Localization-Driven Correlated States of Two Isolated Interacting Helical Edges

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 inter-edge interactions generically drives the entire system to a gapless localized state, preempting all other intra-edge instabilities. For weaker interactions, an anti-symmetric interlocked fluid, causing a negative perfect drag, can emerge from dirty edges with different densities. We also study the stability of the inter-edge correlated states against finite size and/or finite temperature corrections.
The corresponding experimental signatures are discussed.