Two-Dimensional Lattice Model for the Surface States of Topological Insulators

Abstract

The surface states in three-dimensional (3D) topological insulators (TIs) can be described by a two-dimensional (2D) continuous Dirac Hamiltonian. However, there exists the Fermion doubling problem when putting the continuous 2D Dirac equation into a lattice model. In this letter, we introduce a Wilson term with a zero bare mass into the 2D lattice model to overcome the difficulty. By comparing with a 3D Hamiltonian, we show that the modified 2D lattice model can faithfully describe the low-energy electrical and transport properties of surface states of 3D TIs. So this 2D lattice model provides a simple and cheap way to numerically simulate the surface states of 3D TI nanostructures. Based on the 2D lattice model, we also establish the wormhole effect in a TI nanowire by a magnetic field along the wire and show the surface states being robust against disorder. The proposed 2D lattice model can be extensively applied to study the various properties and effects, such as the transport properties, Hall effect, universal conductance fluctuations, localization effect, etc.. So it paves a new way to study the surface states of the 3D topological insulators.

7 pages, 5 figures

References in corpus (10)

• Discovery (theoretical prediction and experimental observation) of a large-gap topological-insulator class with spin-polarized single-Dirac-cone on the surface
• First direct observation of Spin-textures in Topological Insulators : Spin-resolved ARPES as a probe of topological quantum spin Hall effect and Berry's phase
• Observation of topological surface state quantum Hall effect in an intrinsic three-dimensional topological insulator
• Strong surface scattering in ultrahigh mobility Bi2Se3 topological insulator crystals
• Aharonov-Bohm oscillations in disordered topological insulator nanowires
• Quantum Hall Effect on Top and Bottom Surface States of Topological Insulator (Bi1-xSbx)2Te3 Films
• Anomalous Aharonov-Bohm conductance oscillations from topological insulator surface states
• Disorder-induced enhancement of transport through graphene p-n junctions
• Charge and spin transport in edge channels of a $\nu =0$ quantum Hall system on the surface of topological insulators
• Surface Step Defect in 3D Topological Insulators: Electric Manipulation of Spin and Quantum Spin Hall Effect

Cited by in corpus (23)

• Tunable Josephson diode effect on the surface of topological insulators
• Magnon-mediated superconductivity on the surface of a topological insulator
• Gate voltage controlled thermoelectric figure of merit in three-dimensional topological insulator nanowires
• Confinement and Fermion Doubling Problem in Dirac-like Hamiltonians
• Absence of equilibrium edge currents in theoretical models of topological insulators
• Magnetotransport signatures of three-dimensional topological insulator nanostructures
• Electron-magnon coupling and quasiparticle lifetimes on the surface of a topological insulator
• Altermagnetism-Induced Parity Anomaly in Weak Topological Insulators
• Doubled Shapiro Steps in a Topological Josephson Junction
• Interplay between boundary conditions and Wilson's mass in Dirac-like Hamiltonians
• Generalized eigenproblem without fermion doubling for Dirac fermions on a lattice
• Interplay of Altermagnetic Order and Wilson Mass in the Dirac Equation: Helical Edge States without Time-Reversal Symmetry
• Transport study of the wormhole effect in three-dimensional topological insulators
• Quantum transport through three-dimensional topological insulator p-n junction under magnetic field
• Electrically controlled crossover between $2\pi$- and $4\pi$-Josephson effects through topologically-confined channels in silicene
• Transport in a thin topological insulator with potential and magnetic barriers
• Dynamics of impurity in the environment of Dirac fermions
• Quantum revivals in HgTe/CdTe quantum wells and topological phase transitions
• Anisotropic transport properties in prismatic topological insulator nanowires
• Spin-polarized scanning tunneling microscopy measurement scheme for determining the quantum geometric tensor
• High thermoelectric figure of merit of quantum dot array quantum wires
• Effects of zigzag edge states on the thermoelectric properties of finite graphene nanoribbons
• Scheme for braiding Majorana zero modes in vortices using an STT-matrix