Magnetotransport properties of the Quantum Spin Hall and Quantum Hall states in an inverted HgTe/CdTe and InAs/GaSb quantum wells

TL;DR

This paper theoretically investigates the magnetotransport properties of quantum spin Hall and quantum Hall states in inverted HgTe/CdTe and InAs/GaSb quantum wells, identifying how Hall conductivity varies across topological phases under magnetic fields.

Contribution

It provides a theoretical analysis of the critical magnetic field separating QSH and QH states and demonstrates how Hall conductivity responses can distinguish topological phases.

Findings

Hall conductivity is high in QH regions at low Fermi energy.

Hall conductivity differs significantly between QSH and QH states.

The critical magnetic field expression aligns with previous literature.

Abstract

The quantum spin Hall (QSH) states discovered in an inverted band of InAs/GaSb and HgTe/CdTe quantum wells categorize them among the very superior candidates for topological insulators. In the presence of a magnetic field, these QSH states persist up to a magnetic field equal to the critical field, beyond which the edge states would consist of normal quantum Hall (QH) states. We provide the expression of this critical field which is found consistent with some previous literature. The critical field partitioned the spectrum into two types of quantum states, \textit{viz}. , the Quantum spin Hall (QSH) and Quantum Hall (QH) states. We present a theoretical study of the magnetotransport properties based on the Bernevig-Hughes-Zhang Hamiltonian that describes these QSH states. Our results of the Hall conductivity show the different responses at these two different topological regions. Around the low Fermi energy level, the system has a high Hall conductivity in the QH region, while the same is less dominant in the QSH region. Our results of the Hall conductivity thus help differentiate the type topological phase of the given quantum well.