DMPK Equation for the Edge Transport of Quantum Spin Hall Insulator

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.

Added a few references, and corrected a few typos. 5 pages, 3 figures

References in corpus (7)

• Quantum Spin Hall Insulator State in HgTe Quantum Wells
• A topological Dirac insulator in a quantum spin Hall phase : Experimental observation of first strong topological insulator
• The Helical Liquid and the Edge of Quantum Spin Hall Systems
• A knitting algorithm for calculating Green functions in quantum systems
• Two-dimensional spin-filtered chiral network model for the Z_2 quantum spin-Hall effect
• A proof of the Kramers degeneracy of transmission eigenvalues from antisymmetry of the scattering matrix
• Boundary criticality at the Anderson transition between a metal and a quantum spin Hall insulator in two dimensions