Control of Fano resonances and phase of a multi-terminal Aharanov-Bohm ring with three embedded quantum dots

We study a four-terminal AB-ring with three embedded quantum dots in one arm. A tight-binding model is employed to analytically obtain the transmission through the system. Results show that the magnitude and sharpness of the resonance phase-jumps diminish as a function of the degree of coupling to the extra terminals. The Fano resonance zeros become complex with a non-zero coupling matrix element to the extra terminals. The zeros can be returned to the real energy axis by increasing the flux for values of the coupling less than a critical value. A simple analytical model of the Fano resonances shows naturally how the phase transition across the resonance peak will soften and diminish in the case where the transmission zero energy is no longer real, but complex.