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

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 tightbinding 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 ??-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.

Automated summary

In this paper, a theoretical method is presented to calculate the spatial distribution of Yu-Shiba-Rusinov (YSR) bound states in a two-dimensional superconductor with arbitrary Fermi contours (FCs) in the presence of magnetic impurities. The method is based on the Green's function formalism and approximates an arbitrary contour shape to a regular polygon. The accuracy of this approximation is demonstrated by comparing the results with those obtained from an exact numerical calculation. The method is further applied to study the evolution of YSR states in the presence of impurity atoms and compared with experimental results obtained from scanning tunneling microscopy measurements.