
• Topology-insensitive axion mass in magnetic topological insulators
• Enhanced and stable spin Hall conductivity in a disordered time-reversal and inversion symmetry broken topological insulator thin film
• Magnetic torque oscillations from warped helical surface states in topological insulators
• Concurrence of topological electrons and magnons in the Kagome ferromagnet CoCu3(OH)6Cl2
• Quantum Anomalous Hall Effect in Three-dimensional Topological Insulator/Thin-film Ferromagnetic Metal Bilayer Structure
• High-field charge transport on the surface of Bi${}_2$Se${}_3$
• Anisotropic planar Hall effects in Bi${}_2$Se${}_3$/EuS interfaces: Deciphering the role of proximity induced spin canting and topological spin texture
• Pseudospin-valve effect on transport in junctions of three-dimensional topological insulator surfaces
• Optimizing proximitized magnetic topological insulator nanoribbons for Majorana bound states
• Hexagonal warping effect to Majorana zero modes at ends of superconducting vortex line in doped 3D strong topological insulators
• Unidirectional magneto-transport of linearly dispersing topological edge states
• Inter-quintuple layer coupling and topological phase transitions in the chalcogenide topological insulators
• Quantum-anomalous-Hall current patterns and interference in thin slabs of chiral topological superconductors
• Interlayer Coupling-Induced Quantum Phase Transition in Quantum Anomalous Hall Multilayers
• Nonequilibrium topological spin textures in momentum space
• Role of effective mass anisotropy in realizing a hybrid nodal-line fermion state
• Non-Abelian operation through scattering between chiral Dirac edge modes
• Cyclotron Resonance in Topological Insulators: Non-Relativistic Effects
• Dyadic Greens function for a topological insulator stratified sphere
• Possible two-component pairings in electron-doped Bi${}_2$Se${}_3$ based on a tight-binding model
• Anomalous Linear and Quadratic Nodeless Surface Dirac Cones in Three-Dimensional Dirac Semimetals
• Anomalous Behaviour in the Magneto-Optics of a Gapped Topological Insulator
• Particle-hole asymmetry and quantum confinement effects on the magneto-optical response of topological insulator thin-films
• Influence of Dielectric Environment on Role of Spin-Orbit Interaction for Image Potentials
• Gate-controlled Spin Extraction from Topological Insulator Surfaces
• Superconductivity in doped planar Dirac insulators: A renormalization group study
• Reconstructing the wavefunction of magnetic topological insulators MnBi2Te4 and MnBi4Te7 using spin-resolved photoemission
• Bulk spin conductivity of three-dimensional topological insulator
• Quasiparticle scattering in three-dimensional topological insulators near the thickness limit
• Hard wall edge confinement in 2D topological insulators and the energy of the Dirac Point
• Rotating Majorana Zero Modes in a disk geometry
• Diffusion at the Surface of Topological Insulators
• Engineering Dirac electrons emergent on the surface of a topological insulator
• Spin-Hall conductivity and optical characteristics of noncentrosymmetric quantum spin Hall insulators: the case of PbBiI
• Shear Modulus Anomaly of Unconventional Superconductor in a Symmetry Breaking Field
• Odd-parity longitudinal magnetoconductivity in time-reversal symmetry broken materials
• Theoretical investigation of the applicability of the Meservey-Tedrow technique to the surface states of topological insulators
• Magnetic-flux tunable electronic transport through domain walls in a three-dimensional second-order topological insulator
• Emergent Weyl-like points in periodically modulated systems
• 3D Non-Abelian Anyons: Degeneracy Splitting and Detection by Adiabatic Cooling
• Anderson Impurities In Edge States with Nonlinear and Dissipative Perturbations
• Non-Lifshitz invariants corrections to Dzyaloshinskii-Moriya interaction energy
• Scattering states of a vortex in the proximity-induced superconducting state at the interface of a topological insulator and an s-wave superconductor
• Interaction between spin and Abrikosov vortices in doped topological insulators
• Reentrant topological phase in half-Heusler compounds
