Localization of edge electrons in a 2D topological insulator strip

The edge states in an ideal topological insulator are topologically protected. The same-spin edge states propagate in opposite directions on different sides of the strip and do not mix by tunneling. The interaction with impurities results in interedge same-spin backscattering. At low temperatures, the localization occurs and the conductance of a long wire vanishes. We study this localization in a numerical model of localized scatterers. The localization length is found to be exponentially long with respect to the strip width. The intraedge inelastic forward scattering destroys the coherence. These processes caused by phonons were explored. The transition temperature between kinetic and localization behaviors has been found.