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Published February 18, 2014 | Submitted + Published
Journal Article Open

Semiclassical approach to bound states of a pointlike impurity in a two-dimensional Dirac system

Abstract

The goal of this paper is to provide an intuitive and useful tool for analyzing the impurity-bound-state problem. We develop a semiclassical approach and apply it to an impurity in two-dimensional systems with parabolic or Dirac-like bands. Our method consists of reducing a higher-dimensional problem into a sum of one-dimensional ones using the two-dimensional Green's functions as a guide. We then analyze the one-dimensional effective systems in the spirit of the wave-function-matching method as in the standard one-dimensional quantum model. We demonstrate our method on two-dimensional models with parabolic and Dirac-like dispersion, with the later specifically relevant to topological insulators.

Additional Information

© 2014 American Physical Society. Received 5 August 2013; revised manuscript received 5 January 2014; published 18 February 2014. K.W.K. and G.R. would like to acknowledge support from DARPA through FENA, as well as from the IQIM, an NSF center with the support of the Gordon and Betty Moore Foundation. T.P.B. would like to acknowledge support from NSERC and FQRNT.

Attached Files

Published - PhysRevB.89.085117.pdf

Submitted - 1308.0590v1.pdf

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August 19, 2023
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