• Dirac plasmon polaritons and magnetic modes in topological-insulator nanoparticles
• Superconductivity in three-dimensional interacting doped topological insulators
• Anomalous Josephson Hall effect in doped topological insulators with the nematic superconductivity
• Magneto-transport evidence for strong topological insulator phase in ZrTe5
• Charge qubits based on ultra-thin topological insulator films
• Intrinsic chiral topological superconductor thin films
• Spinor-dominated magnetoresistance driven by the topological phase transition in $\beta$-Ag${}_2$Se
• Landau levels on a surface of weak topological insulators
• Variety of scenarios of the magnetic exchange response in topological insulators
• Tunable Fano and Dicke effects in quantum transport of double quantum dots sandwiched between topological insulators
• Unconventional superconductivity from electronic dipole fluctuations
• Anisotropic transport properties in prismatic topological insulator nanowires
• Coherent suppression and dephasing-induced reentrance of high harmonics in gapped Dirac materials
• Critical behavior of Anderson transitions in higher dimensional Bogoliubov-de Gennes symmetry classes
• Aharanov-Bohm oscillations and perfectly transmitted mode in amorphous topological insulator nanowires
• Pairing around a Single Dirac Point: A Unifying View of Kohn-Luttinger Superconductivity in Chern Bands, Quarter Metals, and Topological Surface States
• Weak topological insulators with step edges: Subband engineering and its effect on electron transport
• Determination of Out-of-plane Spin Polarization of Topological Surface States by Spin Hall Effect Tunneling Spectroscopy
• Anisotropy of the spin Hall effect in a Dirac ferromagnet
• Exact solutions for topological surface states of three-dimensional lattice models
• Enhanced detection of circularly polarized photons with topological materials
• Granular topological insulators
• Microscopic theory of electrically induced spin torques in magnetic Weyl semimetals
• Correlated phases of moat-band excitons in two dimensions
• Electrostatic gating and the interference of chiral Majoranas in thin slabs of magnetic topological insulators
• Signatures of Fractional Quantum Hall States in Topological Insulators
• Simple model for the gap in the surface states of the antiferromagnetic topological insulator MnBi${}_2$Te${}_4$
• Position operators and interband matrix elements of scalar and vector potentials in the 8-band Kane model
• Self-Consistent Model for Gate Control of Narrow-, Broken-, and Inverted-Gap (Topological) Heterostructures
• Theoretical study of X-ray absorption of three-dimensional topological insulator ${\mathrm{Bi}}_2{\mathrm{Se}}_3$
• Theory of topological insulator waveguides: polarization control and the enhancement of the magneto-electric effect
• Super-resonant transport of topological surface states subjected to in-plane magnetic fields
• Crystalline topological states at a topological insulator junction
• High Chern number phase in topological insulator multilayer structures: a Dirac cone model study
• Magnetoresistance from time-reversal symmetry breaking in topological materials
• Current response of a topological insulator to a static Zeeman field
• Modeling and Simulation of Spin Transfer Torque Generated at Topological Insulator/Ferromagnetic Heterostructure
• Non-unique connection between bulk topological invariants and surface physics
• Sensitivity of superconducting states to the impurity location in layered materials
• The focusing effect of electron flow and negative refraction in three dimensional topological insulators
• Hearing the shape of a Dirac drum: Dual quantum Hall states on curved surfaces
• Surface states of gapped electron systems and semi-metals
• Multiband quasiparticle interference in the topological insulator Cu_(x)Bi_(2)Te_(3)
• Time-reversal invariant resonant backscattering on a topological insulator surface driven by a time-periodic gate voltage
• Magnetic-Field Tunable Möbius and Higher-Order Topological Insulators in Three-Dimensional Layered Octagonal Quasicrystals
• Tunable spin-charge conversion in class-I topological Dirac semimetals
• Tunable Dual-Type Weyl Points in Dirac-Weyl Semimetal CaAgBi