Disappearance of integer quantum Hall effect

TL;DR

This paper investigates how the integer quantum Hall effect (IQHE) disappears under strong disorder and weak magnetic fields in lattice models, revealing a universal sequence of plateau disappearance and differences from continuum models.

Contribution

It uncovers the generic sequence of IQHE plateau disappearance and highlights the role of topological invariants in explaining these phenomena in lattice systems.

Findings

Higher IQHE plateaus vanish earlier than lower ones.

Extended levels do not float up but merge after plateau destruction.

Features persist in the weak-field limit as shown by localization-length calculations.

Abstract

The disappearance of integer quantum Hall effect (IQHE) at strong disorder and weak magnetic field is studied in a lattice model. A generic sequence by which the IQHE plateaus disappear is revealed: higher IQHE plateaus always vanish earlier than lower ones, and extended levels between those plateaus do not float up in energy but keep merging together after the destruction of plateaus. All of these features remain to be true in the weak-field limit as shown by the thermodynamic-localization-length calculation. Topological characterization in terms of Chern integers provides a simple physical explanation and suggests a qualitative difference between the lattice and continuum models.