Gapless insulating edges of dirty interacting topological insulators

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.

Anomalous localization at the boundary of an interacting topological insulator

“…However the mechanism in that case is due to the current explicitly breaking time reversal, and requires much larger voltages than the nonlinear form in Eq. (13).…”

“…The generic case of strong interactions and strong disorder has been explored for 2D TI edges through 1D bosonization, 13,20,21 leading (for appropriate disorder and interaction strengths) to a zero-temperature state which breaks time-reversal locally but preserves it on average and may naively appear to be a many-body localized (MBL) 22,23 phase. The phase can be thought of as a spin glass, where domain walls (kinks and anti-kinks) form localized puddles of charge-e/2 fermions (solitons).…”

Localized surfaces of three-dimensional topological insulators

“…IV B and Appendix B. As we will demonstrate, for sufficiently strong interactions, K < 1/2, the junctions become strong impurity barriers that suppress all conduction (before, i.e., for weaker interaction than localization of isolated domain-walls, K < 3/8 [14][15][16]), and break the time-reversal symmetry spontaneously. Our results are consistent with the earlier finding in the helical liquid point contact study with spin-orbit couplings [29].…”

“…As we demonstrate below, for the second case of a network of helical domain-walls, in the presence of interactions, a CII class TI surface indeed displays a phase transition to a gapless insulating surface. The latter exhibits two regimes: a "clogged" regime in which the barriers to transport are the junctions in the network of otherwise delocalized domain-walls [29], and a fully localized regime of interpenetrating one-dimensional (1D) localized helical edge states [16]. These interactioninduced regimes are obtained via standard analysis for helical Luttinger liquids [14][15][16]29].…”

“…Such a localized state breaks the time-reversal symmetry spontaneously, but in "spin glass" fashion, preserving it statistically. It exhibits a localization length that is a non-monotonic function of disorder strength, and is best viewed as a localized insulator of half charge fermionic domain-walls (Luther-Emery [20] fermons) [16]. Such edge localization provides a potential explanation of the puzzling experimental observations in InAs/GaSb TI systems [21][22][23][24].…”