Aharonov--Bohm and Aharonov--Casher effects in meso-scopic physics: A brief review

TL;DR

This paper provides a concise review of the theoretical foundations and applications of the Aharonov--Bohm and Aharonov--Casher effects within mesoscopic physics, highlighting key phenomena and experimental setups.

Contribution

It offers a comprehensive summary of recent theoretical formulations and experimental implications of these quantum effects in mesoscopic systems.

Findings

Analysis of electron interference and persistent currents in mesoscopic rings.

Discussion of spin-orbit coupling and gauge invariance in Aharonov--Casher systems.

Overview of interferometry and conductance phenomena related to these effects.

Abstract

We briefly review the theoretical formulations and applications of the Aharonov--Bohm effect and the Aharonov--Casher effect with emphasis on mesoscopic physics. Topics relating to the Aharonov--Bohm effect include: locality, periodicity, non-integrable phase factors, Abelian gauge theory, interference, the spectrum and persistent current of electrons on a ring pierced by a magnetic field, Onsager reciprocity relations, and Aharonov--Bohm interferometer. Topics relating to the Aharonov--Casher effect include: a magnetic dipole in an electric field, locality, periodicity, non-Abelian gauge invariance, SU(2) non-integrable phase factors, spin-orbit coupling, Pauli equation, Rashba Hamiltonian, Aharonov--Casher interferometer, conductance and polarization in two-channel systems due to the Aharonov--Casher effect.