In 2004 Chris Homes et al. published a Nature paper describing a (fairly) universal scaling relation between the superfluid density and the product of Tc the transition temperature and the dc conductivity at T=Tc. This is a generalisation of the Uemura relation which describes underdoped cuprates.
Jan Zaanen wrote a News and Views piece, Why the temperature is high for the Homes article. It features the figure above. Zaanen combined the Homes relation with the Drude formula for the dc conductivity, "Tanner's law" which found that for optimally doped cuprates the superfluid density was approximately one-quarter of the density of "mobile electrons" defined by the low energy spectral weight (Drude weight) in the optical conductivity. This results in a scattering time which is approximately hbar/ 2 pi kB T. He "sexes" this up by calling it "Planckian dissipation".
I wonder if this is really anything more than the Marginal Fermi liquid picture with the dimensionless coupling constant equal to unity.
Aside: Later Frances Pratt and Steve Blundell showed in a PRL that Homes scaling relation does not hold for molecular superconductors. Previously, Ben Powell and I had noted how the organic charge transfer salts deviated significantly from both a simple BCS picture and the phase fluctuation picture proposed by Emery and Kivelson to explain the Uemura relation in the cuprates.
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