Mesoscopic transport through a normal-metal-quantum-dot-superconductor system with ac responses

We investigate the mesoscopic de transport through the normal-metal-quantum -dot-superconductor (NDS) system with ac biases on the normal metal and on the quantum dot. The Keldysh's nonequilibrium Green-function technique and the BCS theory are used to find the general formulas of the time-averaged c urrent and differential conductance. The transport is associated with the e nergy gap Delta(T) and with the ac fields to exhibit compound effects. We c ompare the results of the NDS system with the normal mesoscopic transport w here Delta(T)=0. There is no normal electron tunneling current in the NDS s ystem if there is only one bias field applied to the quantum dot as 0<V<Del ta(0)/e at zero temperature. However, there may exist normal electron tunne ling current in the system with an ac bias applied to the normal lead even if 0<V<Delta(0)/e at zero temperature. The de current shows steps that corr espond to the resonant peaks of the differential conductance. The resonant peaks are also influenced by the energy gap. The differential conductance e xhibits some discontinuities caused by the density of state in the supercon ducting lead, and by the ac perturbations on the normal lead. [S0163-1829(9 8)00444-5].