Odd-frequency superconductivity near a magnetic impurity in a conventional superconductor

TL;DR

This paper demonstrates that magnetic impurities in conventional superconductors induce odd-frequency pairing, especially spin-triplet components, with their behavior strongly influenced by impurity strength and local density of states.

Contribution

It provides a detailed analysis of odd-frequency pairing near a single magnetic impurity, highlighting the dominance of spin-triplet components at critical impurity strength.

Findings

Odd-frequency spin-triplet pairing dominates at critical impurity strength.

YSR states merge at the middle of the gap at critical impurity strength.

Spin-polarized local density of states mirrors odd-frequency pairing behavior.

Abstract

Superconductor-ferromagnetic heterostructures have been suggested as one of the most promising alternatives of realizing odd-frequency superconductivity. In this work we consider the limit of shrinking the ferromagnetic region to the limit of a single impurity embedded in a conventional superconductor, which gives raise to localized Yu-Shiba-Rusinov (YSR) bound states with energies inside the superconducting gap. We demonstrate that all the sufficient ingredients for generating odd-frequency pairing are present at the vicinity of these impurities. We investigate the appearance of all possible pair amplitudes in accordance with the Berezinskii $SP^{\ast}OT^{\ast} = -1$ rule, being the symmetry under the exchange of spin, spatial, orbital (in our case $O=+1$) and time index, respectively. We study the spatial and frequency dependence of of the possible pairing amplitudes, analyzing their evolution with impurity strength and identifying a reciprocity between different symmetries related through impurity scattering. We show that the odd-frequency spin-triplet pairing amplitude dominates at the critical impurity strength, where the YSR states merge at the middle of the gap, while the even components cancel out close to the impurity. We also show that the spin-polarized local density of states exhibits the same spatial and frequency behavior as the odd-$\omega$ spin-triplet component at the critical impurity strength.