Photon-assisted Andreev tunneling through a mesoscopic hybrid system

The electron tunneling through a mesoscopic hybrid system, a normal-metal--quantum-dot--superconductor (N-QD-S) system where the intradot Coulomb interaction is neglected, in the presence of the time-varying external fields, has been investigated. By using the nonequilibrium Green-function method, the time-dependent current jL(t) and the average current $〈j(t)〉$ are derived. The photon-assisted Andreev tunneling (PAAT) and the normal photon-assisted tunneling (PAT) are studied in detail. In the case of ω<Δ, where {ω} is the frequency of external fields and {Δ} is the energy gap of the superconducting lead, the average current 〈j〉 vs the gate voltage exhibits a series of equal-interval PAAT peaks, with negative peaks on the left-hand side and positive peaks on the right-hand side of the original resonant peak in the absence of the external fields. This is very different from the N-QD-N system. While for ω>Δ, various PAT processes cause a rather complicated dependence of the current on the gate voltage. In addition, the current--bias-voltage characteristics become more complicated: each Andreev reflection peak is split into side-band peaks and each current plateau is split into substep plateaus.