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The boundary of a topological insulator (TI) hosts an anomaly restricting its possible phases: e.g. 3D strong and weak TIs maintain surface conductivity at any disorder if symmetry is preserved on-average, at least when electron interactions on the surface are weak. However the interplay of strong interactions and disorder with the boundary anomaly has not yet been theoretically addressed. Here we study this combination for the edge of a 2D TI and the surface of a 3D weak TI, showing how it can lead to an Anomalous Many Body Localized (AMBL) phase that preserves the anomaly. We discuss how the anomalous Kramers parity switching with pi flux arises in the bosonized theory of the localized helical state. The anomaly can be probed in localized boundaries by electrostatically sensing nonlinear hopping transport with e/2 shot noise. Our AMBL construction in 3D weak TIs fails for 3D strong TIs, suggesting that their anomaly restrictions are distinguished by strong interactions.
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 Emer
The Anderson localization transition is one of the most well studied examples of a zero temperature quantum phase transition. On the other hand, many open questions remain about the phenomenology of disordered systems driven far out of equilibrium. H
We review some experimental and theoretical results on the metal-to-insulator transition (MIT) observed at zero magnetic field (B=0) in several two-dimensional electron systems (2DES). Scaling of the conductance and magnetic field dependence of the c
We study the surface of a three-dimensional spin chiral $mathrm{Z}_2$ topological insulator (class CII), demonstrating the possibility of its localization. This arises through an interplay of interaction and statistically-symmetric disorder, that con
The low-temperature Hall resistivity rho_{xy} of La_{2/3}A_{1/3}MnO_3 single crystals (where A stands for Ca, Pb and Ca, or Sr) can be separated into Ordinary and Anomalous contributions, giving rise to Ordinary and Anomalous Hall effects, respective