Landau Quantization of Massless Dirac Fermions in Topological Insulator

Abstract

The recent theoretical prediction and experimental realization of topological insulators (TI) has generated intense interest in this new state of quantum matter. The surface states of a three-dimensional (3D) TI such as Bi_2Te_3, Bi_2Se_3 and Sb_2Te_3 consist of a single massless Dirac cones. Crossing of the two surface state branches with opposite spins in the materials is fully protected by the time reversal (TR) symmetry at the Dirac points, which cannot be destroyed by any TR invariant perturbation. Recent advances in thin-film growth have permitted this unique two-dimensional electron system (2DES) to be probed by scanning tunneling microscopy (STM) and spectroscopy (STS). The intriguing TR symmetry protected topological states were revealed in STM experiments where the backscattering induced by non-magnetic impurities was forbidden. Here we report the Landau quantization of the topological surface states in Bi_2Se_3 in magnetic field by using STM/STS. The direct observation of the discrete Landau levels (LLs) strongly supports the 2D nature of the topological states and gives direct proof of the nondegenerate structure of LLs in TI. We demonstrate the linear dispersion of the massless Dirac fermions by the square-root dependence of LLs on magnetic field. The formation of LLs implies the high mobility of the 2DES, which has been predicted to lead to topological magneto-electric effect of the TI.

15 pages, 4 figures

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Cited by in corpus (175)

• Topological Insulators
• Topological insulators and superconductors
• Topological Insulator Materials
• Dirac materials
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• Two-dimensional Dirac fermions in a topological insulator: transport in the quantum limit
• One-dimensional Topological Edge States of Bismuth Bilayers
• Surface conduction of topological Dirac electrons in bulk insulating Bi2Se3
• Thickness-independent transport channels in topological insulator Bi2Se3 thin films
• Manifestation of Topological Protection in Transport Properties of Epitaxial Bi2Se3 Thin Films
• Angle Dependent Van Hove Singularities in Slightly Twisted Graphene Bilayer
• Electrically tunable surface-to-bulk coherent coupling in topological insulator thin films
• Josephson supercurrent through a topological insulator surface state
• Thickness-dependent bulk properties and weak anti-localization effect in topological insulator Bi2Se3
• Evidence for electron-electron interaction in topological insulator thin films
• Gate-tuned normal and superconducting transport at the surface of a topological insulator
• Electronic properties of graphene: a perspective from scanning tunneling microscopy and magneto-transport
• Reactive chemical doping of the $B{i}_{2}S{e}_3$ topological insulator
• Electron interaction-driven insulating ground state in Bi2Se3 topological insulators in the two dimensional limit
• Superconductivity in the topological semimetal YPtBi
• Landau quantization and the thickness limit of topological insulator thin films of Sb2Te3
• Epitaxial growth of topological insulator Bi2Se3 film on Si(111) with atomically sharp interface
• Rashba spin-splitting control at the surface of the topological insulator Bi2Se3
• High-Field Shubnikov-de Haas Oscillations in the Topological Insulator Bi${}_2$Te${}_2$Se
• Magneto-Optical Faraday and Kerr Effects in Topological Insulator Films and in Other Layered Quantized Hall Systems
• Fermi Level Tuning of Epitaxial Sb2Te3 Thin Films on Graphene by Regulating Intrinsic Defects and Substrate Transfer Doping
• Superconducting Topological Surface States in Non-centrosymmetric Bulk Superconductor PbTaSe2
• Quantum Oscillations in a Topological Insulator Bi${}_2$Te${}_2$Se with Large Bulk Resistivity (6 $\Omega$cm)
• Persistence of Topological Order and Formation of Quantum Well States in Topological Insulators Bi2(Se,Te)3 under Ambient Conditions
• Quantum interference and Aharonov-Bohm oscillations in topological insulators
