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

TL;DR

This paper investigates how backscattering affects the conductivity of a 2D HgTe topological insulator strip, revealing exponential growth of conductivity with width and analyzing temperature-dependent localization effects.

Contribution

It provides a detailed analysis of backscattering mechanisms and their impact on conductivity and localization in 2D topological insulator strips, including temperature effects.

Findings

Conductivity exponentially increases with strip width.

Localization causes conductance to vanish at low temperature.

Transition temperature between kinetic and localization regimes identified.

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.