Second Order Perturbation Theory for a Superconducting Double Quantum Dot

TL;DR

This paper extends second order perturbation theory to superconducting double quantum dots, providing an efficient analytical approach that closely matches numerical methods for certain regimes, aiding experimental analysis.

Contribution

The authors develop a second order perturbation theory method for superconducting double quantum dots, offering a reliable alternative to numerical techniques.

Findings

Good agreement with Numerical Renormalization Group results in weak to moderate correlation regimes.

Efficient analytical method for calculating in-gap spectra and occupations.

Applicable over a wide parameter range for experimental systems.

Abstract

We extend our approach based on the second order perturbation theory in the Coulomb interaction recently developed for quantum dots coupled to superconducting leads to the superconducting double quantum dot setups. Using our perturbative method we evaluate several single-particle quantities such as on-dot induced gap and generalized occupations together with the Andreev in-gap spectra and compare them with numerically exact results from the Numerical Renormalization Group and Quantum Monte Carlo finding a very good correspondence for not too strongly correlated regimes. Thus we can offer in a wide parameter range this method as an efficient and reliable alternative to the heavy numerical tools exclusively used so far for the description of such experimentally relevant systems.