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.

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

References in corpus (19)

• Quantum Spin Hall Effect in Graphene
• Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells
• $Z_2$ Topological Order and the Quantum Spin Hall Effect
• Quantum Spin Hall Insulator State in HgTe Quantum Wells
• Topological Insulators in Three Dimensions
• A topological Dirac insulator in a quantum spin Hall phase : Experimental observation of first strong topological insulator
• Random-Matrix Theory of Quantum Transport
• Topological invariants of time-reversal-invariant band structures
• The Helical Liquid and the Edge of Quantum Spin Hall Systems
• Stability of the quantum spin Hall effect: effects of interactions, disorder, and Z_2 topology
• Localization in a quantum spin Hall system
• 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
• On the distribution of transmission eigenvalues in disordered wires
• 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
• DMPK Equation for Transmission Eigenvalues in Metallic Carbon Nanotubes
• Conductance distribution in strongly disordered mesoscopic systems in three dimensions
• Universal quantized spin-Hall conductance fluctuation in graphene

Cited by in corpus (6)

• Magnetoconductance of the quantum spin Hall state
• The edge engineering of topological Bi(111) bilayer
• Disorder Effects in Topological States -- Brief Review of the Recent Developments
• Transport study of the wormhole effect in three-dimensional topological insulators
• Universal Conductance Fluctuations in Mesoscopic Systems with Superconducting Leads: Beyond the Andreev Approximation
• Fermi energy sensitive universal conductance fluctuations in anisotropic materials