Two-dimensional systems where the surface of a superconductor is coated with a molecular layer draw recently a lot of attention as they represent ideal setups for studying the competition between magnetism and superconductivity. The physics of such systems can be studied using the superconducting periodic Anderson model which describes a conduction band with superconducting (BCS) pairing hybridized with a non-dispersive band of correlated electrons. We use the dynamical mean-field theory in combination with quantum Monte-Carlo to solve this problem by mapping the lattice model to the superconducting impurity Anderson model with a self-consistently determined bath. This method neglects spatial correlations between lattice sites but the local quantum fluctuations are fully taken into account. We show the behavior of the in-gap Andreev (Yu-Shiba-Rusinov) bands and how the singlet-doublet (zero-pi) quantum phase transition in the local impurity model is reflected in the properties of the lattice model. We also show the limits of usability of diagrammatic techniques such as the iterative perturbation theory for studying superconducting systems.

V. Pokorný and P. Ram, Phys. Rev. B 104, 155102 (2021).