Universal scaling relations in electron-phonon superconductors

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.