Yu-Shiba-Rusinov bound states in the perspective of superconducting electrode spectrum in a single molecule device

Abstract The interplay between strong electronic correlations and superconductivity in quantum impurity systems has emerged as a central theme in the exploration of many-body quantum phenomena. Herein, we aim to investigate how microscopic interaction parameters influence the spectral behavior of superconducting electrodes coupled to a single orbital molecular device. To this end, we employ the single-impurity Anderson model coupled to superconducting leads and solve the system using Wilson’s numerical renormalization group (NRG) method. We focus on the spectral function of the electrodes as we systematically vary the on-site Coulomb repulsion, the superconducting-molecule hybridization strength, and the impurity molecule energy level, both at and away from the particle-hole symmetric point. We find that, similar to the spectral properties of a quantum impurity, the competition between the superconducting energy gap and the Kondo temperature governs the emergence of Yu-Shiba-Rusinov (YSR) bound states and quantum phase transitions between the local spin singlet and doublet ground states. At the particle-hole symmetry, increasing the on-site repulsion drives a singlet-doublet transition, while away from symmetry, the system exhibits a singlet-doublet-singlet ground-state crossover as the energy level is tuned. These transitions are reflected in the spectral function through abrupt shifts in the position and weight of the YSR states. Our findings demonstrate that the electrode spectral function serves as a sensitive probe of underlying quantum phase behavior, offering experimentally accessible signatures of critical points and establishing a detailed connection between interaction parameters and observable spectral features in superconducting molecular devices.