`Holographic' treatment of surface disorder on a topological insulator

TL;DR

This paper introduces an analytical method to study surface disorder effects on topological insulators by reducing the problem to a lower-dimensional Hamiltonian, enabling analysis of larger systems and revealing disorder-related scaling behaviors.

Contribution

The paper presents a new analytical approach that eliminates the bulk to focus on surface states, allowing the study of larger disordered systems in topological insulators.

Findings

Surface states survive strong disorder and shift to the bulk's clean region.

System size for thermodynamic limit increases with disorder.

Edge conductance decreases with increasing disorder.

Abstract

The effect of surface disorder on electronic systems is particularly interesting for topological phases with surface and edge states. Using exact diagonalization, it has been demonstrated that the surface states of a 3D topological insulator survive strong surface disorder, and simply get pushed to a clean part of the bulk. Here we explore a new method which analytically eliminates the clean bulk, and reduces a $D$-dimensional problem to a Hamiltonian-diagonalization problem within the $(D-1)$-dimensional disordered surface. This dramatic reduction in complexity allows the analysis of significantly bigger systems than is possible with exact diagonalization. We use our method to analyze a 2D topological spin-Hall insulator with non-magnetic and magnetic edge impurities, and we calculate the probability density (or local density of states) of the zero-energy eigenstates as a function of edge-parallel momentum and layer index. Our analysis reveals that the system size needed to reach behavior in the thermodynamic limit increases with disorder. We also compute the edge conductance as a function of disorder strength, and chart a lower bound for the length scale marking the crossover to the thermodynamic limit.