Optical properties along the c axis of YBa_2Cu_3O_{6+x}, for x=0.50 -> 0.95: evolution of the pseudogap

Abstract

The reflectance of high-quality, unpolished single crystals of YBa_2Cu_3O_{6+x}, for the doping range x=0.50 -> 0.95, has been measured with radiation polarized along the c axis from approx 50 cm^{-1} to 5000 cm^{-1} between 10 K and 300 K. In highly doped (x=0.95) material, the normal-state conductivity shows a metallic response. For intermediate dopings (x=0.85 -> 0.90) the conductivity is no longer metallic, increasing with temperature, and for low dopings (x=0.50 -> 0.80) this behavior is clearly seen to be caused by a pseudogap at approx 280 cm^{-1}, which develops well above T_c. In the superconducting state, in the optimally-doped material, a gap-like depression develops below T_c but there is residual conductivity to very low frequency indicating either an anisotropic gap, or a gap with nodes. In the underdoped materials the superconductivity-induced changes to the conductivity are harder to see, but it appears that the weight of the condensate originates at frequencies much higher than the conventional weak-coupling value of 3.5k_BT_c.