Persistent Current From the Competition Between Zeeman Coupling and   Spin-Orbit Interaction
  Applying the non-adiabatic Aharonov-Anandan phase approach to a mesoscopic ring with non-interacting many electrons in the presence of the spin-orbit interaction, Zeeman coupling and magnetic flux, we show that the time-reversal symmetry breaking due to Zeeman coupling is intrinsically different from that due to magnetic flux. We find that the direction of the persistent currents induced by the Zeeman coupling changes periodically with the particle number, while the magnetic flux determines the direction of the induced currents by its sign alone. 
Tie-Zheng Qian, Ya-Sha Yi and Zhao-Bin Su(Institute of Theoretical   Physics, Chinese Academy of Sciences)