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Hall of Mirrors Scattering from an Impurity in a Quantum Wire

J. Y. Vaishnav·A. Itsara·E. J. Heller
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Abstract

This paper develops a scattering theory to examine how point impurities affect transport through quantum wires. While some of our new results apply specifically to hard-walled wires, others--for example, an effective optical theorem for two-dimensional waveguides--are more general. We apply the method of images to the hard-walled guide, explicitly showing how scattering from an impurity affects the wire's conductance. We express the effective cross section of a confined scatterer entirely in terms of the empty waveguide's Green's function, suggesting a way in which to use semiclassical methods to understand transport properties of smooth wires. In addition to predicting some new phenomena, our approach provides a simple physical picture for previously observed effects such as conductance dips and confinement-induced resonances.

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J. Y. Vaishnav, A. Itsara, E. J. Heller. 2006-02-21. Hall of Mirrors Scattering from an Impurity in a Quantum Wire. https://doi.org/10.1103/physrevb.73.115331

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