Hexagonal Warping Effects in the Surface States of Topological Insulator Bi${}_2$Te${}_3$

Abstract

A single two-dimensinoal Dirac fermion state has been recently observed on the surface of topological insulator Bi${}_2$Te${}_3$ by angle-resolved photoemission spectroscopy (ARPES). We study the surface band structure using $k\cdot p$ theory and find an unconventional hexagonal warping term, which is the counterpart of cubic Dresselhaus spin-orbit coupling in rhombohedral structures. We show that this hexagonal warping term naturally explains the observed hexagonal snow-flake Fermi surface. The strength of hexagonal warping is characterized by a single parameter, which is extracted from the size of the Fermi surface. We predict a number of testable signatures of hexagonal warping in spectroscopy experiments on Bi${}_2$Te${}_3$. We also explore the possibility of a spin-density wave due to strong nesting of the Fermi surface.

4 pages, 3 figures, published version

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Cited by in corpus (423)

• Topological Insulators
• Topological insulators and superconductors
• Topological Insulator Materials
• Colloquium: Topological Band Theory
• Dirac materials
• Model Hamiltonian for Topological Insulators
• A topological crystalline insulator (TCI) phase via topological phase transition and crystalline mirror symmetry
• Experimental realization of an intrinsic magnetic topological insulator
• Three-Dimensional Topological Insulators
• Electronic structure of quantum materials studied by angle-resolved photoemission spectroscopy
• STM imaging of electronic waves on the surface of Bi${}_2$Te${}_3$: topologically protected surface states and hexagonal warping effects
• Floquet topological insulators
• Coexistence of the topological state and a two-dimensional electron gas on the surface of Bi2Se3
• Spin Polarization and Transport of Surface States in the Topological Insulators Bi2Se3 and Bi2Te3 from First Principles
• Observation of topological order in a Superconducting doped topological insulator (based on the Bi2Se3 class)
• Ambipolar Field Effect in Topological Insulator Nanoplates of (BixSb1-x)2Te3
• Hedgehog Spin-texture and Berry's Phase tuning in a Magnetic Topological Insulator
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• Model for Metal-Insulator Transition in Graphene Superlattices and Beyond
• Emergent quantum confinement at topological insulator surfaces
• Large magnetic gap at the Dirac point in a Mn-induced Bi${}_2$Te${}_3$ heterostructure
• A van der Waals antiferromagnetic topological insulator with weak interlayer magnetic coupling
• Electrically controllable surface magnetism on the surface of topological insulator
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• Observation of Single Dirac Cone Topological Surface State in Compounds TlBiTe2 and TlBiSe2 from a New Topological Insulator Family
• Photoemission Spectroscopy of Magnetic and Non-magnetic Impurities on the Surface of the Bi${}_2$Se${}_3$ Topological Insulator
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• Observation of Chiral Surface Excitons in a Topological Insulator Bi${}_2$Se${}_3$
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• Density Functional Study of Ternary Topological Insulator Thin Films
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• Quantum critical points of Helical Fermi Liquids
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• Theory of current-driven dynamics of spin textures on a surface of topological insulators
• Strain-driven nematicity of the odd-parity superconductivity in Sr${}_x$Bi${}_2$Se${}_3$
• Hexagonal warping on spin texture, Hall conductivity and circular dichroism of Topological Insulator
• Observation of surface states on heavily indium doped SnTe(111), a superconducting topological crystalline insulator
• Observation of Planar Hall Effect in Topological Insulator -- Bi${}_2$Te${}_3$
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• Calculation of divergent photon absorption in ultrathin films of a topological insulator
• Electrically tunable spin polarization of chiral edge modes in a quantum anomalous Hall insulator
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• Quantized and half-quantized Anomalous Hall effect induced by in-plane magnetic field
• Dirac cone engineering in Bi${}_2$Se${}_3$ thin films
• Spin-textures, Berry's phase and Quasiparticle Interference in Bi2Te3: A Topological Insulator with Warped Surface States
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• Unoccupied topological surface state in Bi${}_2$Te${}_2$Se
• Direct Evidence for Time-Reversal Symmetry Breaking in Topological Superconductor Sr0.1Bi2Se3
