Renormalization effects in interacting quantum dots coupled to superconducting leads

TL;DR

This paper investigates subgap transport in an interacting quantum dot connected to superconducting and normal leads, introducing a $1/\Delta$ expansion and a resummation method to improve accuracy over mean-field approaches.

Contribution

It develops a $1/\Delta$ expansion and a resummation approach for better modeling of Andreev bound states in quantum dots with finite superconducting gap.

Findings

The $1/\Delta$ expansion improves accuracy over mean-field methods.

Resummation approach effectively calculates Andreev bound states for finite $\Delta$.

Results agree well with numerical exact solutions.

Abstract

We study subgap transport through an interacting quantum dot tunnel coupled to one normal and two superconducting leads. To check the reliability of an approximation of an infinitely-large gap $\Delta$ in the superconducting leads and weak tunnel coupling to the normal lead, we perform a $1/\Delta$ expansion, and we analyze next-to-leading order corrections in the tunnel coupling to the normal lead. Furthermore, we propose a resummation approach to calculate the Andreev bound states for finite $\Delta$. The results are substantially more accurate than those obtained by mean-field treatments and favorably compare with numerical exact results.