Josephson current through a single Anderson impurity coupled to BCS leads

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.