Correlated Electrons in High Temperature Superconductors

TL;DR

This review discusses theoretical models and experimental findings related to high temperature superconductors, emphasizing strongly correlated electron models like the Hubbard and t-J models, and their ability to explain cuprate properties and superconductivity.

Contribution

It provides a comprehensive comparison of computational and analytical approaches to correlated electron models, highlighting their success in explaining key experimental phenomena in cuprates.

Findings

Hubbard-like models explain unusual cuprate properties

Numerical results support d-wave superconductivity in models

Models reproduce optical and photoemission features

Abstract

Theoretical ideas and experimental results concerning high temperature superconductors are reviewed. Special emphasis is given to calculations carried out with the help of computers applied to models of strongly correlated electrons proposed to describe the two dimensional ${\rm Cu O_2}$ planes. The review also includes results using several analytical techniques. The one and three band Hubbard models, and the ${\rm t-J}$ model are discussed, and their behavior compared against experiments when available. Among the conclusions of the review, we found that some experimentally observed unusual properties of the cuprates have a natural explanation through Hubbard-like models. In particular abnormal features like the mid-infrared band of the optical conductivity $\sigma(\omega)$, the new states observed in the gap in photoemission experiments, the behavior of the spin correlations with doping, and the presence of phase separation in the copper oxide superconductors may be explained, at least in part, by these models. Finally, the existence of superconductivity in Hubbard-like models is analyzed. Some aspects of the recently proposed ideas to describe the cuprates as having a $\dx2y2$ superconducting condensate at low temperatures are discussed. Numerical results favor this scenario over others....(continues).