Spin conductances and spin polarization components in a three-terminal ring subject to Rashba coupling

Spin dependent transport in one-dimensional (1D) three-terminal rings is investigated in the presence of the Rashba spin-orbit coupling (RSOC). We focus on the spin dependent conductances and the components of the spin polarization vectors of the currents in the outgoing terminals. For this purpose, the transmission coefficients with respect to the σx, σy and σz basis are obtained, and the three components of the spin polarization vectors are evaluated analytically. The total conductances, the spin dependent conductances and the polarization components are obtained as functions of the incident electron energy, as well as the RSOC strength, for the totally symmetric, partially symmetric and asymmetric cases. It is found that the spin polarizations corresponding to the σy basis are zero, and that there is a symmetry in the total conductances, the spin dependent conductances and the polarization components for symmetric cases, i.e., G1 = G2, g1τ=g2−τ, and P1i=−P2i(i=x,z). This symmetry is attributed to the rotational symmetry in the symmetrically coupled rings. For asymmetric cases, however, it is broken by the asymmetric lead-ring configuration.