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Scaling relations and the dirty limit in high-temperature superconductors

Abstract :

Recently, we proposed a scaling relation between the superfluid density, critical temperature (T c ), and the dc conductivity just above T c ; this relation is valid for many different electron and hole-doped cuprates, both in the metallic copper-oxygen planes, as well as along the poorly-conducting c -axis.  This universal scaling relation implies that (i) these materials are in the dirty limit (the normal-state scattering rate is larger than roughly twice the superconducting gap maximum), and (ii) that the energy-scale for the superconductivity scaled with T c .  This was in opposition to the conventional wisdom, which stated that the cuprates were in the clean limit (the scattering rate is much smaller than the superconducting gap), and that in the underdoped materials the pseudogap was increasing with decreasing T c .  Recent improvements in optical techniques have allowed us to directly observe the optical signature of the superconducting gaps in the electron-doped materials; comparison with the scattering rate shows that they are in the dirty limit, a result that appears to be generally true for all cuprates.  This view is further supported when the anisotropic nature of the Fermi surface is taken into account.  Finally, recent ARPES results indicate that the small pseudogap and T c both decrease with decreasing doping.  This suggests that while the superconductivity is probably mean-field like at optimal doping, in the underdoped materials it may driven by the proximity effect.