Robustness of spin filtering against current leakage in a Rashba-Dresselhaus-Aharonov-Bohm interferometer

In an earlier paper [A. Aharony, Y. Tokura, G. Z. Cohen, O. Entin-Wohlman, and S. Katsumoto, Phys. Rev. B 84, 035323 (2011)], we proposed a spin filter that was based on a diamond-like interferometer, subject to both an Aharonov-Bohm flux and (Rashba and Dresselhaus) spin-orbit interactions. Here, we show that the full polarization of the outgoing electron spins remains the same even when one allows leakage of electrons from the branches of the interferometer. Once the gate voltage on one of the branches is tuned to achieve an effective symmetry between them, this polarization can be controlled by the electric and/or magnetic fields, which determine the spin-orbit interaction strength and the Aharonov-Bohm flux.