Spin precession and time-reversal symmetry breaking in quantum transport of electronsthrough mesoscopic rings

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Abstract
We consider the motion of electrons through a mesoscopic ring in the presence of a spin-orbit interaction, Zeeman coupling, and magnetic flux. The coupling between the spin and the orbital degrees of freedom results in the geometric and the dynamical phases associated with a cyclic evolution of a spin state. Using a non- adiabatic Aharonov-Anandan phase approach, we obtain the exact solution of the system and identify the geometric and the dynamical phases for the energy eigenstates. Spin precession of electrons encircling the ring can lead to various interference phenomena such as oscillating persistent current and conductance. We investigate the transport properties of the ring connected to current leads to explore the roles of the time-reversal symmetry and its breaking therein with the spin degree of freedom being fully taken into account. We derive an exact expression for the transmission probability through the ring. We point out that the time-reversal symmetry breaking due to Zeeman coupling can totally invalidate the picture that spin precession results in an effective, spin-dependent Aharonov-Bohm flux for interfering electrons. We carry out numerical computation to illustrate the joint effects of the spin-orbit interaction, Zeeman coupling, and magnetic flux. By examining the resonant tunneling of electrons in the weak-coupling limit, we establish a connection between the observable time-reversal symmetry-breaking effects manifested by the persistent current and by the transmission probability. For a ring formed by a two-dimensional electron gas, we propose an experiment in which the direction of the persistent current can be determined by the flux dependence of the transmission probability. That experiment also serves to detect if the electron-electron interaction can qualitatively alter the electronic states.
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