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arXiv:1303.4230 · Annals of Physics

The Aharonov–Bohm effect in scattering theory

Yu. A. Sitenko, N.D. Vlasii

Published Oct 1, 2013• 3 citations
arXivHTMLPDF
DOI
10.1016/j.aop.2013.09.018

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We present a unified treatment of the Aharonov-Bohm (AB) effect for two-dimensional multiband electronic systems possessing isotropic band structures. We propose an integral representation of the AB scattering state of an electron scattered by an infinitely thin solenoid. Moreover, we derive the asymptotic form of the AB scattering state and obtain the differential cross section from that. We found a remarkable result, namely, that this cross section is the same for all isotropic systems and agrees with that obtained first by Aharonov and Bohm for spinless free-particle systems. To demonstrate the generality of our theory, we consider several specific multiband systems relevant to condensed matter physics.