Half-integer quantum Hall effect of disordered Dirac fermions at a topological insulator surface

Abstract

The unconventional (half-integer) quantum Hall effect for a single species of Dirac fermions is analyzed. We discuss possible experimental measurements of the half-integer Hall conductance $g_{xy}$ of topological insulator surface states and explain how to reconcile Laughlin's flux insertion argument with half-integer $g_{xy}$. Using a vortex state representation of Landau Level wavefunctions, we calculate current density beyond linear response, which is in particular relevant to the topological image monopole effect. As a major result, the field theory describing the localization physics of the quantum Hall effect of a single species of Dirac fermions is derived. In this connection, the issue of (absent) parity anomaly is revisited. The renormalization group flow (RG) and the resulting phase diagram are extensively discussed. Starting values of the RG flow are given by the semiclassical conductivity tensor which is obtained from the Boltzmann transport theory of the anomalous Hall effect.

References in corpus (96)

• The electronic properties of graphene
• Two-Dimensional Gas of Massless Dirac Fermions in Graphene
• Topological Insulators
• Topological insulators and superconductors
• Experimental Observation of Quantum Hall Effect and Berry's Phase in Graphene
• Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells
• Quantum Spin Hall Insulator State in HgTe Quantum Wells
• Berry Phase Effects on Electronic Properties
• Anomalous Hall effect
• Topological Insulators in Three Dimensions
• Topological Insulators with Inversion Symmetry
• Experimental Observation of the Quantum Anomalous Hall Effect in a Magnetic Topological Insulator
• 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 Field Theory of Time-Reversal Invariant Insulators
• Room-Temperature Quantum Hall Effect in Graphene
• Topological invariants of time-reversal-invariant band structures
• Quantized Anomalous Hall Effect in Magnetic Topological Insulators
• Quantum Spin Hall Effect
• Anderson Transitions
• Periodic table for topological insulators and superconductors
• Chiral Anomaly and Classical Negative Magnetoresistance of Weyl Metals
• Unconventional Integer Quantum Hall effect in graphene
• Wave-packet dynamics in slowly perturbed crystals: Gradient corrections and Berry-phase effects
• Josephson Current and Noise at a Superconductor-Quantum Spin Hall Insulator-Superconductor Junction
• Electronic Properties of Graphene in a Strong Magnetic Field
• Three dimensional topological invariants for time reversal invariant Hamiltonians and the three dimensional quantum spin Hall effect
• Seeing the magnetic monopole through the mirror of topological surface states
• Magnetoelectric polarizability and axion electrodynamics in crystalline insulators
• Model Hamiltonian for Topological Insulators
• Scaling Theory of the Integer Quantum Hall Effect
• Quantum Anomalous Hall Effect in Hg${}_{1-y}$Mn${}_y$Te Quantum Wells
• Trajectory of Anomalous Hall Effect toward the Quantized State in a Ferromagnetic Topological Insulator
• Berry phase, hyperorbits, and the Hofstadter spectrum: semiclassical dynamics in magnetic Bloch bands
• Berry phase correction to electron density of states in solids
• Transport of Dirac quasiparticles in graphene: Hall and optical conductivities
• Quantum Hall Effect from the Topological Surface States of Strained Bulk HgTe
• Surface quantized anomalous Hall current and magneto-electric effect in magnetically disordered topological insulators
• Single particle Green's functions and interacting topological insulators
• Semiclassical theories of the anomalous Hall effect
• Electromagnetic and gravitational responses and anomalies in topological insulators and superconductors
• Anomalous Hall effect in 2D Dirac band: link between Kubo-Streda formula and semiclassical Boltzmann equation approach
• Surface State Magnetization and Chiral Edge States on Topological Insulators
• Quantized Anomalous Hall Effect in Two-Dimensional Ferromagnets - Quantum Hall Effect from Metal -
• Topological quantization in units of the fine structure constant
• Tunable Surface Conductivity in Bi2Se3 Revealed in Diffusive Electron Transport
• THz response and colossal Kerr rotation from the surface states of the topological insulator Bi${}_2$Se${}_3$
• Orbital magnetoelectric coupling in band insulators
• Magneto-Optical Faraday and Kerr Effects in Topological Insulator Films and in Other Layered Quantized Hall Systems
• Random Network Models and Quantum Phase Transitions in Two Dimensions
• Surface States of Topological Insulators
• Quantum criticality and minimal conductivity in graphene with long-range disorder
• Low energy theory of disordered graphene
• Topological BF field theory description of topological insulators
• Topological insulators in magnetic fields: Quantum Hall effect and edge channels with non-quantized θ-term
• Berry phase correction to electron density in solids and "exotic" dynamics
• Boltzmann-equation approach to anomalous transport in a Weyl metal
• Theory of Anomalous Quantum Hall Effects in Graphene
• Optical Hall conductivity in ordinary and graphene QHE systems
• Disordered 2d quasiparticles in class D: Dirac fermions with random mass, and dirty superconductors
• The surface states of topological insulators - Dirac fermion in curved two dimensional spaces
• Surface-edge state and half quantized Hall conductance in topological insulators
• Coordinate shift in the semiclassical Boltzmann equation and the anomalous Hall effect
• Equivalent topological invariants of topological insulators
• Wormhole Effect in a Strong Topological Insulator
• Electric-Magnetic Duality and Topological Insulators
• Surface state charge dynamics of a high-mobility three dimensional topological insulator
• Parallel field magnetoresistance in topological insulator thin films
• Thin topological insulator film in a perpendicular magnetic field
• Terahertz Kerr and Reflectivity Measurements on the Topological Insulator Bi2Se3
• Effective QED Actions: Representations, Gauge Invariance, Anomalies and Mass Expansions
• Quantum Hall Effect of Massless Dirac Fermions in a Vanishing Magnetic Field
• Dynamics in the quantum Hall effect and the phase diagram of graphene
• Parity measurement in topological Josephson junctions
• Absence of a metallic phase in charge-neutral graphene with a random gap
• Topological Insulators Avoid the Parity Anomaly
• Terahertz Quantum Hall Effect in a Topological Insulator
• The instanton vacuum of generalized $C{P}^{N-1}$ models
• Two-Dimensional Instantons with Bosonization and Physics of Adjoint $QC{D}_2$
• Theta renormalization, electron-electron interactions and super universality in the quantum Hall regime
• High magnetic field theory for the local density of states in graphene with smooth arbitrary potential landscapes
• Quantum Hall effect in a singly and doubly connected 3D topological insulator
• Quantum transport properties of two-dimensional electron gases under high magnetic fields
• Three-Dimensional Topological Insulator in a Magnetic Field: Chiral Side Surface States and Quantized Hall Conductance
• Anomalous galvanomagnetism, cyclotron resonance and microwave spectroscopy of topological insulators
• Landau level states on a topological insulator thin film
• Interaction and disorder effects in 3D topological insulator thin films
• Quantum Hall criticality and localization in graphene with short-range impurities at the Dirac point
• Quantum Hall Effect in Thin Films of Three-Dimensional Topological Insulators
• Topological Magneto-Electric Effect Decay
• Cancellation of quantum anomalies and bosonization of three-dimensional time-reversal symmetric topological insulators
• Magnetoelectric effect in topological insulator films beyond the linear response regime
• Dynamical scaling analysis of the optical Hall conductivity in the quantum Hall regime
• Signatures of Rashba Spin-Orbit Interaction in Charge and Spin Properties of Quantum Hall Systems
• Two parameter flow of σ_{xx}(ω) - σ_{xy}(ω) for the graphene quantum Hall system in ac regime
• Finite size effects on the statistical angle of an electron induced dyon in proximity to a topological insulator

