Interplay of h∕e and h∕2e oscillations in gate-controlled Aharonov-Bohm rings

Spin interference caused by the Rashba spin-orbit interaction in a gate-controlled Aharonov-Bohm ring is studied by the analysis of the conductance oscillations as a function of both the gate voltage and the external magnetic field. Using the scattering matrix formalism, we take into account the transmission and reflection of particles on the scattering points where the two one-dimensional leads connect to the ring and study their effect on the phase. The variations of amplitude of transmission and reflection caused by quantum scatterers for particles moving inside and outside the ring are shown to define a parity of the h∕e and h∕2e conductance oscillations.