Field dependence of the vortex core size probed by STM

TL;DR

This study analyzes the vortex core size in superconductors using STM, revealing field-dependent and independent behaviors in single and multigap materials, and provides an analytic model for the density of states distribution.

Contribution

The paper introduces an analytic expression for the DOS distribution at zero bias in superconductors, linking vortex core size to material properties and magnetic field, validated by STM data.

Findings

Vortex core size in single-gap superconductor decreases with increasing magnetic field.

In multigap superconductors, the core size remains field independent across bands.

The derived model accurately reproduces experimental STM data across different materials.

Abstract

We study the spatial distribution of the density of states (DOS) at zero bias N(r) in the mixed state of single and multigap superconductors. We provide an analytic expression for N(r) based on deGennes' relation between DOS and the order parameter that reproduces well Scanning Tunneling Microscopy (STM) data in several superconducting materials. In the single gap superconductor $\beta$-Bi$_2$Pd, we find that N(r) is governed by a length scale $\xi_H=\sqrt{\phi_0/2\pi H}$, which decreases in rising fields. The vortex core size $\cal C$, defined via the slope of the order parameter at the vortex center, $\cal C$ $\propto (d \Delta /dr |_{r \to 0})^{-1}$, differs from $\xi_H$ by a material dependent numerical factor. For two gap superconductors 2H-NbSe$_{1.8}$S$_{0.2}$ and 2H-NbS$_2$, we find that $\cal C$ is field independent and has the same value for both bands. We conclude that, independently of the magnetic field induced variation of the order parameter values in both bands, the spatial variation of the order parameter close to the vortex core is the same for all bands.