# Localized surfaces of three dimensional topological insulators

## TL;DR

This paper investigates the surface states of a three-dimensional topological insulator, showing how interactions and disorder can localize the surface fermions into distinct regimes with potential experimental implications.

## Contribution

It introduces a novel understanding of localization mechanisms on the surface of 3D topological insulators involving domain-wall networks and identifies two distinct localized phases.

## Key findings

- Identification of a 'clogged' localized regime due to junctions in the domain-wall network.
- Discovery of a 'fully localized' regime where all domain-walls are localized.
- Discussion of experimental signatures for these localized phases.

## Abstract

We study the surface of a three-dimensional spin chiral $\mathrm{Z}_2$ topological insulator (class CII), demonstrating the possibility of its localization. This arises through an interplay of interaction and statistically-symmetric disorder, that confines the gapless fermionic degrees of freedom to a network of one-dimensional helical domain-walls that can be localized. We identify two distinct regimes of this gapless insulating phase, a `clogged' regime wherein the network localization is induced by its junctions between otherwise metallic helical domain-walls, and a `fully localized' regime of localized domain-walls. The experimental signatures of these regimes are also discussed.