# Edge stability and edge quantum criticality in 2D interacting topological insulators

## TL;DR

This paper uses quantum Monte Carlo simulations to study the stability of helical edge states in 2D topological insulators with interactions, revealing conditions for robustness and edge magnetic order, and uncovering universal critical properties.

## Contribution

First sign-free QMC simulation of an interacting 2D TI model showing edge state robustness and magnetic quantum criticality with fractionalized charges at domain walls.

## Key findings

- Helical edge states are robust against two-particle backscattering with moderate Coulomb repulsion.
- Strong Coulomb interactions can gap edge states and induce magnetic order.
- Fractionalized e/2 charge appears at magnetic domain walls on edges.

## Abstract

Robustness of helical edge states in 2D topological insulators (TI) against strong interactions remains an intriguing issue. Here, by performing the first sign-free quantum Monte Carlo (QMC) simulation of the Kane-Mele-Hubbard-Rashba model which describes an interacting 2D TI with two-particle backscattering on edges, we verify that the gapless helical edge states are robust against a finite range of two-particle backscattering when the Coulomb repulsion is not strong. However, when the Coulomb repulsion is strong enough, the helical edge states can be gapped by infinitesimal two-particle backscattering, resulting in edge magnetic order. We further reveal universal properties of the magnetic edge quantum critical point (EQCP). At magnetic domain walls on edges, we find that a fractionalized charge of e/2 emerges. Implications of our results to recent transport experiments in the InAs/GaSb quantum well, which is a 2D TI with strong interactions, will also be discussed.