Metal insulator transition in modulated quantum Hall systems

TL;DR

This paper investigates the quantum Hall effect in modulated 2D electron systems with disorder, identifying how critical energies for extended states merge under strong disorder depending on symmetry.

Contribution

It provides a numerical analysis of the metal-insulator transition in modulated quantum Hall systems, highlighting the merging behavior of critical energies under varying disorder conditions.

Findings

Critical energies are identified via scaling of Hall conductivity and localization length.

Under strong disorder, critical energies from subbands merge into one.

The merging behavior depends on the symmetry of disorder and periodic potential.

Abstract

The quantum Hall effect is studied numerically in modulated two-dimensional electron systems in the presence of disorder. Based on the scaling property of the Hall conductivity as well as the localization length, the critical energies where the states are extended are identified. We find that the critical energies, which are distributed to each of the subbands, combine into one when the disorder becomes strong, in the way depending on the symmetry of the disorder and/or the periodic potential.