• Fully gapped topological surface states in Bi${}_2$Se${}_3$ films induced by a d-wave high-temperature superconductor
• Disordered Topological Insulators: A Non-Commutative Geometry Perspective
• Massive Dirac surface states in topological insulator/magnetic insulator heterostructures
• In-plane magnetic anisotropy of Fe atoms on Bi${}_2$Se${}_3$(111)
• Transport in two-dimensional topological materials: recent developments in experiment and theory
• Transport in three-dimensional topological insulators: theory and experiment
• Probing topological quantum matter with scanning tunnelling microscopy
• Fermi level tuning and a large activation gap achieved in the topological insulator Bi_{2}Te_{2}Se by Sn doping
• Room-temperature quantum spin Hall edge state in a higher-order topological insulator Bi${}_4$Br${}_4$
• Electronic and optical properties of graphene nanoribbons in external fields
• Generation of entangled photons in graphene in a strong magnetic field
• Electronic states and magnetic response of MnBi2Te4 by scanning tunneling microscopy and spectroscopy
• Gate-tuned Differentiation of Surface-conducting States in Bi1.5Sb0.5Te1.7Se1.3 Topological-insulator Thin Crystals
• Magneto-optical and Magneto-electric Effects of Topological Insulators in Quantizing Magnetic Fields
• Weak Antilocalization and Conductance Fluctuation in a Sub-micrometer-sized Wire of Epitaxial Bi2Se3
• Topological Surface States with Persistent High Spin Polarization across Dirac Point in Bi${}_2$Te${}_2$Se and Bi${}_2$Se${}_2$Te
• Hofstadter Topology: Non-crystalline Topological Materials at High Flux
• Toward the intrinsic limit of topological insulator Bi2Se3
• Topological p-n Junction
• Quasi-ballistic transport of Dirac fermions in a Bi2Se3 nanowire
• Ultrafast Electron Dynamics in the Topological Insulator Bi2Se3 Studied by Time-Resolved Photoemission Spectroscopy
• Hybridization wave as the 'Hidden Order' in URu${}_2$Si${}_2$
• Influence of Topological Edge States on the Properties of Al/Bi2Se3/Al Hybrid Josephson Devices
• Experimental realization of SQUIDs with topological insulator junctions
• Quasiparticle interference on type-I and type-II Weyl semimetal surfaces: a review
• The Role of Odd-Frequency Pairing in Multiband Superconductors
• Weak antilocalization and electron-electron interaction in coupled multiple-channel transport in a Bi${}_2$Se${}_3$ thin film
• Drive the Dirac Electrons into Cooper Pairs in SrxBi2Se3
• Tunneling into clean Heavy Fermion Compounds: Origin of the Fano Lineshape
• Imaging two-component nature of Dirac-Landau levels in the topological surface state of Bi2Se3
• Edge states and integer quantum Hall effect in topological insulator thin films
• Topological surface states interacting with bulk excitations in the Kondo insulator SmB${}_6$ revealed via planar tunneling spectroscopy
• Topological Crystalline Insulator Nanostructures
• Topological surface states of Bi2Se3 with the coexistence of Se vacancies
• Quasiparticle Interference Studies of Quantum Materials
• Restoring Pristine Bi2Se3 Surface with an Effective Se Decapping Process
• Electronic States of Wires and Slabs of Topological Insulators: Quantum Hall Effects and Edge Transport
• Visualizing Landau levels of Dirac electrons in a one dimensional potential
• Effect of bulk charged impurities on the bulk and surface transport in three-dimensional topological insulators
• Spin-based Mach-Zehnder interferometry in topological insulator p-n junctions
• Quantum transport in disordered systems under magnetic fields: A study based on operator algebras
• Solution to the hole-doping problem and tunable quantum Hall effect in Bi${}_2$Se${}_3$ thin films
• Metal-Insulator Transition in Variably Doped (Bi1-xSbx)2Se3 Nanosheets
• Ambipolar transport in bulk crystals of a topological insulator by gating with ionic liquid
• Robust Nodal Structure of Landau Level Wave Functions Revealed by Fourier Transform Scanning Tunneling Spectroscopy
• Scanning Tunneling Microscopy of Gate Tunable Topological Insulator Bi2Se3 Thin Films
• Observation of three-dimensional Dirac semimetal state in topological insulator Bi2Se3
• Ripple modulated electronic structure of a 3D topological insulator
