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Physical Review Letters

Spin Motive Force and Faraday Law for Electrons in Mesoscopic Rings

Chang‐Mo Ryu

Published Feb 5, 1996• 24 citations
Publisher

Abstract

The spin motive force and Faraday law for electrons due to the time-dependent Aharonov-Casher effect are studied by using the Goldhaber-Anandan gauge theory for a low energy spin particle. The spin motive force and Faraday law associated with the time-dependent magnetic field are also discussed based on the same gauge theory. The gauge theoretic approach provides a unified view for the various spin motive forces and spin Faraday laws.

DOI
10.1103/physrevlett.76.968

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The spin motive force and Faraday law for electrons due to the time-dependent Aharonov-Casher effect are studied by using the Goldhaber-Anandan gauge theory for a low energy spin particle. The spin motive force and Faraday law associated with the time-dependent magnetic field are also discussed based on the same gauge theory. The gauge theoretic approach provides a unified view for the various spin motive forces and spin Faraday laws.
Based on a gauge-theoretic approach, an equivalence between the Aharonov-Bohm effect of a solenoid and the Aharonov-Casher effect of a charged rod is explicitly demonstrated. It is shown that a time-dependent Aharonov-Casher phase can induce a motive force via the SU(2)spin{)}_{\mathrm{spin}})spin​ gauge field. The intrinsic non-Abelian nature of the SU(2)spin{)}_{\mathrm{spin}})spin​ gauge field predicts the non-Abelian Faraday law, subject to further experimental verification.
We have studied the spin motive force induced by the time-dependent nonadiabatic Aharonov–Casher (AC) phase. It has been shown that the spin motive force has the new term explicitly dependent on the Aharonov–Anandan (AA) phase. This AA phase dependent term could be obtained both in the canonical and path-integral formulations. In path-integral formulations this AA dependent term originates from the nontrivial path-ordering nature of a non-Abelian spin gauge group. We also have shown that this term can be understood as the rotating frame effect in the classical equation of motion for the spin angular momentum. With this term the duality between the Aharonov–Bohm and the AC effect reaches the Newton's third law in the classical limit.
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.
Simple analogues of two fundamental physical phenomena, Faraday's law of induction, and the Aharonov–Bohm effect, have been predicted by Ady Stern of Tel Aviv University, Israel, in the behaviour of electrons in a ring in a magnetic field (Phys. Rev. Lett. (1992) 68 1022). The surprising twist is that it is the electron's spin, rather than its charge, which plays the central role. These effects are associated with the quantum geometric (or Berry) phase, a discovery in elementary quantum mechanics which has generated great excitement in the last eight years.