# Topological phase transitions in an inverted InAs/GaSb quantum well driven by tilted magnetic fields

## TL;DR

This paper investigates how tilted magnetic fields influence topological phase transitions in an inverted InAs/GaSb quantum well, revealing reentrant pseudo quantum spin Hall states driven by magnetic field orientation and strength.

## Contribution

It demonstrates the reentrant behavior of pseudo quantum spin Hall states under tilted magnetic fields and elucidates the underlying mechanisms involving Landau level bending and mixing.

## Key findings

- High magnetic fields induce a metallic state from the pseudo quantum spin Hall phase.
- Reentrant pseudo quantum spin Hall states occur with increasing out-of-plane magnetic field.
- Quantized conductance remains robust against disorder, confirming topological protection.

## Abstract

The helical edge states in a quantum spin Hall insulator are presumably protected by time- reversal symmetry. However, even in the presence of magnetic field which breaks time-reversal symmetry, the helical edge conduction can still exist, dubbed as pseudo quantum spin Hall effect. In this work, the effects of the magnetic fields on the pseudo quantum spin Hall effect and the phase transitions are studied. We show that an in-plane magnetic field drives a pseudo quantum spin Hall state to metallic state at a high field. Moreover, at a fixed in-plane magnetic field, an increasing out-of-plane magnetic field leads to a reentrance of pseudo quantum spin Hall state in an inverted InAs/GaSb quantum well. The edge state probability distribution and Chern numbers are calculated to verify that the reentrant states are topologically nontrivial. The origin of the reentrant behavior is attributed to the nonmonotonic bending of Landau levels and the Landau level mixing caused by the orbital effect induced by the in-plane magnetic field. The robustness to disorder is demonstrated by the numerically calculated quantized conductance for disordered nanowires within Landauer-B\"uttiker formalism.