Abstract
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.
Highlights
In the past few years, coherent ring conductors have drawn significant attention because of their relevance to fundamental physics as well as their potential applications
We have studied the effects of Zeeman splitting on spin transportation in onedimensional (1D) three-terminal Rashba rings under a weak magnetic field
The Zeeman term in the Hamiltonian has been treated by perturbation theory
Summary
In the past few years, coherent ring conductors have drawn significant attention because of their relevance to fundamental physics as well as their potential applications. Szanfran et al attributed the vanishing oscillation amplitude to the magnetic forces, which leads to a preferential injection of the electron wave function into one of the arms of the ring.[23] In the presence of ZS the coherence of spin currents will be disturbed, the decoherence may reduce the visibility of the AB oscillations. It is necessary to study the effect of ZS in quantum rings under a weak magnetic field, and to clarify the conditions under which ZS can be neglected. We have derived the transmission functions for spin-dependent electron transport in a 3-lead Rashba ring, and they have been used to investigate zero-conductance resonances in such systems.[17]. In the presence of RSOC, the single-particle Hamiltonian for an electron in a 1D ring under a uniform perpendicular magnetic field can be written as. The spinors χμ(φ) are generally not aligned with BR, but have a tilt angle γ number nrejμla=tijv√eEto+tΦheAμCz/d2iπre. ction
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