Kondo effect in quantum dots: A non-crossing approximation study

Abstract

In this thesis, non-equilibrium Green's function techniques in combination with the time-dependent non-crossing aprroximation are utilized to calculate the transient currents through a quantum dot in the Kondo regime subject to sudden perturbations. We first present novel numerical algorithms which enable relatively fast calculations. We then employ these algorithms to study the transient current through a quantum dot which is symmetrically coupled to metallic leads and its coupling to the leads is abruptly switched such that the Kondo effect is present in the final state. The timescales for the approach to equilibrium are shown to be the same as the ones when the energy level of the dot is suddenly switched. Finally, we study the transient currents in a quantum dot asymmetrically coupled to metallic leads resulting from the abrupt change of the dot level. We show that for asymmetric coupling, sharp features in the density of states of the leads can induce oscillations in the current through the dot. The amplitude of these oscillations increases as the temperature is reduced and saturates below the Kondo temperature. We discuss the microscopic origin of these oscillations and comment on the possibility for their experimental detection.