DMPK Equation for the Edge Transport of Quantum Spin Hall Insulator

TL;DR

This paper develops a DMPK equation for the edge transport in quantum spin Hall insulators, revealing unique statistical properties that reflect their topological classification and differ from conventional 1D conductors.

Contribution

It introduces a new DMPK equation tailored for quantum spin Hall insulators with multiple edge states, linking ensemble statistics to topological classification.

Findings

Edge transport in quantum spin Hall insulators exhibits unique ensemble statistics.

The statistics reflect the Z2 topological classification of the insulators.

Quantum spin Hall insulators act as a new type of 1D quantum conductor.

Abstract

Using the random matrix theory, we investigate the ensemble statistics of edge transport of a quantum spin Hall insulator with multiple edge states in the presence of quenched disorder. Dorokhov-Mello-Pereyra-Kumar equation applicable for such a system is established. It is found that a two-dimensional quantum spin Hall insulator is effectively a new type of one-dimensional (1D) quantum conductor with the different ensemble statistics from that of the ordinary 1D quantum conductor or the insulator with an even number of Kramers edge pairs. The ensemble statistics provides a physical manifestation of the Z2-classification for the time-reversal invariant insulators.