Gapless insulating edges of dirty interacting topological insulators

Understand

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.