Size and mass of Cooper pairs determined by low-energy $\mu$SR and PNR

TL;DR

This study directly measures the size of Cooper pairs in an extreme type-I superconductor using advanced low-energy muon spin rotation and polarized neutron reflectometry techniques, providing a universal expression linking key superconducting parameters.

Contribution

It introduces a general experimentally verified expression linking the Pippard coherence length, electron-phonon renormalization, and London penetration depth applicable to all superconductors.

Findings

Determined the Pippard coherence length directly in a superconductor.

Established a universal relation between coherence length, renormalization factor, and penetration depth.

Validated the expression across different superconducting states.

Abstract

The Pippard coherence length $\xi_0$ (the size of a Cooper pair) in an extreme type-I superconductor was determined directly through high-resolution measurement of the nonlocal electrodynamic effect combining low-energy muon spin rotation spectroscopy and polarized neutron reflectometry. The renormalization factor $Z$=m_cp*/2m (m_cp* and m are the mass of the Cooper pair and the electron, respectively) resulting from the electron-phonon interaction, and the temperature dependent London penetration depth $\lambda_L(T)$ were determined as well. A general expression linking $\xi_0$, $Z$ and $\lambda_L(0)$ is introduced and experimentally verified. This expression allows one to determine experimentally the Pippard coherence length in \textit{any} superconductor, independent of whether the electrodynamics is local or nonlocal, conventional or unconventional.