Nonperturbative expression for the transmission through a leaky chiral edge mode

Kun Woo Kim, Israel Klich, and Gil Refael
Phys. Rev. B 89, 104204 – Published 24 March 2014

Abstract

Chiral edge modes of topological insulators and Hall states exhibit nontrivial behavior of conductance in the presence of impurities or additional channels. We present a simple formula for the conductance through a chiral edge mode coupled to a disordered bulk. For a given coupling matrix between the chiral mode and bulk modes, and a Green's function matrix of bulk modes in real space, the renormalized Green's function of the chiral mode is expressed in closed form as a ratio of determinants. We demonstrate the usage of the formula in two systems: (i) a 1d wire with random on-site impurity potentials for which we found that the disorder averaging is made simpler with the formula, and (ii) a quantum Hall fluid with impurities in the bulk for which the phase picked up by the chiral mode due to the scattering with the impurities can be conveniently estimated.

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  • Received 27 July 2013
  • Revised 12 February 2014

DOI:https://doi.org/10.1103/PhysRevB.89.104204

©2014 American Physical Society

Authors & Affiliations

Kun Woo Kim1, Israel Klich2, and Gil Refael1

  • 1Department of Physics, California Institute of Technology, 1200 East California Boulevard, MC 114-36, Pasadena, California 91125, USA
  • 2Department of Physics, University of Virginia, Charlottesville, Virginia 22904, USA

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Issue

Vol. 89, Iss. 10 — 1 March 2014

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