Interplay between Kondo and Andreev-Josephson effects in a quantum dot coupled to one normal and two superconducting leads

TL;DR

This paper investigates the complex interplay between Kondo and Andreev-Josephson effects in a quantum dot system with one normal and two superconducting leads, revealing how tuning parameters influences the crossover between different quantum states.

Contribution

It provides a detailed analysis of the crossover between Kondo and Cooper-pairing states using NRG calculations in a Y-shaped junction with superconducting and normal leads.

Findings

The Andreev resonance level approaches the Fermi level during the crossover.

Strong coupling induces a Kondo effect with a renormalized resonance width.

Asymmetry in the Josephson junction affects the dominance of SC or Kondo states.

Abstract

We study low-energy transport through a quantum dot coupled to one normal and two superconducting (SC) leads in a junction of Y-shape. In this geometry a crossover between Kondo dominated and Cooper-pairing dominated states occurs by tuning the parameters such as the quantized energy level of the dot and the Josephson phase, which induces a supercurrent flowing between the two SC leads through the dot. Furthermore, Andreev scattering takes place at the interface between the dot and normal lead. The low-lying energy states of this system can be described by a local Fermi-liquid theory for interacting Bogoliubov particles. In a description based on an Anderson impurity model we calculate transport coefficients, renormalized parameters and spectral function, using Wilson's numerical renormalization group (NRG) approach, in the limit of large SC gap. Our results demonstrate how the Andreev resonance level approaches the Fermi level in the crossover region between Cooper-pairing singlet state and strong coupling situation as the impurity level or Josephson phase are varied. The strong coupling situation shows a Kondo effect with a significantly renormalized resonance width. The crossover is smeared when the coupling between the dot and normal lead is large. Furthermore, asymmetry in the Josephson junction suppresses the cancellations of the SC proximity for finite Josephson phase, and it favors the SC singlet state rather than the Kondo singlet.