Scaling of Yu-Shiba-Rusinov energies in the weak-coupling Kondo regime

TL;DR

This study investigates the behavior of Yu-Shiba-Rusinov states in a weak-coupling Kondo regime, revealing that their energies follow classical spin model predictions, which is relevant for understanding Majorana states.

Contribution

It demonstrates the correlation between YSR bound state energies and Kondo resonance intensity in a weak-coupling regime on superconductors, supporting classical spin models.

Findings

YSR energies follow classical spin predictions

Weak-coupling Kondo resonances observed in MnPc-NH3 molecules

Correlation established between YSR energies and Kondo resonance intensity

Abstract

The competition of the free spin state of a paramagnetic impurity on a superconductor with its screened counterpart is characterized by the energy scale of Kondo screening $k_BT_K$ compared to the superconducting pairing energy $\Delta$. When the experimental temperature suppresses Kondo screening, but preserves superconductivity, i.e., when $\Delta/k_B > T > T_K$, this description fails. Here, we explore this temperature range in a set of manganese phthalocyanine molecules decorated with ammonia (MnPc-NH$_3$) on Pb(111). We show that these molecules suffice the required energy conditions by exhibiting weak-coupling Kondo resonances. We correlate the energy of the Yu-Shiba-Rusinov (YSR) bound states inside the superconducting energy gap with the intensity of the Kondo resonance. We reveal that the bound state energy follows the expectations for a classical spin on a superconductor. This finding is important in view of many theoretical predictions using a classical spin model, in particular for the description of Majorana bound states in magnetic nanostructures on superconducting substrates.