# Breakdown of the Hebel-Slichter effect in superconducting graphene due to the emergence of Yu-Shiba-Rusinov states at magnetic resonant scatterers

## TL;DR

This paper studies how magnetic impurities and Yu-Shiba-Rusinov states affect spin relaxation in superconducting graphene, revealing a breakdown of the Hebel-Slichter effect at resonances due to spectral weight redistribution.

## Contribution

It demonstrates that Yu-Shiba-Rusinov states cause the Hebel-Slichter effect to fail at resonances, providing new insights into quasiparticle spin dynamics in superconducting graphene.

## Key findings

- Hebel-Slichter effect observed off resonance
- Resonant impurities lead to Yu-Shiba-Rusinov states
- Spin relaxation decreases with temperature at resonance

## Abstract

Employing analytical methods and quantum transport simulations we investigate the relaxation of quasiparticle spins in graphene proximitized by an $s$-wave superconductor in the presence of resonant magnetic and spin-orbit active impurities. Off resonance, the relaxation increases with decreasing temperature when electrons scatter off magnetic impurities---the Hebel-Slichter effect---and decreases when impurities have spin-orbit coupling. This distinct temperature~dependence (not present in the normal state) uniquely discriminates between the two scattering mechanisms. However, we show that the Hebel-Slichter picture breaks down at resonances. The emergence of Yu-Shiba-Rusinov bound states within the superconducting gap redistributes the spectral weight away from magnetic resonances. The result is opposite to the Hebel-Slichter expectation: the spin relaxation decreases with decreasing temperature. Our findings hold for generic $s$-wave superconductors with resonant magnetic impurities, but also, as we show, for resonant magnetic Josephson junctions.