Nonlocal effect and dimensions of Cooper pairs measured by low-energy muons and polarized neutrons in type-I superconductors

Abstract

The Pippard coherence length ${\ensuremath{\xi}}_{0}$ (the size of a Cooper pair) in two extreme type-I superconductors (In and Sn) 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 ${\ensuremath{\lambda}}_{\mathrm{L}}(T)$ were determined as well. An expression linking ${\ensuremath{\xi}}_{0}$, $Z$, and ${\ensuremath{\lambda}}_{\mathrm{L}}(0)$ is introduced and experimentally verified. This expression allows one to determine experimentally the Pippard coherence length in any superconductor, independent of whether the superconductor is local or nonlocal, conventional or unconventional.