Quantum interference and Aharonov-Bohm oscillations in topological insulators

Abstract

Topological insulators have an insulating bulk but a metallic surface. In the simplest case, the surface electronic structure of a 3D topological insulator is described by a single 2D Dirac cone. A single 2D Dirac fermion cannot be realized in an isolated 2D system with time-reversal symmetry, but rather owes its existence to the topological properties of the 3D bulk wavefunctions. The transport properties of such a surface state are of considerable current interest; they have some similarities with graphene, which also realizes Dirac fermions, but have several unique features in their response to magnetic fields. In this review we give an overview of some of the main quantum transport properties of topological insulator surfaces. We focus on the efforts to use quantum interference phenomena, such as weak anti-localization and the Aharonov-Bohm effect, to verify in a transport experiment the Dirac nature of the surface state and its defining properties. In addition to explaining the basic ideas and predictions of the theory, we provide a survey of recent experimental work.

23 pages, 17 figures. Submitted to Rep. Prog. Phys

References in corpus (157)

• The electronic properties of graphene
• Topological Insulators
• Topological insulators and superconductors
• Quantum Spin Hall Effect in Graphene
• Quantum Spin Hall Insulator State in HgTe Quantum Wells
• Superconducting proximity effect and Majorana fermions at the surface of a topological insulator
• Unpaired Majorana fermions in quantum wires
• Topological Insulators in Three Dimensions
• 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
• Paired states of fermions in two dimensions with breaking of parity and time-reversal symmetries, and the fractional quantum Hall effect
• Electronic transport in two dimensional graphene
• Classification of topological insulators and superconductors in three spatial dimensions
• New directions in the pursuit of Majorana fermions in solid state systems
• Random-Matrix Theory of Quantum Transport
• Novel Symmetry Classes in Mesoscopic Normal-Superconducting Hybrid Structures
• Topological invariants of time-reversal-invariant band structures
• Topological Crystalline Insulators
• Anderson Transitions
• Crossover of Three-Dimensional Topological Insulator of Bi2Se3 to the Two-Dimensional Limit
• Topological Crystalline Insulators in the SnTe Material Class
• Topological Surface States Protected From Backscattering by Chiral Spin Texture
• Experimental realization of a topological crystalline insulator in SnTe
• Three dimensional topological invariants for time reversal invariant Hamiltonians and the three dimensional quantum spin Hall effect
• Evidence for Helical Edge Modes in Inverted InAs/GaSb Quantum Wells
• Weak localisation magnetoresistance and valley symmetry in graphene
• Quantum-limited shot noise in graphene
• Bose-Einstein Condensation of Excitons in Bilayer Electron Systems
• Topological crystalline insulator states in Pb(1-x)Sn(x)Se
• The Quantum Spin Hall Effect: Theory and Experiment
• Odd-Parity Topological Superconductors: Theory and Application to Cu${}_x$Bi${}_2$Se${}_3$
• Scaling Theory of the Integer Quantum Hall Effect
• Aharonov-Bohm interference in topological insulator nanoribbons
• Hexagonal Warping Effects in the Surface States of Topological Insulator Bi${}_2$Te${}_3$
• The Helical Liquid and the Edge of Quantum Spin Hall Systems
• Experimental demonstration of the topological surface states protected by the time-reversal symmetry
• Large bulk resistivity and surface quantum oscillations in the topological insulator Bi2Te2Se
• A topological crystalline insulator (TCI) phase via topological phase transition and crystalline mirror symmetry
• Antiferromagnetic topological insulators
• Three-Dimensional Topological Insulators
• Gate-Voltage Control of Chemical Potential and Weak Anti-localization in Bismuth Selenide
• Massive Dirac fermions and spin physics in an ultrathin film of topological insulator
• Topological origin of subgap conductance in insulating bilayer graphene
• Two-dimensional Dirac fermions in a topological insulator: transport in the quantum limit
• Stability of the quantum spin Hall effect: effects of interactions, disorder, and Z_2 topology
