Homes scaling and BCS

It is argued on the basis of the BCS theory that the zero-$T$ penetration depth satisfies $λ^{-2}(0)\proptoσT_c$ ($σ$ is the normal state dc conductivity) not only in the extreme dirty limit $ξ_0/\ell \gg 1$, but in a broad range of scattering parameters down to $ξ_0/\ell \sim 1$ ($ξ_0$ is the zero-$T$ BCS coherence length and $\ell$ is the mean-free path). Hence, the scaling $λ^{-2}(0)\proptoσT_c$, suggested as a new universal property of superconductors,\cite{Homes} finds a natural explanation within the BCS theory.

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