Transient dynamics and steady state behavior of the Anderson-Holstein model with a superconducting lead

TL;DR

This paper investigates the nonequilibrium dynamics and steady-state properties of the Anderson-Holstein model with a superconducting lead, revealing phonon effects and validating analytical approaches with numerical methods.

Contribution

It provides an analytical description of the model in the deep Kondo limit and introduces a rate equation approach for phonon interactions, validated against diagrammatic Monte Carlo simulations.

Findings

Enhanced phonon sidebands at small voltages due to superconducting density of states

Good agreement between analytical methods and numerical simulations

Distinct behaviors observed with and without phonons in the model

Abstract

We analyze the nonequilibrium dynamics and steady-state behavior of the two-terminal Anderson-Holstein model with a superconducting and a normal conducting lead. In the deep Kondo limit we develop an analytical description if no phonons are included and a rate equation approach when phonons are present. Both cases are compared with the numerically exact diagrammatic Monte Carlo method obtaining a good agreement. For small voltages we find a pronounced enhancement of phonon sidebands due to the SC DOS.