• Oscillatory crossover from two dimensional to three dimensional topological insulators
• STM imaging of electronic waves on the surface of Bi${}_2$Te${}_3$: topologically protected surface states and hexagonal warping effects
• Quantum Hall Effect from the Topological Surface States of Strained Bulk HgTe
• Spin Polarization and Transport of Surface States in the Topological Insulators Bi2Se3 and Bi2Te3 from First Principles
• Bulk Fermi surface coexistence with Dirac surface state in Bi${}_2$Se${}_3$: a comparison of photoemission and Shubnikov-de Haas measurements
• Impurity effect on weak anti-localization in the topological insulator Bi2Te3
• Bulk Band Gap and Surface State Conduction Observed in Voltage-Tuned Crystals of the Topological Insulator Bi${}_2$Se${}_3$
• Effective continuous model for surface states and thin films of three dimensional topological insulators
• Landau Quantization of Massless Dirac Fermions in Topological Insulator
• Ambipolar Field Effect in Topological Insulator Nanoplates of (BixSb1-x)2Te3
• Quantum interference in macroscopic crystals of non-metallic Bi${}_2$Se${}_3$
• Unconventional Josephson Effect in Hybrid Superconductor-Topological Insulator Devices
• Surface conduction of topological Dirac electrons in bulk insulating Bi2Se3
• Effect of Disorder on Transport in Graphene
• Crossover between weak localization and weak antilocalization in magnetically doped topological insulator
• Thickness-independent transport channels in topological insulator Bi2Se3 thin films
• Manifestation of Topological Protection in Transport Properties of Epitaxial Bi2Se3 Thin Films
• Observation of Dirac Holes and Electrons in a Topological Insulator
• Anomalous Finite Size Effects on Surface States in the Topological Insulator Bi${}_2$Se${}_3$
• Demonstration of one-parameter scaling at the Dirac point in graphene
• Electrically tunable surface-to-bulk coherent coupling in topological insulator thin films
• Spatial Fluctuations of Helical Dirac Fermions on the Surface of Topological Insulators
• Competition between weak localization and antilocalization in topological surface states
• 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
• Surface State Transport and Ambipolar Electric Field Effect in Bi2Se3 Nanodevices
• Gate-tuned normal and superconducting transport at the surface of a topological insulator
• Majorana Fermions in Proximity-coupled Topological Insulator Nanowires
• Momentum-Resolved Landau-Level Spectroscopy of Dirac Surface State in Bi2Se3
• Topological delocalization of two-dimensional massless Dirac fermions
• Electron interaction-driven insulating ground state in Bi2Se3 topological insulators in the two dimensional limit
• Tunable Surface Conductivity in Bi2Se3 Revealed in Diffusive Electron Transport
• Electronic Structure of the Topological Insulator Bi2Se3 Using Angle-Resolved Photoemission Spectroscopy: Evidence for a Nearly Full Surface Spin Polarization
• Impurity-induced states on the surface of 3D topological insulators
• The strong side of weak topological insulators
• Aharonov-Bohm oscillations in disordered topological insulator nanowires
• Weak localization of bulk channels in topological insulator thin film
• Giant topological insulator gap in graphene with 5d adatoms
• Inelastic electron backscattering in a generic helical edge channel
• Divergence of the Classical trajectories and Weak Localization
• Topological Aspect and Quantum Magnetoresistance of $\beta$-Ag${}_2$Te
• Direct Measurement of the Out-of-Plane Spin Texture in the Dirac Cone Surface State of a Topological Insulator
• Angular-dependent oscillations of the magnetoresistance in Bi_2Se_3 due to the three-dimensional bulk Fermi surface
• Berry phase of non-ideal Dirac fermions in topological insulators
• Semiclassical Theory of Chaotic Quantum Transport
• High-Field Shubnikov-de Haas Oscillations in the Topological Insulator Bi${}_2$Te${}_2$Se
• Quantum Oscillations in a Topological Insulator Bi${}_2$Te${}_2$Se with Large Bulk Resistivity (6 $\Omega$cm)
• Quantum oscillations in a topological insulator Bi_{1-x}Sb_{x}
• Two-dimensional surface charge transport in topological insulators
• Topology, Delocalization via Average Symmetry and the Symplectic Anderson Transition
