Evolution of individual quantum Hall edge states in the presence of disorder

TL;DR

This paper numerically investigates how individual quantum Hall edge states evolve under disorder, revealing differences between states with high Chern numbers and the impact of disorder on their stability and localization.

Contribution

It introduces a detailed numerical analysis of high Chern number edge states and their evolution with disorder, highlighting differences from the n=1 case and their stability characteristics.

Findings

High Chern number edge states differ significantly from n=1 states.

Edge states from lower Landau levels are well localized and stable.

Higher Landau level edge states are more extended and less stable at high Fermi energies.

Abstract

Employing the Bloch eigenmode matching approach, we numerically study the evolution of individual quantum Hall edge states with respect to disorder. As shown by the two-parameter renormalization group flow of the Hall and Thouless conductances, quantum Hall edge states with high Chern number n are completely different from that of n=1 case. Two categories of individual edge modes are evaluated in a quantum Hall system with high Chern number. Edge states from the lowest Landau level have similar eigenfunctions which are well localized at the system edge and independent of the Fermi energy. On the other hand, at fixed Fermi energy, the edge state from higher Landau levels has larger expansion, which leads to less stable quantum Hall states at high Fermi energies. By presenting the local current density distribution, the influence of disorder on eigenmode-resolved edge states is vividly demonstrated.