Since the discovery of superconductivity at elevated temperatures in the copper oxide materials there has been a considerable effort to find universal trends and correlations amongst physical quantities, as a clue to the origin of the superconductivity. One of the earliest patterns that emerged was the linear scaling of the superfluid density (rho(s)) with the superconducting transition temperature (T(c)), which marks the onset of phase coherence. This is referred to as the Uemura relation, and it works reasonably well for the underdoped materials. It does not, however, describe optimally doped (where T(c) is a maximum) or overdoped materials. Similarly, an attempt to scale the superfluid density with the d.c. conductivity (sigma(dc)) was only partially successful. Here we report a simple scaling relation (rho(s) proportional, variant sigma(dc)T(c), with sigma(dc) measured at approximately T(c)) that holds for all tested high-T(c) materials. It holds regardless of doping level, nature of dopant (electrons versus holes), crystal structure and type of disorder, and direction (parallel or perpendicular to the copper-oxygen planes).

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Analysis of the interlayer infrared conductivity of cuprate high-transition temperature superconductors reveals an anomalously large energy scale extending up to midinfrared frequencies that can be attributed to formation of the superconducting condensate. This unusual effect is observed in a va- riety of materials, including Tl2Ba2CuO6+x, La2-xSrxCuO4, and YBa2Cu3O6.6, which show an incoherent interlayer response in the normal state. Midinfrared range condensation was examined in the context of sum rules that can be formulated for the complex conductivity. One possible interpretation of these experiments is in terms of a kinetic energy change associated with the superconducting transition.