Electron-boson spectral density function of underdoped Bi ₂Sr₂CaCu₂O_8+δ and YBa ₂Cu₃O_6.50

We investigate the electron-boson spectral density function, I2χ(ω,T), of the CuO₂ plane in underdoped Bi ₂Sr₂CaCu₂O_8+δ (Bi-2212) and underdoped YBa₂Cu₃O_6.50 (Y-123) using the Eliashberg formalism. We apply a new (in-plane) pseudogap model to extract the electron-boson spectral function. For extracting the spectral function we assume that the spectral density function consists of two components: a sharp mode and the broad Millis-Monien-Pines mode. We observe that both the resulting spectral density function and the intensity of the pseudogap show strong temperature dependences: the sharp mode takes the most spectral weight of the function, the peak position of the sharp mode shifts to a lower frequency, and the depth of the pseudogap, 1-N(0,T), increases as the temperature decreases. We observe also that the total spectral weight of the electron-boson density and the mass enhancement coefficient increase as the temperature decreases. We estimate fictitious (maximum) superconducting transition temperatures, T_c(T), from the extracted spectral functions at various temperatures using a generalized McMillan formula. The estimated (maximum) T_c also shows a strong temperature dependence; it is higher than the actual T_c at all measured temperatures and decreases with decreasing temperature. Since with decreasing temperature the pseudogap gets stronger and the maximum T_c gets lower, we propose that the pseudogap may suppress superconductivity in cuprates.