The fate of the Kondo cloud in a superconductor

TL;DR

This paper investigates the behavior of the Kondo screening cloud in superconductors, revealing that the cloud persists in both phases but with varying degrees of screening, and introduces a universal measure related to impurity properties.

Contribution

It demonstrates the existence of the Kondo cloud in both screened and unscreened phases within superconductors and links its properties to experimentally measurable quantities.

Findings

The Kondo cloud exists in both quantum phases.

Screening is complete in the screened phase, partial in the unscreened phase.

The compensation measure is universal and related to the impurity's g-factor.

Abstract

Magnetic impurities embedded in a metal are screened by the Kondo effect, signaled by the formation of an extended correlation cloud, the so-called Kondo or screening cloud. In a superconductor, the Kondo state turns into sub-gap Yu-Shiba-Rusinov (Shiba) states, and a quantum phase transition occurs between screened and unscreened phases once the superconducting energy gap $\Delta$ becomes sufficiently large compared to the Kondo temperature, $T_K$. Here we show that, although the Kondo state does not form in the unscreened phase, the Kondo cloud does exist in both quantum phases. However, while screening is complete in the screened phase, it is only partial in the unscreened phase. Compensation, a quantity introduced to characterize the integrity of the cloud, is universal, and shown to be related to the magnetic impurities' $g$-factor, monitored experimentally by bias spectroscopy.