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We report on a study of the electromagnetic response of three different families of high-T c superconductors that in combination allowed us to cover the whole doping range from under-to overdoped. The discussion is focused on the ab-plane charge dynamics in the pseudogap state which is realized in underdoped materials below a characteristic temperature T * , a temperature that can significantly exceed the superconducting transition temperature T c . We explore the evolution of the pseudogap response by changing the doping level, by varying the temperature from above to below T * , or by introducing impurities in the underdoped compounds. We employ a memory function analysis of the ab-plane optical data that allows us to observe the effect of the pseudogap most clearly. We compare the infrared data with other experimental results, including the c-axis optical response, dc transport, and angle-resolved photoemission.

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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