Quantum Hall effect in a p-type heterojunction with a lateral surface quantum dot superlattice

TL;DR

This paper investigates the quantization of Hall conductance in a p-type heterojunction with a lateral quantum dot superlattice, introducing a new calculation method and analyzing topological properties and deviations from quantization.

Contribution

It proposes a novel method for calculating Hall conductance in a 2D hole gas with periodic potential using wavefunction singularities in k-space.

Findings

Deviations from quantization rules for Hofstadter butterfly observed

Exchange of Chern numbers between magnetic subbands discussed

New insights into topological properties of hole wavefunctions obtained

Abstract

The quantization of Hall conductance in a p-type heterojunction with lateral surface quantum dot superlattice is investigated. The topological properties of the four-component hole wavefunction are studied both in r- and k-spaces. New method of calculation of the Hall conductance in a 2D hole gas described by the Luttinger Hamiltonian and affected by lateral periodic potential is proposed, based on the investigation of four-component wavefunction singularities in k-space. The deviations from the quantization rules for Hofstadter "butterfly" for electrons are found, and the explanation of this effect is proposed. For the case of strong periodic potential the mixing of magnetic subbands is taken into account, and the exchange of the Chern numbers between magnetic subands is discussed.