The electron-boson spectral density function of underdoped Bi$_2$Sr$_2$CaCu$_2$O$_{8+\delta}$ and YBa$_2$Cu$_3$O

TL;DR

This study analyzes the electron-boson spectral density in underdoped cuprates using a new pseudogap model, revealing temperature-dependent features that suggest the pseudogap suppresses superconductivity.

Contribution

It introduces a novel in-plane pseudogap model to extract the electron-boson spectral function in underdoped cuprates, highlighting the pseudogap's impact on spectral features and superconductivity.

Findings

The spectral density function shows a dominant sharp mode that shifts to lower frequency as temperature decreases.

The pseudogap deepens and the spectral weight increases with decreasing temperature.

Estimated maximum superconducting transition temperature decreases with temperature, indicating pseudogap suppression of superconductivity.

Abstract

We investigate the electron-boson spectral density function, $I^2\chi(\omega,T)$, of CuO$_2$ plane in underdoped Bi$_2$Sr$_2$CaCu$_2$O$_{8+\delta}$ (Bi-2212) and underdoped YBa$_2$Cu$_3$O$_{6.50}$ (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 (MMP) mode. We observe that both the resulting spectral density function and the intensity of the pseudogap show strong temperature dependences: the sharp mode takes most spectral weight of the function and the peak position of the sharp mode shifts to lower frequency and the depth of pseudogap, $1-\tilde{N}(0,T)$, is getting deeper as temperature decreases. We observe also that the total spectral weight of the electron-boson density and the mass enhancement coefficient increase as 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 temperature lowering. Since as lowering temperature the pseudogap is getting stronger and the maximum $T_c$ is getting lower we propose that the pseudogap may suppress the superconductivity in cuprates.