Quantum Hall effect in a singly and doubly connected 3D topological insulator

TL;DR

This paper analyzes the quantum Hall effect on the surface states of 3D topological insulators with complex geometries, proposing a flux ramping experiment to measure quantized Hall conductivity free from edge state contamination.

Contribution

It derives analytical formulas for energy spectra in complex geometries and suggests a novel flux ramping method for measuring quantized Hall conductivity in topological insulators.

Findings

Quantized Hall conductivity can be measured via flux ramping experiments.

Zeeman coupling and interactions lead to odd integer quantum Hall states.

Backgating enables arbitrary integer Hall conductance values.

Abstract

The surface states of topological insulators, which behave as charged massless Dirac fermions, are studied in the presence of a quantizing uniform magnetic field. Using the method of D.H. Lee[1], analytical formula satisfied by the energy spectrum is found for a singly and doubly connected geometry. This is in turn used to argue that the way to measure the quantized Hall conductivity is to perform the Laughlin's flux ramping experiment and measure the charge transferred from the inner to the outer surface, analogous to the experiment in Ref.[2]. Unlike the Hall bar setup used currently, this has the advantage of being free of the contamination from the delocalized continuum of the surface edge states. In the presence of the Zeeman coupling, and/or interaction driven Quantum Hall ferromagnetism, which translate into the Dirac mass term, the quantized charge Hall conductivity sigma_{xy}=n e^2/h, with n=0,\pm 1,\pm 3,\pm 5... Backgating of one of the surfaces leads to additional Landau level splitting and in this case n can be any integer.