Universal scaling relations in electron-phonon superconductors

TL;DR

This paper demonstrates that Homes scaling relations, linking superfluid density and dc conductivity, are universal across various superconductors due to impurity and electron-phonon scattering effects, extending beyond cuprates and BCS theory.

Contribution

It reveals the universality of Homes scaling relations in electron-phonon superconductors through combined numerical and analytical methods.

Findings

Homes scaling relations are valid across a wide class of superconductors.

Large impurity or inelastic scattering leads to linear scaling.

Homes scaling is more fundamental than cuprate or BCS-specific physics.

Abstract

We study linear scaling relations in electron-phonon superconductors. By combining numerical and analytical techniques, we find linear Homes scaling relations between the zero-temperature superfluid density and the normal-state dc conductivity. This phenomenon arises via either a large impurity scattering rate or inelastic scattering of electrons and Einstein phonons at large electron-phonon coupling. Thus, our Letter shows that Homes scaling is more universal than either cuprate or BCS-like physics and is, instead, a fundamental result in a wide class of superconductors.