Direct Observation of the Scale Relation between Density of States and Pairing Gap in a Dirty Superconductor

TL;DR

This study experimentally confirms a scale relation between the density of states and pairing gap in a dirty superconductor under magnetic fields, extending its validity and enabling a new method to measure coherence length.

Contribution

It provides the first direct experimental observation of the scale relation in a dirty superconductor under magnetic fields and demonstrates its practical use for measuring coherence length.

Findings

The NbC superconductor is homogeneous and dirty.

The density of states and pairing gap follow de Gennes' scale relation.

The scale relation holds at magnetic fields well below the upper critical field.

Abstract

Theories and experiments on dirty superconductors are sophisticated but important for both fundamentals and applications. It becomes more challenging when magnetic fields are present, because the field distribution, the electron density of states, and the superconducting pairing potentials are nonuniform. Here we present tunneling microspectroscopic experiments on NbC single crystals and show that NbC is a homogeneous dirty superconductor. When applying magnetic fields to the sample, we observe that the zero-energy local density of states and the pairing energy gap follow an explicit scale relation proposed by de Gennes for homogeneous dirty superconductors in high magnetic fields. Surprisingly, our experimental findings suggest that the validity of the scale relation extends to magnetic field strengths far below the upper critical field and call for new nonperturbative understanding of this fundamental property in dirty superconductors. On the practical side, we use the observed scale relation to drive a simple and straightforward experimental scheme for extracting the superconducting coherence length of a dirty superconductor in magnetic fields.