Mateo Uldemonlins (Université Paris-Saclay, CNRS)

A magnetic impurity on a conventional superconductor is one of the most simple pair-breaking defects that induces in-gap Yu-Shiba-Rusinov (YSR) bound states. Predicted soon after the publication of the BCS theory for superconductivity, they now enjoy a renewed wave of interest thanks to the advancements in atomic functionalization and local imaging techniques. These developments have motivated significant theoretical and experimental efforts in designing complex structures of YSR states in real space to engineer topological superconductivity and the long-sought topologically protected qubits. The possibilities of engineering collective impurity states (e.g., YSR chains, lattices, etc.) hosting exotic states of matter are crucially influenced by the intricate spatial structure of YSR, which blends together information about substrate bandstructure, pairing function, and impurity coupling. In this talk, I will first introduce the paradigmatic model used to describe a magnetic impurity on a two-dimensional superconductor and discuss the main aspects of YSR physics. Secondly, I will present our recent work on the quasiparticle effect of YSR states, where we use a generalized saddle-point approximation to unveil a simple analytical relationship between the spatial structure of the YSR bound states and the momentum-space anisotropy of the Fermi surface, namely the angular dependent Fermi velocity and curvature of the Fermi surface. I will show that our analytical approximation is quantitatively accurate against tight-binding calculations in lattice models. I will also discuss its application to describe the anisotropy of YSR states observed in scanning tunneling spectroscopy experiments of magnetic impurities on NbSe2.