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 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.