Doping-induced change of optical properties in underdoped cuprate superconductors

We report on the ab-plane optical reflectance measurements of single crystals of Y-doped Bi₂Sr₂CaCu₂O_8+∞ and Pr-doped YBa₂Cu₃O_7-∞ over a wide frequency range from 80 to 40 000 cm^-1 (10 meV-5 eV) and at temperatures between 20 and 300 K. Y and Pr doping both decrease the hole concentration in the CuO₂ planes. This has allowed us to investigate the evolution of ab-plane charge dynamics at doping levels ranging from heavily underdoped to nearly optimally doped. Our results of the low-frequency optical conductivity and spectral weight do not show any features associated with the normal-state pseudogap. Instead, one-component analysis for the optical conductivity shows the low-frequency depression in the scattering rate at T > T_c, signalling entry into the pseudogap state. Alternatively, no clear indications of the normal-state pseudogap are detected in the temperature-dependent zero-frequency free-carrier scattering rate by using two-component analysis. In the superconducting state, there is also no convincing evidence of superconducting gap absorption in all spectra. We find that there is a 'universal correlation' between the numbers of carriers and the transition temperature. This correlation holds whether one considers the number of carriers in the superfluid or the total number of carriers.