Aharonov--Bohm Oscillations and Fano Resonance of a Coupled Dot-Ring System

We derive an exact expression for the transmission coefficient through an Aharonov--Bohm ring with a side-coupled quantum dot using the scattering-matrix approach. We show a sudden AB phase change by π as the quantum dot is tuned across the resonance. The Aharonov--Bohm oscillation amplitude can be modulated effectively by tuning the quantum dot level. The transmission coefficient has an expression of the generalized Fano form with a complex Fano parameter q in the presence of the Aharonov--Bohm flux.