Effect of spin-orbit coupling on zero-conductance resonances in asymmetrically coupled one-dimensional rings

The influence of Rashba spin-orbit coupling on zero conductance resonances appearing in one dimensional ring asymmetrically coupled to two leads is investigated. For this purpose, the transmission function of the corresponding one-electron scattering problem is derived analytically and analyzed in the complex energy plane with focus on the zero-pole structure characteristic of transmission (anti)resonances. The lifting of real conductance zeros due to spin-orbit coupling in the asymmetric Aharonov-Casher (AC) ring is related to the breaking of spin reversal symmetry in analogy to the time-reversal symmetry breaking in the asymmetric Aharonov-Bohm (AB) ring.