Spin geometric phases in hopping magnetoconductance

We identify theoretically the geometric phases of the electrons' spinor that can be detected in measurements of charge and spin transport through Aharonov-Bohm interferometers threaded by a magnetic flux φ (in units of the flux quantum) where Rashba spin-orbit and Zeeman interactions are active. We show that the combined effect of these two interactions produces a sin(φ) [in addition to the usual cos(φ)] dependence of the magnetoconductance, whose amplitude is proportional to the Zeeman field. Therefore, although the magnetoconductance is an even function of the magnetic field, it 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 (even without the Zeeman term) the spin currents are not conserved, implying the generation of magnetization in the terminals attached to the interferometer.