• Anomalous Aharonov-Bohm conductance oscillations from topological insulator surface states
• Insulating behavior in ultra-thin bismuth selenide field effect transistors
• Random resistor network model of minimal conductivity in graphene
• Weak Localization and Antilocalization in Topological Insulator Thin Films with Coherent Bulk-Surface Coupling
• Quantum criticality and minimal conductivity in graphene with long-range disorder
• Low carrier concentration crystals of the topological insulator Bi${}_2$Te${}_2$Se
• Anomalously large conductance fluctuations in weakly disordered graphene
• Edge Dynamics in a Quantum Spin Hall State: Effects from Rashba Spin-Orbit Interaction
• Quantum transport and two-parameter scaling at the surface of a weak topological insulator
• Transport in three-dimensional topological insulators: theory and experiment
• Observation of the superconducting proximity effect and possible evidence for Pearl vortices in a candidate topological insulator
• Interaction-induced criticality in Z_2 topological insulators
• Topological insulators in magnetic fields: Quantum Hall effect and edge channels with non-quantized θ-term
• Quasiparticle Effects in the Bulk and Surface-State Bands of Bi2Se3 and Bi2Te3 Topological Insulators
• Phonon induced backscattering in helical edge states
• The surface states of topological insulators - Dirac fermion in curved two dimensional spaces
• Spin-charge Separated Solitons in a Topological Band Insulator
• Why is the bulk resistivity of topological insulators so small?
• Z2 topological term, the global anomaly, and the two-dimensional symplectic symmetry class of Anderson localization
• Weak antilocalization in HgTe quantum wells and topological surface states: Massive versus massless Dirac fermions
• Stability of Majorana Fermions in Proximity-Coupled Topological Insulator Nanowires
• Prediction of weak topological insulators in layered semiconductors
• STM imaging of impurity resonances on Bi${}_2$Se${}_3$
• Weak Antilocalization and Conductance Fluctuation in a Sub-micrometer-sized Wire of Epitaxial Bi2Se3
• Renormalization group approach for the scattering off a single Rashba impurity in a helical liquid
• Strong potential impurities on the surface of a topological insulator
• Oscillatory angular dependence of the magnetoresistance in a topological insulator Bi_{1-x}Sb_{x}
• Two-dimensional universal conductance fluctuations and the electron-phonon interaction of topological surface states in Bi2Te2Se nanoribbons
• Observations of two-dimensional quantum oscillations and ambipolar transport in the topological insulator Bi2Se3 achieved by Cd doping
• Semiclassical Approach to Chaotic Quantum Transport
• Vortex Lines in Topological Insulator-Superconductor Heterostructures
• Mesoscopic conductance fluctuations in graphene samples
• Proximity effect at superconducting Sn-Bi2Se3 interface
• Non-Abelian Statistics of Axion Strings
• A proof of the Kramers degeneracy of transmission eigenvalues from antisymmetry of the scattering matrix
• Quantum kinetic equation and universal conductance fluctuations in graphene
• Topological insulator in a Bi-Bi${}_2$Se${}_3$ infinitely adaptive superlattice phase
• Observation of a Highly Spin Polarized Topological Surface State in GeBi${}_2$Te${}_4$
• Experimental realization of SQUIDs with topological insulator junctions
• Quantum oscillations in topological superconductor candidate Cu${}_{0.25}$Bi${}_2$Se${}_3$
• Probing the surface states in Bi2Se3 using the Shubnikov-de Haas effect
• Universal conductance fluctuations in Dirac materials in the presence of long-range disorder
• Interaction-driven topological insulator states in strained graphene
• 2D transport and screening in topological insulator surface states
• Half quantum spin Hall effect on the surface of weak topological insulators
• Topological insulator quantum dot with tunable barriers
• Spin and Charge Structure of the Surface States in Topological Insulators
• Critical regime of two dimensional Ando model: relation between critical conductance and fractal dimension of electronic eigenstates
• Integrable sigma models with theta=pi
• Semiclassical theory of weak antilocalization and spin relaxation in ballistic quantum dots