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• Anomalous behavior of the electronic structure of (Bi${}_{1-x}$In${}_x$)${}_2$Se${}_3$ across the quantum-phase transition from topological to trivial insulator
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• Designer Meron Lattice on the Surface of a Topological Insulator
• Giant Inverse Rashba-Edelstein Effect: Application to Monolayer OsBi${}_2$
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• Quantum capacitance of an ultrathin topological insulator film in a magnetic field
• Persistent Coherence and Spin-Polarization of Topological Surface States on Topological Insulators
• Realization of bulk insulating property and carrier manipulation in reversible spin current regime of the ideal topological insulator TlBiSe2
• Evidence for topological proximity effect in graphene coupled to topological insulator
• Hexagonally warped exceptional physics in multi-Weyl semimetals
• VASP2KP: kp models and Lande g-factors from ab initio calculations
• Modulated Helical Metals at Magnetic Domain Walls of Pyrochlore Iridium Oxides
• Strongly anisotropic spin-orbit splitting in a two-dimensional electron gas
• Theory of bilinear magneto-electric resistance from topological-insulator surface states
• Gap Generation in Topological Insulator Surface States by non-Ferromagnetic Magnets
• Kondo holes in topological Kondo insulators: Spectral properties and surface quasiparticle interference
• Modeling Near-Surface Bound Electron States in Three-Dimensional Topological Insulator: Analytical and Numerical Approaches
• Defect Role in the Carrier Tunable Topological Insulator (Bi${}_{1-x}$Sb${}_x$)${}_2$Te${}_3$ Thin Films
• Symmetry analysis of strain, electric and magnetic fields in the ${\text{Bi}}_2{\text{Se}}_3$-class of topological insulators
• Band bending at the surface of Bi${}_2$Se${}_3$ studied from first principles
• A general route to form topologically-protected surface and bulk Dirac fermions along high-symmetry lines
• Engineering the in-plane anomalous Hall effect in Cd${}_3$As${}_2$ thin films
• Topological metal behavior in GeBi2Te4 single crystals
• Two-dimensional Josephson vortex lattice and anomalously slow decay of the Fraunhofer oscillations in a ballistic SNS junction with a warped Fermi surface
• Imaging ambipolar two-dimensional carriers induced by the spontaneous electric polarization of a polar semiconductor BiTeI
• Interface symmetry and spin control in topological insulator-semiconductor heterostructures
• Tunable unconventional Kondo effect on topological insulator surfaces
• Non-linear ballistic response of quantum spin-Hall edge states
• Origin of Rashba-splitting in the quantized subbands at Bi2Se3 surface
• Gapless Topological Superconductors - Model Hamiltonian and Realization
• Engineered Near-Perfect Back-Scattering on Surface of Topological Insulator with Non-Magnetic Impurities
• Optical Conductivity of Topological Insulator Thin Films in a Quantizing Magnetic Field
• Observation of antiphase coherent phonons in the warped Dirac cone of Bi${}_2$Te${}_3$
• Novel anisotropic spin singlet pairings in Cu${}_x$Bi${}_2$Se${}_3$ and Bi${}_2$Te${}_3$
• Time-Reversal Phase Transition at the Edge of 3d Topological Band Insulator
• Sputtering induced re-emergence of the topological surface state in Bi${}_2$Se${}_3$
• Electron beam splitting at topological insulator surface states and a proposal for electronic Goos-Hanchen shift measurement
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• Nematic superconductivity in Cu${}_x$Bi${}_2$Se${}_3$: The surface Andreev bound states
• Topological insulator ribbon: Surface states and dynamical response
• Laser-based angle-resolved photoemission spectroscopy with micrometer spatial resolution and detection of three-dimensional spin vector
• Topological Phase Transition-Induced Tri-Axial Vector Magnetoresistance in (Bi1-xInx)2Se3 Nanodevices
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• Theory of the Spin Seebeck Effect at a Topological-Insulator/Ferromagnetic-Insulator Interface
• Interlayer RKKY Coupling in Bulk Rashba Semiconductors under Topological Phase Transition
• Effects of surface-bulk hybridization in 3D topological `metals'
• Band tilt induced nonlinear Nernst effect in topological insulators: An efficient generation of high-performance spin polarization
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• Josephson effect in normal and ferromagnetic topological insulator planar, step and edge junctions
• Mesoscopic electron focusing in topological insulators
• Revisiting Quasiparticle Scattering Interference in High-Temperature Superconductors: The Problem of Narrow Peaks
• Intrinsic Contribution to Non-linear Thermoelectric Effect
