Magnetic Impurities on Superconducting Surfaces: Phase Transitions and the Role of Impurity-Substrate Hybridization

TL;DR

This paper investigates how magnetic impurities on superconducting surfaces influence Yu-Shiba-Rusinov states, emphasizing the importance of impurity-substrate hybridization and proposing the Anderson impurity model as a more accurate theoretical framework.

Contribution

It demonstrates the relevance of the Anderson impurity model over the traditional Kondo model for describing YSR states on superconducting surfaces.

Findings

YSR state energy correlates with impurity-substrate hybridization.

The Anderson impurity model accurately explains experimental observations.

The model helps determine the quantum phase transition state.

Abstract

Spin-dependent scattering from magnetic impurities inside a superconductor gives rise to Yu-Shiba-Rusinov (YSR) states within the superconducting gap. As such, YSR states have been very successfully modeled with an effective scattering potential (Kondo impurity model). Using a scanning tunneling microscope, we exploit the proximity of the tip to a surface impurity and its influence on the YSR state to make a quantitative connection between the YSR state energy and the impurity-substrate hybridization. We corroborate the coupling between impurity and substrate as a key energy scale for surface derived YSR states using the Anderson impurity model in the mean field approximation, which accurately explains our observations. The model allows to decide on which side of the quantum phase transition the system resides based on additional conductance measurements. We propose that the Anderson impurity model is much more appropriate to describe YSR states from impurities on a superconducting surface than the Kondo impurity model, which is more appropriate for impurities inside a superconductor. We thus provide a first step towards a more quantitative comparison of experimental data with fully correlated calculations based on the Anderson impurity model.