• Weak (anti-)localization in doped Z_2-topological insulator
• The Berry phase and the phase of the Shubnikov-de Haas oscillations in three-dimensional topological insulators
• Aharonov-Casher effect in Bi${}_2$Se${}_3$ square-ring interferometers
• Effect of Electron-electron Interaction on Surface Transport in Three-Dimensional Topological Insulators
• Quantum Hall effect in a singly and doubly connected 3D topological insulator
• High Quality Ultrathin Bi2Se3 Films on CaF2 and CaF2/Si by Molecular Beam Epitaxy with a Radio Frequency Cracker Cell
• Experimental evidence on the Altshuler-Aronov-Spivak interference of the topological surface states in the exfoliated Bi2Te3 nanoflakes
• Global phase diagram of two-dimensional Dirac fermions in random potentials
• Sondheimer Oscillation as a Fingerprint of Surface Dirac Fermions
• Probing the Band Topology of Mercury Telluride through Weak Localization and Antilocalization

Cited by in corpus (91)

• Colloquium: Topological Band Theory
• Quantum transport in Rashba spin-orbit materials: A review
• Room temperature high frequency transport of Dirac fermions in epitaxially grown Sb_2Te_3 based topological insulators
• Finite-temperature conductivity and magnetoconductivity of topological insulators
• Magnetic field induced helical mode and topological transitions in a quasi-ballistic topological insulator nanoribbon with circumferentially quantized surface state sub-bands
• Observation of Anderson localization in ultrathin films of three-dimensional topological insulators
• Photon Drag Effect in (Bi${}_{1-x}$Sb${}_x$)${}_2$Te${}_3$ Three Dimensional Topological Insulators
• Quasi-ballistic transport of Dirac fermions in a Bi2Se3 nanowire
• Spin-helical transport in normal and superconducting topological insulators
• Electronic materials with nanoscale curved geometries
• Probing Spin Helical Surface States in Topological HgTe Nanowires
• Parallel field magnetoresistance in topological insulator thin films
• A comprehensive review on topological superconducting materials and interfaces
• Majorana qubits in topological insulator nanoribbon architecture
• Weak localization and weak anti-localization in topological insulators
• Weak antilocalization and electron-electron interaction in coupled multiple-channel transport in a Bi${}_2$Se${}_3$ thin film
• Nanowires: A route to efficient thermoelectric devices
• Enhanced electron dephasing in three-dimensional topological insulators
• Robust Transport Signatures of Topological Superconductivity in Topological Insulator Nanowires
• Infrared/Terahertz Spectra of the Photogalvanic Effect in (Bi,Sb)Te based Three Dimensional Topological Insulators
• Stepwise quantized surface states and delayed Landau level hybridization in Co cluster-decorated BiSbTeSe2 topological insulator devices
• Pseudo-ballistic transport in 3D topological insulator quantum wires
• Terahertz Photogalvanic Spectroscopy of Three Dimensional Topological Insulators
• Spin-based Mach-Zehnder interferometry in topological insulator p-n junctions
• Surface-to-bulk scattering in topological insulator films
• Conductivity Corrections for Topological Insulators with Spin-Orbit Impurities: A New Hikami-Larkin-Nagaoka Formula
• Resolving the Dirac Cone on the Surface of Bi2Te3 Topological Insulator Nanowires by Field-Effect Measurements
• Weak Localization and Antilocalization in Topological Materials with Impurity Spin-Orbit Interactions
• Persistent currents in Dirac fermion rings
• Quantum electronic transport of topological surface states in beta-Ag2Se nanowire
• Higher-order Fabry-Pérot Interferometer from Topological Hinge States
• Opto-Electronic Characterization of Three Dimensional Topological Insulators
• Detecting Perfect Transmission in Josephson Junctions on the Surface of Three Dimensional Topological Insulators
• Spin-orbit interaction induced spin selective transmission through a multi-terminal mesoscopic ring
• Theory of a chiral Fermi liquid: general formalism
• Reversal of thermoelectric current in tubular nanowires
• Tunable interaction-induced localization of surface electrons in antidot nanostructured Bi2Te3 thin films
• Conditions for fully gapped topological superconductivity in topological insulator nanowires
• Towards the manipulation of topological states of matter: A perspective from electron transport
