Abstract

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. A fundamental understanding of the formation of YSR states in small atomic clusters is essential for revealing the topological properties of the YSR band structure.

Here, it is theoretically discussed how the electronic structure determines the spatial profile of individual YSR states and the interactions between the states. It is shown how the shape of the Fermi surface leads to a long-ranged anisotropic extension of YSR states in the vicinity of magnetic impurities [1]. It is explained how the spin-orbit coupling influences the hybridization of YSR bound states of dimers with ferromagnetic and antiferromagnetic spin alignments [2], and how it gives rise to a topologically non-trivial YSR band structure in ferromagnetic chains [3]. The theoretical concepts are illustrated by their experimental realizations in specific materials.

[1] H. Kim, L. Rózsa, D. Schreyer, E. Simon, and R. Wiesendanger, Nat. Commun. 11, 4573 (2020).
[2] P. Beck, L. Schneider, L. RÛzsa, K. Palot·s, A. L·szlÛffy, L. Szunyogh, J. Wiebe, and R. Wiesendanger, Nat. Commun. 12, 2040 (2021).
[3] L. Schneider, P. Beck, J. Neuhaus-Steinmetz, L. RÛzsa, T. Posske, J. Wiebe, and R. Wiesendanger, Nat. Nanotechnol. 17, 384 (2022).