Universal scaling of tunable Yu-Shiba-Rusinov states across the quantum phase transition

TL;DR

This study demonstrates a universal scaling law for Yu-Shiba-Rusinov states across quantum phase transitions, using precise experimental measurements and theoretical modeling to clarify the relationship between Kondo temperature and YSR states.

Contribution

It provides the first experimental verification of the universal scaling of YSR states across the quantum phase transition with high quantitative accuracy.

Findings

YSR states exhibit continuous universal scaling across QPTs.

Accurate extraction of Kondo temperature using NRG fitting.

Experimental validation of theoretical universal scaling law.

Abstract

Quantum magnetic impurities give rise to a wealth of phenomena attracting tremendous research interest in recent years. On a normal metal, magnetic impurities generate the correlation-driven Kondo effect. On a superconductor, bound states emerge inside the superconducting gap called the Yu-Shiba-Rusinov (YSR) states. Theoretically, quantum impurity problems have been successfully tackled by numerical renormalization group (NRG) theory, where the Kondo and YSR physics are shown to be unified and the normalized YSR energy scales universally with the Kondo temperature divided by the superconducting gap. However, experimentally the Kondo temperature is usually extracted from phenomenological approaches, which gives rise to significant uncertainties and cannot account for magnetic fields properly. Using scanning tunneling microscopy at 10mK, we apply a magnetic field to several YSR impurities on a vanadium tip to reveal the Kondo effect and employ the microscopic single impurity Anderson model with NRG to fit the Kondo spectra in magnetic fields accurately and extract the corresponding Kondo temperature unambiguously. Some YSR states move across the quantum phase transition (QPT) due to the changes in atomic forces during tip approach, yielding a continuous universal scaling with quantitative precision for quantum spin-1/2 impurities.