Three-Dimensional Topological Insulator in a Magnetic Field: Chiral Side Surface States and Quantized Hall Conductance

TL;DR

This paper investigates the surface states of a 3D topological insulator under a magnetic field, revealing chiral states responsible for quantized Hall conductance and analyzing their robustness against impurities.

Contribution

It introduces a tight-binding model to study surface state transport in magnetic fields and links the quantized Hall conductance to the number of Dirac cones.

Findings

Chiral surface states cause quantized Hall conductance of (2n+1)e^2/h.

Robustness of conductance depends on the parity of Dirac cone number.

Proposes an experimental setup for transport measurement.

Abstract

Low energy excitation of surface states of a three-dimensional topological insulator (3DTI) can be described by Dirac fermions. By using a tight-binding model, the transport properties of the surface states in a uniform magnetic field is investigated. It is found that chiral surface states parallel to the magnetic field are responsible to the quantized Hall (QH) conductance $(2n+1)\frac{e^2}{h}$ multiplied by the number of Dirac cones. Due to the two-dimension (2D) nature of the surface states, the robustness of the QH conductance against impurity scattering is determined by the oddness and evenness of the Dirac cone number. An experimental setup for transport measurement is proposed.