Unified Description of the Aharonov-Bohm Effect in Isotropic Multiband Electronic Systems

TL;DR

This paper provides a unified theoretical framework for the Aharonov-Bohm effect in isotropic multiband electronic systems, showing the differential cross section is universal across such systems and matching the original spinless case.

Contribution

It introduces an integral representation of the AB scattering state and demonstrates the universality of the differential cross section in isotropic multiband systems.

Findings

The AB scattering cross section is the same for all isotropic systems.

The derived cross section matches the original Aharonov-Bohm result for spinless particles.

The theory applies to various multiband systems relevant to condensed matter physics.

Abstract

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 {\it 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.