We have studied a mesoscopic double-ring system connected in parallel and coupled to two electron reservoirs. The system is composed of one-dimensional ordered chains, and the two rings are threaded by magnetic fluxes ${\mathrm{\Phi }}_1$ and ${\mathrm{\Phi }}_2$, respectively. In the framework of the tight-binding model, the analytical and numerical calculations show that the transmission coefficient T is periodic in fluxes ${\mathrm{\Phi }}_1$ and ${\mathrm{\Phi }}_2$ with a period 2${\mathrm{\Phi }}_0$,${\mathrm{\Phi }}_0$=hc/e. For the system there are resonant states (T=1) and antiresonant states (T=0), the distribution of which displays a very remarkable symmetry. © 1996 The American Physical Society.

• Received 6 October 1995

DOI:https://doi.org/10.1103/PhysRevB.53.6943