Electron transport in multiply connected Aharonov-Bohm rings

We investigate the transmission coefficient and persistent current of periodically arranged Aharonov-Bohm rings coupled to external leads. A general theory of quantum waveguide based on the transfer matrix method is developed and is used to study one-dimensional periodic ring structures. A precise expression for the transmission coefficient is derived. The results show that in the contacted ring case the conduction band electrons give rise to periodically arranged persistent currents in the structure, while the band gap electrons can cause giant persistent currents in the first few loops. We also observe isolated transmission peaks in the periodically arranged rings connected via leads.