| Summary: | Spin-dependent transport in one-dimensional (1D) three-terminal Rashba rings is investigated under a weak magnetic field, and we focus on the Zeeman splitting (ZS) effect. For this purpose, the interaction between the electron spin and the weak magnetic field has been treated by perturbation theory. ZS removes the spin degeneracy, and breaks both the time reversal symmetry and the spin reversal symmetry of the ring system. Consequently, all conductance zeros are lifted and turned into conductance dips. Aharonov-Bohm (AB) oscillations can be found in both branch conductances and the total conductance as a function of the magnetic field. In a relatively high magnetic field, the decoherence caused by ZS decreases the amplitude of the branch conductance and increases that of the total conductance. The results have been compared with those reported in the published literature, and a reasonable agreement is obtained. The conductance as a function of the Rashba spin-orbit coupling (RSOC) strength has also been investigated. As the RSOC strength increases, the role of ZS becomes weaker and weaker; ZS can even be neglected when B ≤ 0.1 T.
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