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MP: Fachverband Theoretische und Mathematische Grundlagen der Physik

MP 1: Many-body Theory I

MP 1.9: Talk

Monday, March 18, 2024, 12:40–13:00, HL 001

Unified description of the Aharonov–Bohm effect in isotropic multiband electronic systems — •Róbert Németh and József Cserti — Department of Physics of Complex Systems, ELTE Eötvös Loránd University, Pázmány Péter sétány 1/A, H-1117 Budapest, Hungary

A unified treatment of the Aharonov–Bohm (AB) effect is presented for two-dimensional multiband electronic systems possessing isotropic band structures. We propose a complex contour integral representation of the AB scattering states of an electron scattered by an infinitely thin solenoid. Moreover, we derive the asymptotic forms of these scattering states and obtain the differential cross section from those. A remarkable result is found, 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 [Phys. Rev. 115, 485 (1959)]. To demonstrate the generality of our theory, it is applied to several specific multiband systems relevant to condensed matter physics. Finally, we extend our approach to the case of the non-Abelian AB effect, that is, the scattering of particles on a gauge field corresponding to a noncommutative Lie group.

Keywords: Aharonov--Bohm effect; Two-dimensional systems; Scattering theory; Differential cross section; Non-Abelian gauge theories