Phonon-assisted transport through quantum dots with normal and superconducting leads

Abstract

We investigate electronic transport through a vibrating quantum dot coupled to a normal and a superconducting lead. It is shown that in such a system, the interplay of Cooper pairs and phonons gives rise to phonon-assisted Andreev tunnelings. These tunnelings manifest themselves as resonant peaks separated by a half of the phonon energy in the current as a function of the dot level, while phonon-assisted normal tunnelings produce steps separated by the phonon energy in the current as a function of the bias voltage. While the steps are easily smeared out by increasing the temperature, the peaks are found to be robust. Our calculation is performed from the low-voltage subgap regime to the high-voltage supergap regime, allowing an systematic exploration of the phonon-assisted transport spectroscopy subject to normal and BCS density of states in the leads.