Quantum Hall effect of the surface states in topological insulator

TL;DR

This paper investigates the quantum Hall effect on the surface states of topological insulators, revealing quantized conductance depending on the Dirac fermion mass and discussing experimental realization.

Contribution

It provides a theoretical analysis of the quantum Hall effect in topological insulator surface states, highlighting the role of Dirac fermion mass and boundary conditions.

Findings

Quantized Hall conductance depends on the sign of the Dirac fermion mass.

Zero mode behavior varies near the boundary based on mass sign.

Experimental conditions for observing the effect are discussed.

Abstract

We study the quantum Hall effect in the surface states of topological insulator in the presence of a perpendicular magnetic field in the framework of edge states. Motion of Dirac fermions will form descrete Landau levels, among which a fully saturated zero mode will have different behaviors near the boundary according to the sign of the effective mass for Dirac fermions. The Hall conductance is quantized to be n (n is an integer) in the unit of e^2/h for a positive mass, n+1 for a negative mass, and n+1/2 for massless fermions. In topological insulator the massive term to the Dirac fermions can be the Zeeman coupling in a magnetic field or be induced by the finite-size effect in an ultrathin film. For example the g-factor of Bi_2Se_3 is positive and give rise to a positive mass term for Dirac fermions. We address experimental realization of the quantum Hall effect in topological insulators.