• Quantum transport in topological surface states of Bi${}_2$Te${}_3$ nanoribbons
• Curvature effect on spin polarization in a three-terminal geometry in presence of Rashba spin-orbit interaction
• Observation of multichannel quantum coherent transport and electron-electron interaction in Bi2Te3 single crystal
• Magnetotransport signatures of three-dimensional topological insulator nanostructures
• Dirac points of electron energy spectrum, band-contact lines, and electron topological transitions of 3 1/2 kind in three-dimensional metals
• Geometric phases and the Sagnac effect: Foundational aspects and sensing applications
• Adjustable quantum interference oscillations in Sb-doped Bi2Se3 topological insulator nanoribbons
• Interface symmetry and spin control in topological insulator-semiconductor heterostructures
• Nonlocal Edge State Transport in Topological Insulators
• Indications of the topological transport by the universal conductance fluctuations in the Bi2Te2Se microflakes
• Gate-induced decoupling of surface and bulk state properties in selectively-deposited Bi${}_2$Te${}_3$ nanoribbons
• Topological Effects on the Magnetoconductivity in Topological Insulators
• Evidence for pressure-induced node-pair annihilation in Cd3As2
• Suppression of scattering in quantum confined 2D-helical Dirac systems
• Transport of Massless Dirac Fermions in Non-topological Type Edge States
• Conductance fluctuations and disorder induced $\nu =0$ quantum Hall plateau in topological insulator nanowires
• Superconducting proximity effect in $d$-wave cuprate/ graphene heterostructures
• Topological insulator ring with magnetic impurities
• Perfect transmission and Aharanov-Bohm oscillations in topological insulator nanowires with nonuniform cross section
• Quantum Interference Effects in Topological Nanowires In a Longitudinal Magnetic Field
• Phonon-induced magnetoresistivity of Weyl semimetal nanowires
• Collective spin modes in Fermi liquids with spin-orbit coupling
• Tunneling Aharonov-Bohm interferometer on helical edge states
• Spin and charge transport through helical Aharonov-Bohm interferometer with strong magnetic impurity
• Phase diagram and phonon-induced backscattering in topological insulator nanowires
• Transport in topological insulator nanowires
• Thermoelectric current in topological insulator nanowires with impurities
• Theory of magnetotransport in shaped topological insulator nanowires
• Influence of Helical Spin Structure on the Magnetoresistance of an Ideal Topological Insulator
• Electron interferometry and quantum spin Hall phase in silicene
• Casimir effect in hemisphere capped tubes
• Aharonov-Bohm effect with an effective complex-valued vector potential
• Bulk effects on topological conduction on the surface of 3-D topological insulators
• Design of spin-orbital-textures in ferromagnetic/topological insulator interfaces
• Quasiparticle cooling using a Topological insulator-Superconductor hybrid junction
• Topological bound states for quantum charges
• Tunable helical crystals
• Topological phases of amorphous matter
• Wave-particle duality of electrons with spin-momentum locking
• Universal Conductance Fluctuations of Topological Insulators
• Magnetic forces in the absence of a classical magnetic field
• Persistent currents in topological and trivial confinement in silicene
• A Mean-Field Study of Quantum Oscillations in Two-Dimensional Kondo Insulators
• Intertwined topological phases in TaAs2 nanowires with giant magnetoresistance and quantum coherent surface transport
• Aharonov-Bohm oscillations caused by non-topological surface states in Dirac nanowires
• Random-gate-voltage induced Al'tshuler-Aronov-Spivak effect in topological edge states
• Effective Hamiltonian of topologically protected qubit in a helical crystal
• Aharonov--Bohm effect, electrodynamics postulates, and Lorentz condition
• Anisotropic transport properties in prismatic topological insulator nanowires
• Aharanov-Bohm oscillations and perfectly transmitted mode in amorphous topological insulator nanowires
• In-plane magnetic field-driven symmetry breaking in topological insulator-based three-terminal junctions
• Super-resonant transport of topological surface states subjected to in-plane magnetic fields