Theory for Superconducting Properties of the Cuprates: Doping Dependence of the Electronic Excitations and Shadow States

TL;DR

This paper presents a theoretical study of the doping dependence of superconducting properties in the 2D Hubbard model, revealing optimal doping levels, the influence of magnetic correlations, and the emergence of shadow states affecting electronic spectra.

Contribution

It introduces a comprehensive theoretical framework combining FLEX and Eliashberg theories to analyze doping effects on $T_c$, gap functions, and shadow states in cuprate superconductors.

Findings

Maximum $T_c$ at 13% doping

Overdoped $T_c$ decreases due to weakened antiferromagnetic correlations

Shadow states influence electronic excitation spectra

Abstract

The superconducting phase of the 2D one-band Hubbard model is studied within the FLEX approximation and by using an Eliashberg theory. We investigate the doping dependence of $T_c$, of the gap function $\Delta ({\bf k},\omega)$ and of the effective pairing interaction. Thus we find that $T_c$ becomes maximal for $13 \; \%$ doping. In {\it overdoped} systems $T_c$ decreases due to the weakening of the antiferromagnetic correlations, while in the {\it underdoped} systems due to the decreasing quasi particle lifetimes. Furthermore, we find {\it shadow states} below $T_c$ which affect the electronic excitation spectrum and lead to fine structure in photoemission experiments.