Dirac Fermions and Topological Phases in Magnetic Topological Insulator Films

Abstract

We develop a Dirac fermion theory for topological phases in magnetic topological insulator films. The theory is based on exact solutions of the energies and the wave functions for an effective model of the three-dimensional topological insulator (TI) film. It is found that the TI film consists of a pair of massless or massive Dirac fermions for the surface states, and a series of massive Dirac fermions for the bulk states. The massive Dirac fermion always carries zero or integer quantum Hall conductance when the valence band is fully occupied while the massless Dirac fermion carries a one-half quantum Hall conductance when the chemical potential is located around the Dirac point for a finite range. The magnetic exchange interaction in the magnetic layers in the film can be used to manipulate either the masses or chirality of the Dirac fermions and gives rise to distinct topological phases, which cover the known topological insulating phases, such as quantum anomalous Hall effect, quantum spin Hall effect and axion effect, and also the novel topological metallic phases, such as half quantized Hall effect, half quantum mirror Hall effect, and metallic quantum anomalous Hall effect.

arXiv comment101 pages, 33 figures

References in corpus (94)

• Topological Insulators
• Topological insulators and superconductors
• Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells
• $Z_2$ Topological Order and the Quantum Spin Hall Effect
• Quantum Spin Hall Insulator State in HgTe Quantum Wells
• Berry Phase Effects on Electronic Properties
• Superconducting proximity effect and Majorana fermions at the surface of a topological insulator
• 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
• 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
• Topological Field Theory of Time-Reversal Invariant Insulators
• Spin Hall effect
• Classification of topological quantum matter with symmetries
• Novel Symmetry Classes in Mesoscopic Normal-Superconducting Hybrid Structures
• Topological invariants of time-reversal-invariant band structures
• Topological insulators and superconductors: ten-fold way and dimensional hierarchy
• Quantized Anomalous Hall Effect in Magnetic Topological Insulators
• Quantum Spin Hall Effect
• Magnetic-field-induced quantized anomalous Hall effect in intrinsic magnetic topological insulator MnBi${}_2$Te${}_4$
• Three Dimensional Dirac Semimetal and Quantum Transports in Cd3As2
• QCD Phenomenology based on a Chiral Effective Lagrangian
• Colloquium: Topological Band Theory
• Crossover of Three-Dimensional Topological Insulator of Bi2Se3 to the Two-Dimensional Limit
• Chern Numbers in Discretized Brillouin Zone: Efficient Method of Computing (Spin) Hall Conductances
• Majorana Zero Modes and Topological Quantum Computation
• Intrinsic magnetic topological insulators in van der Waals layered MnBi${}_2$Te${}_4$-family materials
• Topological orders and Edge excitations in FQH states
• Emergent Phenomena Induced by Spin-Orbit Coupling at Surfaces and Interfaces
• 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
• High-precision realization of robust quantum anomalous Hall state in a hard ferromagnetic topological insulator
• Seeing the magnetic monopole through the mirror of topological surface states
• Magnetoelectric polarizability and axion electrodynamics in crystalline insulators
• Topological quantization of the spin Hall effect in two-dimensional paramagnetic semiconductors
• Topological axion states in magnetic insulator MnBi${}_2$Te${}_4$ with the quantized magnetoelectric effect
• Realization of Quantum Spin Hall State in Monolayer 1T'-WTe2
• Robust axion insulator and Chern insulator phases in a two-dimensional antiferromagnetic topological insulator
• Observation of the Quantum Spin Hall Effect up to 100 Kelvin in a Monolayer Crystal
• Berry Curvature on the Fermi Surface: Anomalous Hall Effect as a Topological Fermi-Liquid Property
• Quantum Anomalous Hall Effect in Hg${}_{1-y}$Mn${}_y$Te Quantum Wells
• Experimental realization of an intrinsic magnetic topological insulator
• Trajectory of Anomalous Hall Effect toward the Quantized State in a Ferromagnetic Topological Insulator