• Superconducting proximity effect in $d$-wave cuprate/ graphene heterostructures
• The Interplay of Topological Surface and Bulk Electronic States in Bi2Se3
• Landau theory of helical Fermi liquids
• Electronic standing waves on the surface of the topological insulator Bi2Te3
• Spin polarized STM spectra of Dirac Fermions on the surface of a topological insulator
• Ab-initio Theory of Fourier-transformed Quasiparticle Interference Maps and Application to the Topological Insulator Bi${}_2$Te${}_3$
• Magnetic response of Majorana Kramers pairs with an order-two symmetry
• Surface-state spin textures in strained bulk HgTe: strain-induced topological phase transitions
• Transforming a Surface State of Topological Insulator by a Bi Capping Layer
• Topological Magnetoelectric Response in Ferromagnetic Axion Insulators
• Lattice-matched heterojunctions between topological and normal insulators: A first-principles study
• Density Waves Instability and a Skyrmion Lattice on the Surface of Strong Topological Insulators
• Gapped Dirac cones and spin texture in thin film topological insulator
• Ultrafast Evolution of Bulk, Surface and Surface Resonance States in Photoexcited Bi${}_2$Te${}_3$
• Strained topological insulator spin field effect transistor
• Non-linear antidamping spin-orbit torque originating from intra-band transport on the warped surface of a topological insulator
• Switchable quantized conductance in topological insulators revealed by the Shockley-Ramo theorem
• Nematic superconductivity in topological insulators induced by hexagonal warping
• Effective low energy theory for surface Andreev bound states of superconducting phases in generalized Bernevig-Hughes-Zhang models
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• Selective Control of Surface Spin Current in Topological Materials based on Pyrite-type OsX2 (X = Se, Te) Crystals
• Revisiting the physical origin and nature of surface states in inverted-band semiconductors
• Nonlinear response in a non-centrosymmetric topological insulator
• A Dirac-fermion approach and its application to design high Chern numbers in magnetic topological insulator multilayers
• Nonlinear Hall effect in Rashba systems with hexagonal warping
• Odd-frequency superconductivity induced in topological insulators with and without hexagonal warping
• Confining electrons on a topological insulator surface using potentials and a magnetic field
• Selective Trapping of Hexagonally Warped Topological Surface States in a Triangular Quantum Corral
• Tunnel Magnetoresistance scan of a pristine three-dimensional topological insulator
• Chiral p-wave superconductivity in Sb(111) thin films close to Van Hove singularities
• Scattering properties of the three-dimensional topological insulator Sb2Te3: Coexistence of topologically trivial and non-trivial surface states with opposite spin-momentum helicity
• Conductance of gated junctions as a probe of topological interface states
• Dirac Nodal Line and Rashba Splitting Surface States in Nonsymmorphic ZrGeTe
• THz Photodetector using sideband-modulated transport through surface states of a 3D Topological Insulator
• Observability of superconductivity in Sr-doped Bi2Se3 at the surface using scanning tunneling microscope
• Experimental demonstration of a magnetically induced warping transition in a topological insulator mediated by rare-earth surface dopants
• Trigonal warping induced terraced spin texture and nearly perfect spin polarization in graphene with Rashba effect
• Exceptional Dirac states in a non-centrosymmetric superconductor, BiPd
• Cherenkov sound on a surface of a topological insulator
• Room-temperature nonlinear transport and microwave rectification in antiferromagnetic MnBi${}_2$Te${}_4$ films
• Dielectric screening of surface states in a topological insulator
• Spin texture of an irradiated warped topological insulator surface
• The influence of proximity induced ferromagnetism, superconductivity and Fermi-velocity on evolution of Berry phase in Bi${}_2$Se${}_3$ topological insulator
• Lifshitz transition in dirty nematic superconductor
• Proximity induced ferromagnetism, superconductivity, and finite-size effects on the surface and edge states of topological insulator nanostructures
• Single monkey-saddle singularity of a Fermi surface and its instabilities
• Electrical control of intrinsic nonlinear Hall effect in antiferromagnetic topological insulator sandwiches
• Spin-polarized electronic surface states of Re(0001): an ab-initio investigation
• Plasmon modes in the magnetically doped Single Layer and Multilayers of Helical Metals
• Quasiparticle interference in doped topological insulators with nematic superconductivity
