Dynamics of Fano-Like Resonances in Double-Quantum-Dot Systems

Abstract

Quantum interference effects appearing in mesoscopic heterostructures have been extensively studied in static conditions over the last decades. It is interesting to examine the dynamics of these phenomena and get insight into the process of the formation of interference patterns. In this work, we analyze the time required for the formation of Fano-like resonances in a double quantum dot system. We examined the time evolution of conductance upon establishing an abrupt connection between quantum dots. Asymmetric Fano lines are characterized by the close coexistence of resonant enhancement and resonant suppression. Therefore, we pay particular attention to voltages, which in the static case, correspond to both these features. Our research shows that the analyzed resonances are characterized by two time scales: (i) the first one related to charge oscillations between subsystems and mostly governed by the interdot coupling constant and the relative position of energy levels of quantum dots, and (ii) the second one associated to the electron scattering on a continuum of states and responsible for the relaxation. We also show that the time required for achieving a static solution is different for voltages corresponding to local minima and local maxima.