Backscattering in a 2D topological insulator and conductivity of a 2D strip

Abstract

A strip of 2D HgTe topological insulator is studied. The same-spin edge states in ideal system propagate in opposite directions on different sides of the strip and do not mix by tunneling. Impurities, edge irregularities, and phonons produce transitions between the contra-propagating edge states on different edges. This backscattering determines the conductivity of an infinitely long strip. It is found that the conductivity exponentially grows with the strip width. The conductivity at finite temperature is determined within the framework of the kinetic equation. In the same approximation the non-local resistance coefficients of 4-terminal strip are found. At low temperature the localization occurs and 2-terminal conductance of long wire vanishes, but with the exponentially long (with respect to the strip width) localization length. The transition temperature between kinetic and localization behaviors has been found.