Josephson current through a single Anderson impurity coupled to BCS leads

TL;DR

This paper studies the Josephson current through a quantum dot with Coulomb interactions between superconducting leads, revealing a quantum phase transition and providing accurate predictions for current behavior at various temperatures.

Contribution

It combines functional and numerical renormalization group methods to analyze the Josephson current through an Anderson impurity, clarifying the phase transition and offering reliable results at manageable computational costs.

Findings

Identifies a quantum phase transition driven by T_K/ and phase difference .

Provides accurate zero- and finite-temperature current data.

Demonstrates the effectiveness of truncated functional renormalization group for practical analysis.

Abstract

We investigate the Josephson current J(\phi) through a quantum dot embedded between two superconductors showing a phase difference \phi. The system is modeled as a single Anderson impurity coupled to BCS leads, and the functional and the numerical renormalization group frameworks are employed to treat the local Coulomb interaction U. We reestablish the picture of a quantum phase transition occurring if the ratio between the Kondo temperature T_K and the superconducting energy gap \Delta or, at appropriate T_K/\Delta, the phase difference \phi or the impurity energy is varied. We present accurate zero- as well as finite-temperature T data for the current itself, thereby settling a dispute raised about its magnitude. For small to intermediate U and at T=0 the truncated functional renormalization group is demonstrated to produce reliable results without the need to implement demanding numerics. It thus provides a tool to extract characteristics from experimental current-voltage measurements.