Yu-Shiba-Rusinov states in two-dimensional superconductors with arbitrary Fermi contours

Abstract

Magnetic impurities on a superconductor induce subgap Yu-Shiba-Rusinov (YSR) bound states, localized at the impurity site and fading away from it for distances up to several nanometers. In this paper, we present a theoretical method to calculate the spatial distribution of the YSR spectrum of a two-dimensional superconductor with arbitrary Fermi contours (FCs) in the presence of magnetic impurities. Based on the Green's function (GF) formalism, we obtain a general analytical expression by approximating an arbitrary contour shape to a regular polygon. This method allows us to show the connection between the spatial decay (and, hence, the extension) of YSR states and the shape of the FC of the host superconductor. We demonstrate the accuracy of this approximation by comparing the results with those obtained from an exact numerical calculation based on a tight-binding Hamiltonian. We further apply the analytical formalism to compute the evolution of YSR states in the presence of a nearby impurity atom, and compare the results with scanning tunneling microscopy measurements on interacting manganese dimers on the β−Bi2Pd superconductor. The method can be easily extended to any arbitrary number of magnetically coupled impurities, thus providing a useful tool for simulating the spectral properties of interacting YSR states in artificial atomic nanostructures.

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