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 $\mathrm{\Phi }$ (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 $sin\left(\mathrm{\Phi }\right)$ [in addition to the usual $cos\left(\mathrm{\Phi }\right)$] 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.

Figure 1

Illustration of our model. A triangular Aharonov-Bohm interferometer is threaded by a magnetic flux $\mathrm{\Phi }$ (in units of the flux quantum). The interferometer is coupled to two reservoirs. One of its arms carries a quantum dot. A Zeeman field normal to the plane of the triangle affects both the dot and the arms of the loop. An electric field normal to the plane of the triangle generates a Rashba spin-orbit interaction on the links forming the triangle.