• Antiferromagnetic topological insulators
• Quantum Spin Hall Effect and Topologically Invariant Chern Numbers
• Scale-Invariant Dissipationless Chiral Transport in Magnetic Topological Insulators beyond the Two-Dimensional Limit
• Topological Anderson Insulator
• Massive Dirac fermions and spin physics in an ultrathin film of topological insulator
• Chiral Topological Superconductor From the Quantum Hall State
• Oscillatory crossover from two dimensional to three dimensional topological insulators
• Giant Magneto-optical Kerr Effect and Universal Faraday Effect in Thin-film Topological Insulators
• Dynamical Axion Field in Topological Magnetic Insulators
• Finite size effects of helical edge states in HgTe/CdTe quantum wells
• Theory of the topological Anderson insulator
• Observation of Quantum Spin Hall States in InAs/GaSb Bilayers under Broken Time-Reversal Symmetry
• Effective continuous model for surface states and thin films of three dimensional topological insulators
• Surface quantized anomalous Hall current and magneto-electric effect in magnetically disordered topological insulators
• High-Chern-Number and High-Temperature Quantum Hall Effect without Landau Levels
• Realization of the Axion Insulator State in Quantum Anomalous Hall Sandwich Heterostructures
• Magnetic modulation doping in topological insulators toward higher-temperature quantum anomalous Hall effect
• Highly-ordered wide bandgap materials for quantized anomalous Hall and magnetoelectric effects
• Axion Electrodynamics in Topological Materials
• Topological Anderson Insulator in Three Dimensions
• Quantized topological magnetoelectric effect of the zero-plateau quantum anomalous Hall state
• Chiral topological superconductor and half-integer conductance plateau from quantum anomalous Hall plateau transition
• Quantum Anomalous Hall Effect with Higher Plateaus
• Tuning Chern Number in Quantum Anomalous Hall Insulators
• Surfaces of Axion Insulators
• Fermi-surface calculation of the anomalous Hall conductivity
• Topological magneto-electric effects in thin films of topological insulators
• Weyl fermions and the anomalous Hall effect in metallic ferromagnets
• Quantum anomalous Hall effect driven by magnetic proximity coupling in all-telluride based heterostructure
• Surface-edge state and half quantized Hall conductance in topological insulators
• Topological Insulators with Commensurate Antiferromagnetism
• Intrinsic magnetic topological insulators
• Surface states and chiral symmetry on the lattice
• Bulk-edge correspondence for Chern topological phases: A viewpoint from a generalized index theorem
• Magnetized Topological Insulator Multilayers
• Half-Quantized Hall Effect and Power Law Decay of Edge Current Distribution
• Edge states and integer quantum Hall effect in topological insulator thin films
• Two-dimensional topological insulator state in cadmium arsenide thin films
• Observation of Emergent Spacetime Supersymmetry at Superconducting Quantum Criticality
• Half-Quantized Hall Effect at the Parity-Invariant Fermi Surface
• Quantization and $2\pi$ Periodicity of the Axion Action in Topological Insulators
• The Bulk-Hinge Correspondence and Three-Dimensional Quantum Anomalous Hall Effect in Second Order Topological Insulators
• Tangent fermions: Dirac or Majorana fermions on a lattice without fermion doubling
• Helical Symmetry Breaking and Quantum Anomaly in Massive Dirac Fermions
• Signature of Parity Anomaly: Crossover from One Half to Integer Quantized Hall Conductance in a Finite Magnetic Field
• Fractional Electromagnetic Response in Three-Dimensional Chiral Anomalous Semimetal
• On the half-quantized Hall conductance of massive surface electrons in magnetic topological insulator films
• Metallic Quantized Anomalous Hall Effect without Chiral Edge States
• Anomalous Coherence Length of Majorana Zero Modes at Vortices in Superconducting Topological Insulators

Cited by in corpus (4)

• Floating Edge Bands in the Bernevig-Hughes-Zhang model with Altermagnetism
• Parity Anomalous Semimetal with Minimal Conductivity Induced by an In-Plane Magnetic Field
• Absence of Parity Anomaly in Massive Dirac Fermions on a Lattice
• Exact solutions for topological surface states of three-dimensional lattice models