Fano resonances through quantum dots in tunable Aharonov-Bohm rings

The main goal of the present work is to investigate novel resonant phenomena which may arise in the AB rings with specially-designed dots. First, we investigate the total transmission probability through the coupled double quantum dots (QDs) embedded in one of the arms of the AB ring with a magnetic flux passing through its center. We calculate the electron transmission through this AB ring with three short-range potential barriers using a scattering matrix at each junction and a transfer matrix in each arm. The Fano resonance splitting and disappearing in the transmission can be seen by adjusting the interaction between coupled QDs, whose coupling is controlled by the modulation of the center potential barrier. We also show the Fano resonance shifting to the higher energy by changing the interaction parameter, and the swing from Breit-Wigner to Fano resonance (or vice-versa) by tuning the magnetic AB flux threading through the AB ring. Secondly, we study the effects of an asymmetry in the arm by inserting an attractive potential well (dot) in one arm. The combined transmission resonance effects (Young\´s interference, T-stub and Fano resonances) as a function of parameters of the ring structure and the potential well will be presented. For large amplitude of the potential dot, the transmission zeroes are seen to match the theory of resonance due to reflections from a closed "T-stub". Fano-interference in an asymmetric AB ring with an embedded attractive potential appears when quasi-bound states in the dot coherently interact and interfere with propagating waves in the arms. Our theoretical AB-ring model is compared to experimental results from measurements of an asymmetric ring fabricated in a GaAs/AlGaAs-heterostructure, where Fano resonances have been observed (Keyser et al., 2002).