A weak coupling CTQMC study of the single impurity and periodic Anderson models with s-wave superconducting baths

TL;DR

This paper uses weak-coupling CTQMC to analyze a magnetic impurity coupled to s-wave superconductors, revealing a first order transition between singlet and doublet states and its implications for the periodic Anderson model.

Contribution

It applies an unbiased weak-coupling CTQMC method to study impurity and lattice models with superconducting baths, highlighting the first order transition and spectral features.

Findings

First order transition between singlet and doublet states as a function of gap Δ.

Reproduction of the transition in the periodic Anderson model within DMFT.

Coherent superposition of Andreev bound states in the singlet phase.

Abstract

We apply the unbiased weak-coupling continuous time quantum Monte Carlo (CTQMC) 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 DMFT, this impurity problem provides a link to the periodic Anderson model 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-like, superposition of Andreev bound states. In the doublet or local moment phase the single particle spectral function is characterized by incoherent quasiparticle excitations.