Niobium's intrinsic coherence length and penetration depth revisited using low-energy muon spin spectroscopy and secondary-ion mass spectrometry

TL;DR

This study precisely measures the intrinsic coherence length and penetration depth in oxygen-doped niobium using advanced depth-resolved techniques, revealing that clean niobium is near the boundary between type-I and type-II superconductivity.

Contribution

It provides direct, nanoscale measurements of key superconducting length scales in niobium, refining their values and implications for its classification as a superconductor.

Findings

Intrinsic penetration depth $\\lambda_L$ is approximately 29 nm.

Coherence length $\xi_0$ is approximately 40 nm.

Niobium's Ginzburg-Landau parameter suggests it is near the type-I/type-II boundary.

Abstract

We report direct, simultaneous measurements of the London penetration depth ($\lambda_L$) and Bardeen-Cooper-Schrieffer (BCS) coherence length ($\xi_0$) in oxygen-doped niobium, with impurity concentrations spanning the "clean" to "dirty" limits. Two depth-resolved techniques - low-energy muon spin spectroscopy (LE-$\mu$SR) and secondary-ion mass spectrometry (SIMS) - were used to quantify the element's Meissner screening profiles, analyzed within a framework that accounts for nonlocal electrodynamics. The analysis indicates intrinsic length scales of $\lambda_L = 29.1(10)$ nm and $\xi_0 = 39.9(25)$ nm, corresponding to a Ginzburg-Landau (GL) parameter of $\kappa = 0.70(5)$. The obtained $\lambda_L$ and $\kappa$ values, accurately quantified at the nanoscale, are smaller than values commonly used in applications and modeling, and indicate that clean niobium lies at the boundary between type-I and type-II superconductivity, supporting the contemporary view that its intrinsic state may be type-I.