Localization-Driven Correlated States of Two Isolated Interacting Helical Edges

TL;DR

This paper investigates how disorder and interactions in two helical edges of topological insulators lead to localized states, novel interedge fluid phases, and stable correlated states with distinct transport signatures.

Contribution

It reveals that disorder and interactions induce a gapless localized state and identifies a stable antisymmetric interlocked fluid phase with negative drag.

Findings

Disorder and interactions drive the system to a localized state.

A stable antisymmetric interlocked fluid with negative drag emerges.

Interlocked fluid states are robust against intraedge perturbations at zero temperature.

Abstract

We study the localization-driven correlated states among two isolated dirty interacting helical edges as realized at the boundaries of two-dimensional $\mathbb{Z}_2$ topological insulators. We show that an interplay of time-reversal symmetric disorder and strong interedge interactions generically drives the entire system to a gapless localized state, preempting all other intraedge instabilities. For weaker interactions, an antisymmetric interlocked fluid, causing a negative perfect drag, can emerge from dirty edges with different densities. We also find that the interlocked fluid states of helical edges are stable against the leading intraedge perturbation down to zero temperature. The corresponding experimental signatures including zero-temperature and finite-temperature transport are discussed.