Doping dependent optical properties of Bi₂Sr ₂CaCu₂O_8+δ

We report on the ab-plane reflectance of the high temperature superconductor Bi₂Sr₂CaCu₂O_8+δ (Bi-2212). Measurements on samples spanning the doping range from underdoped with T_c ≤ 67K (UD), to optimally doped with T_c ≤ 96K (OPT), to overdoped with T_c ≤ 60K (OD) were made from room temperature down to the superconducting state regime. The measured reflectance data were analysed to extract the optical conductivity and the real and imaginary parts of the free carrier optical self-energy. We get an estimate of the dc resistivity from the low frequency extrapolation of the optical conductivity and the superfluid density from the imaginary part of the optical conductivity. The conductivity sum rule can be related to the changes of the kinetic energy of the system. When this system becomes a superconductor, the kinetic energy decreases in the underdoped samples and increases in the overdoped ones. The optical self-energy, obtained from the extended Drude model, is dominated by two channels of interaction: a sharp mode and a broad background. The amplitude of the mode is strongly doping and temperature dependent whereas the background decreases weakly with doping and is nearly temperature independent.