Yu-Shiba-Rusinov states in 2D superconductors with arbitrary Fermi contours

TL;DR

This paper introduces a theoretical method to calculate the spatial distribution of Yu-Shiba-Rusinov states in 2D superconductors with arbitrary Fermi contours, linking Fermi surface shape to YSR state decay and extension.

Contribution

The authors develop an analytical Green's Function-based approach for arbitrary Fermi contours, enabling detailed YSR state analysis in complex 2D superconductors.

Findings

Connection between Fermi contour shape and YSR state decay

Application to manganese dimers on $eta$-Bi2Pd superconductor

Method extension to multiple interacting impurities

Abstract

Magnetic impurities on a superconductor induce sub-gap Yu-Shiba-Rusinov (YSR) bound states, localized at the impurity site and fading away from it for distances up to several nanometers. In this article, 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 further apply this formalism to compute the evolution of YSR states in the presence of a nearby impurity atom, and compare the results with Scanning Tunneling Microscopy (STM) measurements on interacting manganese dimers on the $\beta$-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.