Mathematical and Physical Aspects of Topologically Protected States

Localization at the Edge of 2D Topological Insulator by Kondo Impurities

Boris Altshuler

Columbia University


One-dimensional helical edge of a two-dimensional topological insulator is believed to be an ideal conductor, i.e. to be characterized by the universal conductance. This means that in contrast with ordinary one-dimensional particles, which are known to be always localized by arbitrary weak disorder, the states of chiral electrons are extended regardless of disorder. I will discuss the effect of localized spins - Kondo impurities. Provided that the electron-spin couplings is anisotropic this system can be mapped to the problem of the pinning of the ordinary charge density wave by a disordered potential. This mapping proves that arbitrary weak anisotropic disorder in coupling of chiral electrons with spin impurities eliminates effects of the topology and leads to the Anderson localization of the edge states. I will analyze existing experimental results in view of this conclusion.