A new model of metal/semiconductor/metal double-quantum-ring connected in series is proposed and the transport properties in this model are theoretically studied. The results imply that the transmission coefficient shows periodic variations with increasing semiconductor ring size. The effects of the magnetic field and Rashba spin-orbit interaction on the transmission coefficient for two kinds of spin state electrons are different. The number of the transmission coefficient peaks is related to the length ratio between the upper arm and the half circumference of the ring. In addition, the transmission coefficient shows oscillation behavior with enhanced external magnetic field, and the corresponding average value is related to the two leads' relative position.
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