Impurity-Induced Bound States in Superconductors with Spin-Orbit Coupling

We study the effect of strong spin-orbit coupling (SOC) on bound states induced by impurities in superconductors. The presence of SOC breaks the SU(2)-spin symmetry and causes the superconducting order parameter to have generically both singlet (s-wave) and triplet (p-wave) components. We find that in the presence of SOC the spectrum of Yu-Shiba-Rusinov (YSR) states is qualitatively different in s-wave and p-wave superconductors, a fact that can be used to identify the superconducting pairing symmetry of the host system. We also predict that, in the presence of SOC, the spectrum of the impurity-induced bound states depends on the orientation of the magnetic moment S of the impurity and, in particular, that by changing the orientation of S, the fermion-parity of the lowest energy bound state can be tuned. We then study the case of a dimer of magnetic impurities and show that, in this case, the YSR spectrum for a p-wave superconductor is qualitatively very different from the one for an s-wave superconductor even in the limit of vanishing SOC.