Yu-Shiba-Rusinov bound states studied by tuning the electron density at the Fermi energy

We studied the nature of Yu-Shiba-Rusinov (YSR) bound states in response to the potential scattering $U$ by tuning the electron density at the Fermi energy. By comparing two systems, Mn-phthalocyanine molecules on Pb(111) and Co atoms on PbSe/Pb(111), we demonstrate that the sign of $U$ can be unambiguously determined by varying the electron density at the Fermi energy. We further show that $U$ competes with the exchange interaction $JS$ in the formation of YSR bound states. Our work provides insights into the interactions between magnetic atoms and superconductors at a fundamental level.