• Anomalous Josephson Hall effect in magnet/triplet superconductor junctions
• Interfacing topological insulators and ferrimagnets: Bi${}_2$Te${}_3$ and Fe${}_3$O${}_4$ heterostructures grown by molecular beam epitaxy
• Anomalous Hall effect from a non-Hermitian viewpoint
• Anomalous thermoelectric properties of a Floquet topological insulator with spin momentum non-orthogonality
• Magneto-Transport and High-Resolution Angle-Resolved Photoelectron Spectroscopy Studies of Palladium Doped Bi${}_2$Te${}_3$
• Proximity-Induced Superconductivity at Non-Helical Topological Insulator Interfaces
• Anisotropic spin gaps in BiAg${}_2$-Ag/Si(111)
• Kramers-Weyl fermions in the chiral charge density wave material (TaSe${}_4$)${}_2$I
• Symmetry-driven anisotropic coupling effect in antiferromagnetic topological insulator: Mechanism for high-Chern-number quantum anomalous Hall state
• Momentum-dependent spin selection rule in photoemission with glide symmetry
• Elastic scattering of surface states on three-dimensional topological insulators
• Scanning tunneling spectroscopy investigations of superconducting-doped topological insulators: Experimental pitfalls and results
• Controllable spin splitting in 2D Ferroelectric few-layer ${$γ}$-GeSe
• Breakdown of bulk-projected isotropy in surface electronic states of topological Kondo insulator SmB${}_6$(001)
• Anisotropic Fabry-Pérot resonant states confined within nano-steps on the topological insulator surface
• A programmable $k\cdot p$ Hamiltonian method and application to magnetic topological insulator MnBi${}_2$Te${}_4$
• Interplay between exchange split Dirac and Rashba-type surface states in MnBi${}_2$Te${}_4$/BiTeI interface
• 2D compressibility of surface states on 3D topological insulators
• Effect of Perturbative Hexagonal Warping on Quantum Capacitance in Ultra-Thin Topological Insulators
• Transport of Dirac electrons in a random magnetic field in topological heterostructures
• Nonlinear thermoelectric probes of anomalous electron lifetimes in topological Fermi liquids
• Ab initio k.p theory of spin-momentum locking: Application to topological surface states
• Transport signatures of surface potentials on three-dimensional topological insulators
• Friedel oscillation near a van Hove singularity in two-dimensional Dirac materials
• The anomalous spin texture as the probe for interactions in $B{i}_{2-y}S{b}_{y}S{e}_{x}T{e}_{3-x}$
• Local and global patterns in quasiparticle interference: a reduced response function approach
• Landau levels in a topological insulator
• Visualizing Pairing Symmetry in Nematic Superconductors using spin-polarized spectroscopy of magnetic impurities
• Odd-frequency pairs and anomalous proximity effect in nematic and chiral states of superconducting topological insulators
• Electrically tunable high-Chern-number quasiflat bands in twisted antiferromagnetic topological insulators
• Quantum Capacitance of a Topological Insulator-Ferromagnet Interface
• Wave-particle duality of electrons with spin-momentum locking
• Current-induced spin and orbital polarization in the ferroelectric Rashba semiconductor GeTe
• Magnetic scattering with spin-momentum locking: Single scatterers and diffraction grating
• Asymmetric Cherenkov acoustic reverse in topological insulators
• Strong Spin-Orbit Torque effect on magnetic defects due to topological surface state electrons in Bi${}_2$Te${}_3$
• Strain induced spin vortex and Majorana Kramer's pairs in doped topological insulators with nematic superconductivity
• Surface state transport in double-gated and magnetized topological insulators with hexagonal warping effects
• Magnus spin Hall and spin Nernst effects in gapped 2D Rashba systems
• Doping-controlled surface conduction in topological insulators with warping effects
• Magnetic torque oscillations from warped helical surface states in topological insulators
• Effective Hamiltonian for surface states of \ce{Bi2Te3} nanocylinders with hexagonal warping
• High-field charge transport on the surface of Bi${}_2$Se${}_3$
• Pseudospin-valve effect on transport in junctions of three-dimensional topological insulator surfaces
• Non-orthogonal Spin-Momentum Locking
• Nonlinear planar magnetotransport as a probe of the topology of surface states
• Spin-orbit torques due to topological insulator surface states: an in-plane magnetization as a probe of extrinsic spin-orbit scattering
• Raman tensor for two-dimensional massive Dirac fermions
• Dirac-like fermions anomalous magneto-transport in a spin-polarized oxide two-dimensional electron system
• Reconstructing the wavefunction of magnetic topological insulators MnBi2Te4 and MnBi4Te7 using spin-resolved photoemission
• Interaction Approach to Anomalous Spin Texture in Warped Topological Insulators
