Disorder effects in topological insulator nanowires

TL;DR

This paper investigates how Coulomb impurities affect the electronic properties of topological insulator nanowires, showing that dielectric contrast influences potential fluctuations and that high impurity concentrations suppress observable subband oscillations.

Contribution

It provides a detailed calculation of Coulomb potential fluctuations in TI nanowires considering dielectric contrast and impurity effects, advancing understanding of disorder impacts on Majorana device feasibility.

Findings

Potential fluctuations can reach about three times the subband gap due to dielectric effects.

High impurity concentrations suppress observable subband oscillations.

Resistivity due to impurities shows no clear subband-related oscillations at high doping levels.

Abstract

Three-dimensional topological insulator (TI) nanowires with quantized surface subband spectra are studied as a main component of Majorana bound states (MBS) devices. However, such wires are known to have large concentration $N \sim 10^{19}$ cm$^{-3}$ of Coulomb impurities. It is believed that a MBS device can function only if the amplitude of long-range fluctuations of the random Coulomb potential $\Gamma$ is smaller than the subband gap $\Delta$. Here we calculate $\Gamma$ for recently experimentally studied large-dielectric-constant (Bi$_{1-x}$Sb$_x$)$_2$Te$_{3}$ wires in a small-dielectric-constant environment (no superconductor). We show that provided by such a dielectric-constant contrast, the confinement of electric field of impurities within the wire allows more distant impurities to contribute into $\Gamma$, leading to $\Gamma \sim 3\Delta$. We also calculate a TI wire resistance as a function of the Fermi level and carrier concentration due to scattering on Coulomb and neutral impurities, and do not find observable discrete subband-spectrum related oscillations at $N \gtrsim 10^{18}$ cm$^{-3}$.