Yu-Shiba-Rusinov states assisted by asymmetric Coulomb repulsion in a bipartite molecular device

Abstract

Interfacing magnetism with superconducting condensates are promising candidates holding Majorana bound states with which fault-tolerant quantum computation could be implemented. Within this field, understanding the detailed dynamics is important both for fundamental reasons and for the development of innovative quantum technologies. Herein, motivated by a molecular magnet Tb2Pc3 interacting with a superconducting Pb(111) substrate, which results in spin-orbital Yu-Shiba-Rusinov (YSR) states, as is affirmed by a theoretical simulation with the aid of the numerical renormalization group technique [see Nat. Commun. 13. 6388 (2022)], we study the YSR states and quantum phase transitions in a bipartite molecular device adsorbed on an s−wave superconducting substrate. We highlight the effect of asymmetric Coulomb repulsion by computing the spectrum function and spin correlation function in various parameter regimes. We demonstrate that if one impurity is non-interacting, there are no YSR states in both impurities with any repulsion value in the other impurity. Whereas if the repulsion in one impurity is strong, the YSR states are observed in both impurities, and a quantum phase transition arises as the repulsion in the other impurity sweeps, assisted by the competition between the superconducting singlet (Cooper pair) and the Kondo singlet. The evolution of YSR states distinguishes from the single impurity case and can be well interpreted by the energy scales of the isotropic superconducting gap parameter, as well as the two Kondo temperatures. Our findings provide theoretical insights into the phase diagram of two magnetic impurities on a superconducting host and shine light on the effects induced by asymmetric Coulomb repulsion on many-body interactions.