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

Abstract

We study the effect of strong spin-orbit coupling (SOC) on bound states induced by impurities in superconductors. The presence of spin-orbit coupling 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 superconductor, 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. Our predictions can be used to distinguish the symmetry of the order parameter and have implications for the Majorana proposals based on chains of magnetic atoms placed on the surface of superconductors with strong spin-orbit coupling [1]. PACS numbers: 73.20.Hb, 75.70.Tj, The presence of impurities is almost always unavoidable in condensed matter systems. Often impurities are regarded as a nuisance that spoils the properties of a clean system and complicates the understanding of its properties. However, impurities are in many instances essential to obtain desirable physical effects and can be used as unique atomic-scale probes of the ground state of the host system [2-10]. The study of the effect of impurities in superconductors has been a very active field of research [10]. In an s-wave superconductor magnetic impurities cause the formation of bound states, the Yu-ShibaRusinov (YSR) states [11][12][13]. There has been a significant interest in the properties of YSR states due to theoretical proposals suggesting that a chain of magnetic impurities placed on the surface of a superconductor (SC) would be a very robust, self-tuning, system that should exhibit non-abelian, Majorana, states [14][15][16][17][18]. In these proposals the bound states induced by the chain of magnetic impurities form an impurity band with non-trivial topological character. More recently it has been pointed out that the presence of Rashba spin-orbit coupling (SOC) should facilitate the realization of a topological impurity band of YSR states. [1,[19][20][21]. On the surface, due to the lack of inversion symmetry, some amount of Rashba SOC will be present. Therefore, for the systems considered to realize a topological band of YSR states the presence of Rashba SOC is both unavoidable and beneficial. This assessment has very recently been confirmed by the experimental results presented in Ref. 1, that show some evidence of the presence of Majorana modes at the end of a chain of Fe atoms place...

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