Persistent Currents in Higher Genus Materials and Structures

Persistent charge and spin currents have been usually studied in an isolated ring. However, recent semiclassical calculations and an experiment performed on sixteen connected GaAS/GaAlAs rings provide motivation to study persistent currents in higher genus structures. To this end, we introduce Dirac's second class constraint to explore high genus materials and ring structures. As a specific example we apply this method to compute the persistent charge current in a system of coupled rings.