Evolutions of helical edge states in disordered HgTe/CdTe quantum wells

TL;DR

This paper investigates how nonmagnetic disorder affects helical edge states in HgTe/CdTe quantum wells, revealing a critical disorder strength for edge state emergence, their decline with increasing disorder, and the existence of a metallic phase between topological phases.

Contribution

It provides a detailed analysis of disorder-induced evolution of edge states, including a phase diagram with a critical disorder threshold and the identification of a metallic phase separating topological phases.

Findings

Helical edge states appear above a critical disorder strength after a gap-closing transition.

Edge states decline stepwise with increasing disorder due to finite-width effects.

A metallic phase exists between topologically distinct phases, with an Anderson transition to an insulator at higher disorder.

Abstract

We study the evolutions of the nonmagnetic disorder-induced edge states with the disorder strength in the HgTe/CdTe quantum wells. From the supercell band structures and wave-functions, it is clearly shown that the conducting helical edge states, which are responsible for the reported quantized conductance plateau, appear above a critical disorder strength after a gap-closing phase transition. These edge states are then found to decline with the increase of disorder strength in a stepwise pattern due to the finite-width effect, where the opposite edges couple with each other through the localized states in the bulk. This is in sharp contrast with the localization of the edge states themselves if magnetic disorders are doped which breaks the time-reversal symmetry. The size-independent boundary of the topological phase is obtained by scaling analysis, and an Anderson transition to an Anderson insulator at even stronger disorder is identified, in-between of which, a metallic phase is found to separate the two topologically distinct phases.