Gapless insulating edges of dirty interacting topological insulators

TL;DR

This paper shows that disorder and interactions can turn the edges of a 2D topological insulator into a gapless, insulating, spin-glass-like state that breaks time-reversal symmetry, explaining puzzling experiments.

Contribution

It introduces a new phase where helical edges become insulating and glassy due to disorder and interactions, using helical Luttinger liquid theory and Emery-Luther mapping.

Findings

Edge states become localized and insulating due to disorder and interactions.

The edge state spontaneously breaks time-reversal symmetry in a spin glass manner.

The localization of the edge state exhibits non-monotonic behavior with disorder strength.

Abstract

We demonstrate that a combination of disorder and interactions in a two-dimensional bulk topological insulator can generically drive its helical edge insulating. We establish this within the framework of helical Luttinger liquid theory and exact Emery-Luther mapping. The gapless glassy edge state spontaneously breaks time-reversal symmetry in a `spin glass' fashion, and may be viewed as a localized state of solitons which carry half integer charge. Such a qualitatively distinct edge state provides a simple explanation for heretofore puzzling experimental observations. This phase exhibits a striking non-monotonicity, with the edge growing less localized in both the weak and strong disorder limits.