Full counting statistics of phonon-assisted Andreev tunneling through a quantum dot coupled to normal and superconducting leads

TL;DR

This paper theoretically analyzes the full counting statistics of phonon-assisted Andreev tunneling through a quantum dot between superconducting and normal leads, revealing effects of electron-phonon interactions on transport properties.

Contribution

It generalizes the dressed tunneling approximation to include vibrational effects in Andreev transport, providing explicit formulas and insights into phonon influence on tunneling spectra.

Findings

No phonon side peaks in linear conductance

Negative differential conductance observed

Inelastic resonant peak due to phonon-assisted Andreev reflection

Abstract

We present a theoretical investigation for the full counting statistics of the Andreev tunneling through a quantum dot (QD) embedded between superconducting (SC) and normal leads in the presence of a strong on-site electron-phonon interaction using nonequilibrium Green function method. For this purpose, we generalize the dressed tunneling approximation (DTA) recently developed in dealing with inelastic tunneling in a normal QD system to the Andreev transport issue, which takes account of vibrational effect in evaluation of electronic tunneling self energy in comparison with other simple approaches and meanwhile allows us to derive an explicit analytical formula for the cumulant generating function at the subgap region. We then analyze the interplay of polaronic and SC proximity effects on the Andreev reflection spectrum, current-voltage characteristics, and current fluctuations of the hybrid system. Our main findings include: (1) no phonon side peaks in the linear Andreev conductance; (2) a negative differential conductance stemming from the suppressed Andreev reflection spectrum; (3) a novel inelastic resonant peak in the differential conductance due to phonon assisted Andreev reflection; (4) enhancement or suppression of shot noise for the symmetric or asymmetric tunnel-coupling system respectively.