Anisotropy of Yu-Shiba-Rusinov states in NbSe$_2$

TL;DR

This study analyzes the anisotropic spatial structure of Yu-Shiba-Rusinov states in NbSe2, revealing that the shape is primarily determined by the anisotropic prefactor related to the normal metal's Fermi surface, rather than the exponential decay length.

Contribution

The paper demonstrates that the anisotropic shape of YSR states can be accurately described by the prefactor linked to the normal state's Fermi surface, refining analysis methods for STM data in small-gap superconductors.

Findings

The exponential decay length is larger than observed YSR state extent.

The anisotropic prefactor matches theoretical predictions and shapes the YSR state.

The shape of YSR states relates to the normal metal's Fermi surface properties.

Abstract

The spatial structure of in-gap Yu-Shiba-Rusinov (YSR) bound states induced by a magnetic impurity in a superconductor is the essential ingredient for the possibility of engineering collective impurity states. Recently, a saddle-point approximation [Phys. Rev. B 105, 144503] revealed how the spatial form of a YSR state is controlled by an anisotropic exponential decay length, and an anisotropic prefactor, which depends on the Fermi velocity and Fermi-surface curvature. Here we analyze scanning tunnel microscope (STM) data on YSR states in NbSe$_2$, focusing on a key issue that the exponential decay length predicted theoretically from the small superconducting gap is much larger than the observed extent of YSR states. We confirm that the exponential decay can be neglected in the analysis of the anisotropy. Instead, we extract the anisotropic prefactor directly from the data, matching it to the theoretical prediction, and we establish that the theoretical expression for the prefactor alone captures the characteristic flower-like shape of the YSR state. Surprisingly, we find that up to linear order in the superconducting gap the anisotropic prefactor that determines the shape of YSR states is the same as the anisotropic response to the impurity in the underlying normal metal. Our work points out the correct way to analyze STM data on impurities in small-gap superconductors, and reveals the importance of the normal band structure's curvature and Fermi velocity in designing multi-impurity in-gap states in superconductors.