Photon-assisted Andreev tunneling through a mesoscopic hybrid system

The electron tunneling through a mesoscopic hybrid system, a normal-metal–quantum-dot–superconductor $(N-\mathrm{QD}-S)$ 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 $j_L\mathrm{}\left(t\right)\mathrm{}$ and the average current $〈j\left(t\right)\mathrm{}〉$ are derived. The photon-assisted Andreev tunneling (PAAT) and the normal photon-assisted tunneling (PAT) are studied in detail. In the case of $ħ\omega <\Delta ,$ 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 $N-\mathrm{QD}-N$ system. While for $ħ\omega >\Delta ,$ 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.