Conductivity of a two-dimensional HgTe layer near the critical width: The role of developed edge states network and random mixture of $p$- and $n$-domains

TL;DR

This paper investigates the conductivity of a 2D HgTe quantum well near the topological transition, emphasizing the role of edge state networks and domain mixtures caused by width fluctuations and potential disorder.

Contribution

It introduces a percolation-based model for conductivity in HgTe quantum wells considering width fluctuations and domain mixtures, highlighting the impact of edge states and tunneling.

Findings

Conductance is governed by a network of edge states along zero-gap lines.

Potential fluctuations create a mixture of p- and n-domains affecting transport.

Tunneling across p-n junctions suppresses low-temperature conductivity, but edge states can restore it.

Abstract

The conductivity of a two-dimensional HgTe quantum well with a width $\sim$6.3~nm, close to the transition from ordinary to topological insulating phases, is studied. The Fermi level is supposed to get to the overall energy gap. The consideration is based on the percolation theory. We have found that the width fluctuations convert the system to a random mixture of domains with positive and negative energy gaps with internal edge states formed near zero gap lines. In the case with no potential fluctuations, the conductance of a finite sample is provided by a random edge states network. The zero-temperature conductivity of an infinite sample is determined by the free motion of electrons along the zero-gap lines and tunneling between them. The conductance of a single $p$-$n$ junction, which is crossed by the edge state, is found. The result is applied to the situation when potential fluctuations transform the system to a mixture of $p$- and $n$-domains. It is stated that the tunneling across $p$-$n$ junctions forbids the low-temperature conductivity of a random system, but the latter is restored due to the random edge states crossing the junctions.