Magnetic impurities in conventional superconductors locally break Cooper pairs, leading to the emergence of Yu-Shiba-Rusinov (YSR) bound states. Chains of YSR impurities have been theoretically predicted to give rise to Majorana bound states, representing promising building blocks of topological quantum computers. Revealing the topological properties of YSR bands necessitates a fundamental understanding of the extension of individual YSR states, as well as of the interactions between the states.

 

Here, a theoretical explanation of recent scanning tunneling microscopy and spectroscopy experiments on YSR bound states in elemental superconductors is presented. On the La(0001) surface, YSR states are found to extend up to 30-40 nm distance along certain crystallographic directions, approximately one order of magnitude longer than what has been previously observed in similar setups [1]. This is explained by an effectively reduced dimensionality of the electronic structure, with the scattering processes dominated by surface states with a strongly anisotropic Fermi surface. The presence of multi-orbital YSR states has been observed in the vicinity of Mn adatoms on the Nb(110) surface, with a hybridization and energy splitting of the states in both ferromagnetically and antiferromagnetically aligned dimers [2]. In the antiferromagnetic dimer, such a splitting of the YSR states has been ruled out in theoretical considerations so far, since their degeneracy is protected by Kramers' theorem via an effective time-reversal symmetry. It is shown that this degeneracy is lifted if spin-orbit coupling is taken into account, together with the breaking of inversion symmetry at the surface.

 

[1] H. Kim, L. Rózsa, D. Schreyer, E. Simon, and R. Wiesendanger, Nat. Commun. 11, 4573 (2020).

[2] P. Beck, L. Schneider, L. Rózsa, K. Palotás, A. Lászlóffy, L. Szunyogh, J. Wiebe, and R. Wiesendanger, arXiv:2010.04031.