Zero-conductance resonances and spin-filtering effects in ring conductors subject to Rashba coupling

We investigate the effect of Rashba spin-orbit coupling and of a tunnel barrier on the zero conduc- tance resonances appearing in a one-dimensional conducting Aharonov-Bohm (AB) ring symmet- rically coupled to two leads. The transmission function of the corresponding one-electron problem is derived within the scattering matrix approach and analyzed in the complex energy plane with focus on the role of the tunnel barrier strength on the zero-pole structure characteristic of trans- mission (anti)resonances. The lifting of the real conductance zeros is related to the breaking of the spin-reversal symmetry and time-reversal symmetry of Aharonov-Casher (AC)and AB rings, as well as to rotational symmetry breaking in presence of a tunnel barrier. We show that the polarization direction of transmitted electrons can be controlled via the tunnel barrier strength and discuss a novel spin-filtering design in one-dimensional rings with tunable spin-orbit interaction.