• Unoccupied Topological Surface State in MnBi${}_2$Te${}_4$
• Topological surface states hybridized with bulk states of Bi-doped PbSb2Te4 revealed in quasiparticle interference
• Possible two-component pairings in electron-doped Bi${}_2$Se${}_3$ based on a tight-binding model
• Diffusion at the Surface of Topological Insulators
• Bulk spin conductivity of three-dimensional topological insulator
• Beta-Ag2Te: A topological insulator with strong anisotropy
• Spin texture tunability in Mn${}_{1-x}$Ge${}_x$Bi${}_2$Te${}_4$ through varying Ge Concentration
• Impurity-potential-induced gap at the Dirac point of topological insulators with in-plane magnetization
• Introduction to Topological Insulators
• Hexagonal warping effect to Majorana zero modes at ends of superconducting vortex line in doped 3D strong topological insulators
• Unconventional band structure for a periodically gated surface of a three dimensional Topological Insulator
• Quasiparticle scattering in three-dimensional topological insulators near the thickness limit
• Topological insulator Bi2Te3 films synthesized by metal organic chemical vapor deposition
• Nonequilibrium topological spin textures in momentum space
• Robust topological state against magnetic impurities observed in superconductor PbTaSe2
• Observation of novel interference patterns in Bi2-xFexTe3+d by Fourier transform scanning tunneling spectroscopy
• Theory of tunneling spectroscopy in a superconducting topological insulator
• Non-Lifshitz invariants corrections to Dzyaloshinskii-Moriya interaction energy
• Tunable Fano and Dicke effects in quantum transport of double quantum dots sandwiched between topological insulators
• The evaluation of non-topological components in Berry phase and momentum relaxation time in a gapped 3D topological insulator
• Tunable magnetic anisotropy from higher-harmonics exchange scattering on the surface of a topological insulator
• Direct observation of quantum confinement of massless Dirac fermions in a topological insulator
• Bulk and surface electron scattering in disordered Bi${}_2$Te${}_3$ probed by quasiparticle interference
• Hybridization and Field Driven Phase Transitions in Hexagonally Warped Topological Insulators
• Spin-orbit effects at chiral surfaces
• Pairing around a Single Dirac Point: A Unifying View of Kohn-Luttinger Superconductivity in Chern Bands, Quarter Metals, and Topological Surface States
• Dynamical polarization and the optical response of silicene and related materials
• Classification of spin Hall effect in two-dimensional systems
• Electron scattering in a superlattice of line defects on the surface of topological insulators
• Magnetically induced spin reorientation on the surface of a topological insulator (a surface magnetic topological insulator MBE film)
• Optical conductivity of a Dirac-Fermi liquid
• A spintronic analog of the Landauer residual resistivity dipole on the surface of a disordered topological insulator
• Large bandgap quantum anomalous hall insulator in a designer ferromagnet-topological insulator-ferromagnet heterostructure
• Multiband quasiparticle interference in the topological insulator Cu_(x)Bi_(2)Te_(3)
• Local density of state oscillations in laterally heterostructured topological insulator-semiconductor systems
• Magnetic precession induced spin accumulation in collinear antiferromagnets
• Super-resonant transport of topological surface states subjected to in-plane magnetic fields
• Enhanced detection of circularly polarized photons with topological materials
• Correlated phases of moat-band excitons in two dimensions
• Hexagonal Warping Control of Exceptional Points in Topological Insulator--Ferromagnetic Heterojunctions
• Beyond spin-1/2: Multipolar spin-orbit coupling in noncentrosymmetric crystals with time-reversal symmetry
• Engineering stacking-induced topological phase transitions in bilayer heterostructures
• Proposed Detection of Time Reversal Symmetry in Topological Surface States
• Observation of Dirac cone warping and chirality effects in silicene
• Quasiparticle interference on the surface of Bi${}_2$Se${}_3$ terminated (PbSe)${}_5$(Bi${}_2$Se${}_3$)${}_6$
• Universal classes of disorder scatterings in in-plane anomalous Hall effect
• ToMSGKpoint: A user-friendly package for computing symmetry transformation properties of electronic eigenstates of nonmagnetic and magnetic crystalline materials
• Anomalous quasiparticle lifetime in geometric quantum critical metals
• Spatial aspects of spin polarization of structurally split surface states in thin films with magnetic exchange and spin-orbit interaction
• Phase transition from Weyl to self-linked semimetal using bi-circular laser