Abstract
We identify theoretically the geometric phases of the electrons' spin that can be detected in measurements of charge and spin transport through Aharonov-Bohm interferometers threaded by a magnetic flux $\Phi$ (in units of the flux quantum) in which both the Rashba spin-orbit and Zeeman interactions are active. We show that the combined effect of these two interactions is to produce a $\sin(\Phi)$ [in addition to the usual $\cos(\Phi)$] dependence of the magnetoconductance, whose amplitude is proportional to the Zeeman field. Therefore the magnetoconductance, though an even function of the magnetic field is not a periodic function of it, and the widely-used concept of a phase shift in the Aharonov-Bohm oscillations, as indicated in previous work, is not applicable. We find the directions of the spin-polarizations in the system, and show that in general the spin currents are not conserved, implying the generation of magnetization in the terminals attached to the interferometer.
Highlights
The phase factor induced on the spin wave functions of electrons moving in an electric field is generally attributed to the Aharonov-Casher effect [1], the electromagnetic dual of the Aharonov-Bohm effect [2]
This paper aims to identify the geometric phases of the electrons’ spinor that can be detected in measurements of charge and spin transport through Aharonov-Bohm interferometers in which both the Rashba spin-orbit and Zeeman interactions are active
We found that the Zeeman interaction, which is often ignored in the calculations, causes crucial qualitative changes in the results, which should be observable
Summary
The phase factor induced on the spin wave functions of electrons moving in an electric field is generally attributed to the Aharonov-Casher effect [1], the electromagnetic dual of the Aharonov-Bohm effect [2]. This paper aims to identify the geometric phases of the electrons’ spinor that can be detected in measurements of charge and spin transport through Aharonov-Bohm interferometers in which both the Rashba spin-orbit and Zeeman interactions are active (the latter is due to a magnetic field normal to the plane of the interferometer). When the Zeeman interaction is included, the pattern of the Aharonov-Bohm oscillations is modified: There appears a sin( ) term in the interference-induced transmission, whose amplitude is proportional to the Zeeman field and which vanishes without the spin-orbit interaction. The coefficient of this term depends on details of the triangular structure.
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