Cited by in corpus (34)

• Transport in two-dimensional topological materials: recent developments in experiment and theory
• Experimental signature of parity anomaly in semi-magnetic topological insulator
• Anomalous Hall effect with massive Dirac fermions
• Spectral signatures of the surface anomalous Hall effect in magnetic axion insulators
• Half-Quantized Hall Effect and Power Law Decay of Edge Current Distribution
• Edge states and integer quantum Hall effect in topological insulator thin films
• Using nonlocal surface transport to identify the axion insulator
• Superconductor-insulator transitions: Phase diagram and magnetoresistance
• Gravitational parity anomaly with and without boundaries
• The quest for Casimir repulsion between Chern-Simons surfaces
• Transport Theory of Half-quantized Hall Conductance in a Semi-magnetic Topological Insulator
• Half-Quantized Hall Effect at the Parity-Invariant Fermi Surface
• Parity anomaly in four dimensions
• General nonlinear Hall current in magnetic insulators beyond the quantum anomalous Hall effect
• Light-induced half-quantized Hall effect and axion insulator
• Tunable Coupling between Surface States of a Three-Dimensional Topological Insulator in the Quantum Hall Regime
• Magnetoconductance, Quantum Hall Effect, and Coulomb Blockade in Topological Insulator Nanocones
• Quantum kinetics of anomalous and nonlinear Hall effects in topological semimetals
• Spectrum-wide quantum criticality at the surface of class AIII topological phases: An "energy stack" of integer quantum Hall plateau transitions
• Time-reversal-symmetric topological magnetoelectric effect in three-dimensional topological insulators
• Anomalous Hall Effect on the surface of topological Kondo insulators
• Conductance fluctuations and disorder induced $\nu =0$ quantum Hall plateau in topological insulator nanowires
• Signature of Parity Anomaly: Crossover from One Half to Integer Quantized Hall Conductance in a Finite Magnetic Field
• Interaction effects on quantum Hall transitions: dynamical scaling laws and superuniversality
• Geometrically induced reversion of Hall current in a topological insulator cavity
• Transport in topological insulator nanowires
• Photoinduced electronic and spin properties of two-dimensional electron gases with Rashba spin-orbit coupling under perpendicular magnetic fields
• Chiral edge mode for single-cone Dirac fermions
• Theory of magnetotransport in shaped topological insulator nanowires
• How spectrum-wide quantum criticality protects surface states of topological superconductors from Anderson localization: Quantum Hall plateau transitions (almost) all the way down
• Quantum Restored Symmetry Protected Topological Phases
• Pumping conductance, the intrinsic anomalous Hall effect, and statistics of topological invariants
• Boundary-condition-assisted chiral-symmetry protection of the zeroth Landau level on a two-dimensional lattice
• Hexagonal Warping Control of Exceptional Points in Topological Insulator--Ferromagnetic Heterojunctions