Josephson current through a single Anderson impurity coupled to BCS leads

Abstract

We investigate the Josephson current J(ϕ) through a quantum dot embedded between two superconductors showing a phase difference ϕ. 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 Δor, at appropriate T_K/Δ, the phase difference ϕor 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.

version accepted for publication in PRB