Weak-coupling continuous-time quantum Monte Carlo study of the single impurity and periodic Anderson models with s-wave superconducting baths

We apply the unbiased weak-coupling continuous time quantum Monte Carlo method to review the physics of a single magnetic impurity coupled to s-wave superconducting leads described by the BCS reduced Hamiltonian. As a function of the superconducting gap Delta, we study the signature of the first-order transition between the singlet and doublet (local-moment) states on various quantities. In particular, we concentrate on the Josephson current with 0 to pi phase shift, the crossing of the Andreev bound states in the single-particle spectral function, as well as the local dynamical spin structure factor. Within dynamical mean-field theory, this impurity problem provides a link to the periodic Anderson model (PAM) with superconducting conduction electrons (BCS-PAM). The first-order transition observed in the impurity model is reproduced in the BCS-PAM and is signalized by the crossing of the low-energy excitations in the local density of states. The momentum resolved single-particle spectral function in the singlet state reveals the coherent, Bloch-type, superposition of Andreev bound states. In the doublet or local-moment phase the single-particle spectral function is characterized by incoherent quasiparticle excitations.