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Published March 24, 2014 | Submitted + Published
Journal Article Open

Nonperturbative expression for the transmission through a leaky chiral edge mode

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.

Additional Information

© 2014 American Physical Society. Received 27 July 2013; revised manuscript received 12 February 2014; published 24 March 2014. It is a pleasure to acknowledge useful discussions with Matthew Hastings and Konstantin Efetov as well as funding from the IQIM, an NSF center, supported by the Moore Foundation, and from DARPA through FENA. I.K. acknowledges financial support from NSF CAREER Award No. DMR-0956053.

Attached Files

Published - PhysRevB.89.104204.pdf

Submitted - 1308.0045v1.pdf

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August 20, 2023
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