Quantum-Hall to insulator transition

TL;DR

This paper investigates the transition from quantum Hall to insulator states in a 2D model by analyzing how increasing disorder affects conductivities and critical states, revealing the sequential disappearance of current-carrying states and the decline of Hall conductivity.

Contribution

It provides a numerical study of the quantum Hall to insulator transition, highlighting the disorder-induced disappearance of critical states and the monotonic decline of Hall conductivity.

Findings

Current-carrying states near the band center vanish first with increasing disorder.

Quantized Hall conductivity decreases monotonically to zero as disorder increases.

Critical states' behavior is linked to the transition from quantum Hall to insulator.

Abstract

The crossover from the quantum Hall regime to the Hall-insulator is investigated by varying the strength of the diagonal disorder in a 2d tight-binding model. The Hall and longitudinal conductivities and the behavior of the critical states are calculated numerically. We find that with increasing disorder the current carrying states close to the band center disappear first. Simultaneously, the quantized Hall conductivity drops monotonically to zero also from higher quantized values.