Analysis of Superconductivity in d-p Model on Basis of Perturbation Theory

TL;DR

This paper studies how the energy difference between d and p orbitals affects superconductivity in high-$T_c$ cuprates, revealing that larger differences suppress transition temperature and increase effective mass due to stronger electron correlations.

Contribution

It applies third-order perturbation theory to the d-p model to analyze mass enhancement and $T_c$, providing insights into electron correlation effects in high-$T_c$ superconductors.

Findings

Large energy difference increases mass enhancement factor.

Large energy difference suppresses $T_c$ due to density of state effects.

Electron correlation strength is linked to d-hole number approaching unity.

Abstract

We investigate the mass enhancement factor and the superconducting transition temperature in the d-p model for the high-$\Tc$ cuprates. We solve the \'Eliashberg equation using the third-order perturbation theory with respect to the on-site Coulomb repulsion $U$. We find that when the energy difference between d-level and p-level is large, the mass enhancement factor becomes large and $\Tc$ tends to be suppressed owing to the difference of the density of state for d-electron at the Fermi level. From another view point, when the energy difference is large, the d-hole number approaches to unity and the electron correlation becomes strong and enhances the effective mass. This behavior for the electron number is the same as that of the f-electron number in the heavy fermion systems. The mass enhancement factor plays an essential role in understanding the difference of $\Tc$ between the LSCO and YBCO systems.