How edge states are destroyed in disordered mesoscopic samples?

TL;DR

This paper provides a theoretical phase diagram showing how increasing disorder destroys edge states in mesoscopic samples within the integer quantum Hall regime, using transmission channels and a generalized current density.

Contribution

It introduces a method to visualize and identify surviving edge states under disorder using a generalized current density.

Findings

Edge states are destroyed sequentially with increasing disorder.

Transmission eigen-channels close one by one as edge states are destroyed.

A generalized current density helps identify surviving edge states.

Abstract

We report theoretical investigations on how edge states are destroyed in disordered mesoscopic samples by calculating a "phase diagram" in terms of energy versus disorder strength $(E,W)$, and magnetic field versus disorder strength $(B,W)$, in the integer quantum Hall regime. It is found that as the disorder strength $W$ increases, edge states are destroyed one by one if transmission eigen-channels are used to characterize the edge states. Near the insulating regime, transmission eigen-channels are closed one by one in the same order as edges states are destroyed. To identify those edge states which have survived disorder, we introduce a generalized current density that can be calculated and visualized.