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

TL;DR

This paper introduces a modified 2D lattice model with a Wilson term to accurately simulate the surface states of 3D topological insulators, overcoming fermion doubling and enabling efficient numerical studies of their properties.

Contribution

The authors develop a simple 2D lattice model with a Wilson term that faithfully captures the low-energy surface state physics of 3D TIs, facilitating numerical simulations.

Findings

The modified 2D lattice model accurately reproduces surface state properties.

The model demonstrates the wormhole effect in TI nanowires under magnetic fields.

Surface states remain robust against disorder in the model.

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.