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arXiv:quant-ph/0212102 · Science

Putting a Spin on the Aharonov-Bohm Oscillations

J. Anandan

Published Sep 5, 2002• 8 citations
arXivHTMLPDF

Abstract

An experiment that shows the modulation of the Aharonov-Bohm oscillations of magneto-resistance in a mesoscopic ring is described. Possible theoretical explanations of this modulation due to the interaction of the electron spin with the magnetic and electric fields are considered.
DOI
10.1126/science.1076385

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We study a simple model of dephasing of Aharonov-Bohm oscillations in the transmission of an electron across a mesoscopic ring. A magnetic impurity in one of the arms of the ring couples to the electron spin via an exchange interaction. This interaction leads to spin flip scattering and induces dephasing via entanglement. This is akin to the models evoked earlier to explain destruction of interference due to which-path information in double-slit experiments. Total transmission is found to be symmetric under flux reversal but not the spin polarization.
We present a detailed analysis of the Aharonov-Bohm interference oscillations manifested through transmission of an electron in a mesoscopic ring with a magnetic impurity atom inserted in one of its arms. The electron interacts with the impurity through the exchange interaction leading to exchange spin-flip scattering. Transmission in the spin-flipped and spin-unflipped channels are explicitly calculated. We show that the spin-flipper acts as a dephasor in spite of absence of any inelastic scattering. The spin-conductance (related to spin-polarized transmission coefficient) is asymmetric in the flux reversal as opposed to the two probe conductance which is symmetric under flux reversal.
We calculate the oscillations of the dc conductance across a mesoscopic ring, simultaneously tuned by applied magnetic and electric fields orthogonal to the ring. The oscillations depend on the Aharonov-Bohm flux and of the spin-orbit coupling. They result from mixing of the dynamical phase, including the Zeeman spin splitting, and of geometric phases. By changing the applied fields, the geometric phase contribution to the conductance oscillations can be tuned from the adiabatic (Berry) to the nonadiabatic (Ahronov-Anandan) regime. To model a realistic device, we also include nonzero backscattering at the connection between ring and contacts, and a random phase for electron wave function, accounting for dephasing effects.
The Aharonov–Bohm (AB) interference oscillations manifested through transmission of an electron in a mesoscopic device with a double-ring in the presence of a magnetic impurity serving as the spin-flipper are studied. The spin-flipper is demonstrated to indeed cause the partial decoherence of the AB interference. Moreover, it is found that the spin-up/down transmission coefficients are asymmetric in the flux reversal while the reflection coefficients as well as that the total transmission coefficient are symmetric.
Ever since Yakir Aharonov and David Bohm pointed out, in 1959, that electrons propagating around a magnetic field through a field-free vacuum should exhibit a quite surprising interference effect, its experimental and theoretical investigation has been contributing to our understanding of the fundamental character of the quantum theory. The recent appearance of this Aharonov–Bohm effect in a rather different context may eventually have a profound effect on our view of the solid state on a “mesoscopic” scale—between the microscopic and the truly macroscopic.