Application of the weak-coupling CTQMC method to a quantum dot coupled to superconducting leads

We apply the weak-coupling continuous time quantum Monte Carlo (CTQMC) method to the Anderson-model extended by a BCS term to describe a quantum dot coupled to s-wave superconducting leads. As the superconducting gap Δ grows, our data shows a phase transition from the 0- to π-junction regime of the Josephson current. By examining various spectral functions, we confirm the traditional interpretation that the Kondo-effect at small Δ corresponds to the 0-junction-regime, while the formation of a magnetic moment on the quantum dot leads to the π-phase-shift at large Δ. At constant Δ, the double occupancy as a function of U shows a jump, thereby signaling a first order transition between the singlet and local moment doublet regimes. Within DMFT, this impurity problem provides a link to the periodic Anderson model (PAM) with superconducting conduction electrons. The signature of this first order transition in the impurity model in the PAM is discussed.