• Magnetic quantum oscillations of the topological insulator surface states
• Transport response of topological hinge modes in $\alpha$-Bi${}_4$Br${}_4$
• Effect of Electron-electron Interaction on Surface Transport in Three-Dimensional Topological Insulators
• Superconducting instabilities in a spinful Sachdev-Ye-Kitaev model
• Two-dimensional Massless Dirac Fermions in Antiferromagnetic AFe2As2 (A = Ba, Sr)
• Surface charge conductivity of topological insulator in a magnetic field: effect of hexagonal warping
• Role of Se vacancies on Shubnikov de Haas oscillations in Bi2Se3: a combined magneto-resistance and positron annihilation study
• Response of the topological surface state to surface disorder in TlBiSe${}_2$
• Landau Level Spectroscopy of Dirac Electrons in a Polar Semiconductor with Giant Rashba Spin Splitting
• Semirelativity in Semiconductors: a Review
• Three-Dimensional Topological Insulator in a Magnetic Field: Chiral Side Surface States and Quantized Hall Conductance
• Generation of strain-induced pseudo-magnetic field in a doped type-II Weyl semimetal
• Domain Wall Motion in Thin-Film Magnets/ Topological Insulator Junctions
• Mass acquisition of Dirac fermions in Cr-doped topological insulator Sb2Te3 films
• Tailoring the electronic texture of a topological insulator via its surface orientation
• A low-temperature scanning tunneling microscope capable of microscopy and spectroscopy in a Bitter magnet at up to 34 T
• Faraday rotation due to surface states in the topological insulator (Bi${}_{1-x}$Sb${}_x$)${}_2$Te${}_3$
• Continuous wave lasing between Landau levels in graphene
• Optimizing the Majorana character of SQUIDs with topologically non-trivial barriers
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• Landau level states on a topological insulator thin film
• Severe Dirac Mass Gap Suppression in Sb_2Te_3-based Quantum Anomalous Hall Materials
• Dirac cone shift of a passivated topological Bi2Se3 interface state
• Interaction and disorder effects in 3D topological insulator thin films
• Tunneling in graphene-topological insulator hybrid devices
• Quantum-Hall to Insulator Transition in Ultra-low-carrier-density Topological Insulator Films and a Hidden Phase of the Zeroth Landau Level
• Probing Dirac Fermion Dynamics in Topological Insulator Bi${}_2$Se${}_3$ Films with Scanning Tunneling Microscope
• Anisotropic magneto-optical absorption and linear dichroism in two-dimensional semi-Dirac electron systems
• Effect of magnetic field on a magnetic topological insulator film with structural inversion asymmetry
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• Defect Role in the Carrier Tunable Topological Insulator (Bi${}_{1-x}$Sb${}_x$)${}_2$Te${}_3$ Thin Films
• Landau Levels of Topologically-Protected Surface States Probed by Dual-Gated Quantum Capacitance
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• Quantum transport properties of beta-Bi4I4 near and well beyond the extreme quantum limit
• Transport Properties of Topological Insulators Films and Nanowires
• Quantum Hall Effect in Thin Films of Three-Dimensional Topological Insulators
• Influence of an anomalous temperature-dependence of the phase coherence length on the conductivity of magnetic topological insulators
• Dimensional evolution between one- and two-dimensional topological phases
• Nanoscale Determination of the Mass Enhancement Factor in the Lightly-Doped Bulk Insulator Lead Selenide
• Planar tunneling spectroscopy of the topological Kondo insulator SmB${}_6$
• Spatially resolved Landau level spectroscopy of the topological Dirac cone of bulk-type Sb2Te3(0001): potential fluctuations and quasiparticle lifetime
• Thin films of a three-dimensional topological insulator in a strong magnetic field: a microscopic study
• Interacting Dirac Fermions on a Topological Insulator in a Magnetic Field
• The Interplay of Topological Surface and Bulk Electronic States in Bi2Se3
• Mapping the effect of defect-induced strain disorder on the Dirac states of topological insulators
• Single electron gating of topological insulators
• Formulation of the Relativistic Quantum Hall Effect and "Parity Anomaly"
