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arXiv · 1308.0045

A non-perturbative expression for the transmission through a leaky chiral edge mode

Kun W. Kim·Israel Klich·Gil Refael
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Abstract

Chiral edge modes of topological insulators and Hall states exhibit non-trivial behavior of conductance in the presence of impurities or additional channels. We will 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 function matrix of bulk modes in real space, the renormalized Green 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 onsite impurity potentials for which we found 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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Kun W. Kim, Israel Klich, Gil Refael. 2013-07-31. A non-perturbative expression for the transmission through a leaky chiral edge mode. https://doi.org/10.1103/physrevb.89.104204

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