Fano Resonance and Persistent Currents in a Mesoscopic Open Ring with a Flux Loop in Side-Branch

Persistent circulating currents in a mesoscopic open ring with side-branch structures are derived by transfer matrix method in the framework of quantum waveguide theory on networks. The behavior of transmission probability may show the Fano resonance in the presence of geometric scattering of side-branch structures. It is shown that persistent circulating currents in the main loop with equal length of both arms in the absence of magnetic Aux occur near the Fermi wave vectors where the Fano resonance appears. The numerical results show that a larger persistent current is associated with a stronger Fano resonance. The persistent circulating currents can be controlled by the Aux of side-branch structure.