• Tuning multiple Landau Quantization in Transition-Metal Dichalcogenide with Strain
• Band structure of topological insulators from noise measurements in tunnel junctions
• Berry-phase switch in electrostatically-confined topological surface states
• Non-contact mutual inductance based measurement of an inhomogeneous topological insulating state in Bi2Se3 single crystals with defects
• Thin film of a topological insulator as a spin Hall insulator
• Gate tunable quantum Hall effects in defect-suppressed Bi2Se3 films
• Discovery of highly spin-polarized conducting surface states in the strong spin-orbit coupling semiconductor Sb${}_2$Se${}_3$
• Coulomb drag in topological insulator films
• Reproducible synthetic method for the topological superconductor CuxBi2Se3
• Structural and magneto-transport studies of iron intercalated Bi2Se3 single crystals
• Observability of superconductivity in Sr-doped Bi2Se3 at the surface using scanning tunneling microscope
• Coulomb drag in topological materials
• Quasiparticle states and quantum interference induce by magnetic impurities on a two-dimensional topological superconductor
• Suppression of transport spin-polarization of surface states with emergence of ferromagnetism in Mn-doped Bi2Se3
• Strong magneto-optical effects due to surface states in three-dimensional topological insulators
• Thermoelectric properties of an ultra-thin topological insulator
• Characterizing the chemical potential disorder in the topological insulator (Bi${}_{1-x}$Sb${}_x$)${}_2$Te${}_3$ thin films
• Observation of Landau quantization and standing waves in HfSiS
• Topological nature of the Kondo insulator SmB${}_6$ and its sensitiveness to Sm vacancy
• Electric and thermoelectric transport in graphene and helical metal in finite magnetic fields
• Strong and Weak Three-Dimensional Topological Insulators Probed by Surface Science Methods
• 'Real' gerbes and Dirac cones of topological insulators
• The stability of the fractional quantum Hall effect in topological insulators
• From classical to quantum regime of topological surface states via defect engineering
• Landau levels in a topological insulator
• Edge modes and Fabry-Perot Plasmonic Resonances in anomalous-Hall Thin Films
• Synchrotron-radiation studies of topological insulators
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• Bulk-Boundary Correspondence for Topological Insulators with Quantized Magneto-Electric Effect
• Ultra-high mechanical stretchability and controllable topological phase transitions in two-dimensional arsenic
• Dynamical Gap Generation in Topological Insulators
• Fractional quantum Hall effect of topological surface states under a strong tilted magnetic field
• Bulk spin conductivity of three-dimensional topological insulator
• Ultrafast electron dynamics at the Dirac node of the topological insulator Sb${}_2$Te${}_3$
• Anomalous Linear and Quadratic Nodeless Surface Dirac Cones in Three-Dimensional Dirac Semimetals
• Vacuum polarization at the boundary of a topological insulator
• Unconventional quantum Hall effect in Floquet topological insulators
• Introduction to Topological Insulators
• Evidence for nitrogen gas surface doping of the Bi${}_2$Se${}_3$ topological insulator
• Electronic band structure from quasiparticle interference and Landau quantization in WTe${}_2$
• Gate-controlled Spin Extraction from Topological Insulator Surfaces
• Linear scaling relation between two-dimensional massless Dirac fermion Fermi velocity and Fe-As bond length in iron arsenide superconductor systems
• Landau levels on a surface of weak topological insulators
• Strong photon coupling to high-frequency antiferromagnetic magnons via topological surface states
• Valley polarization of Landau levels driven by residual strain in the ZrSiS surface band
• Super-resonant transport of topological surface states subjected to in-plane magnetic fields
• Interaction-free measurement with mesoscopic devices on a GaAs/AlGaAs heterostructure
• The d-p band-inversion topological insulator in bismuth-based skutterudites
• Current response of a topological insulator to a static Zeeman field