Systems consisting of open mesoscopic rings threaded by a magnetic flux Φ and connected in parallel and in series are studied within the tight-binding model. A recursion method, which allows one to deal with systems consisting of a large number of rings, is found for the calculation of transmission amplitutes. The numerical results show that for systems with rings connected in series and in parallel, the quantum coherence effect plays quite different roles. We found that as the number of rings increases, the magnetic flux Φ will progressively block the transmission through the system for parallel multiring systems (PRS), but not for the serial multiring systems (SRS). In the absence of magnetic flux, the transmission coefficient $T$ in PRS decreases only slightly when the ring number $N$ increases, while $T$ in SRS decreases rapidly with an increasing number of rings.

• Received 1 December 1997

DOI:https://doi.org/10.1103/PhysRevB.57.12994