Transport properties of a quantum dot with superconducting leads

We report a numerical study of transport properties of a quantum dot with superconducting leads. We introduce a general phenomenological model of quantum-dot transport, in which electron tunnel rates are computed within the Fermi-golden-rule approach. The low-temperature current-voltage ($I-V$) characteristics are in qualitative agreement with experimental observations of Ralph et al. [Phys. Rev. Lett. 74, 3241 (1995)]. At higher temperatures, our results reveal interesting effects due to the thermal excitation of quasiparticles in the leads as well as the thermal population of excited quantum levels in the dot. We also study the photon-assisted tunneling phenomena in our system and point out its potential for millimeter wave applications.