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arXiv:cond-mat/9311013 · Reviews of Modern Physics

Correlated electrons in high-temperature superconductors

Elbio R. Dagotto

Published Jul 1, 1994• 3,118 citations
arXivHTMLPDF

Abstract

Theoretical ideas and experimental results concerning high-temperature superconductors are reviewed. Special emphasis is given to calculations performed with the help of computers applied to models of strongly correlated electrons proposed to describe the two-dimensional Cu${\mathrm{O}}_{2}$ planes. The review also includes results using several analytical techniques. The one- and three-band Hubbard models and the $t\ensuremath{-}J$ model are discussed, and their behavior compared against experiments when available. The author found, among the conclusions of the review, 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 $\ensuremath{\sigma}(\ensuremath{\omega})$, 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 ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$ superconducting condensate at low temperatures are discussed. Numerical results favor this scenario over others. It is concluded that computational techniques provide a useful, unbiased tool for studying the difficult regime where electrons are strongly interacting, and that considerable progress can be achieved by comparing numerical results against analytical predictions for the properties of these models. Future directions of the active field of computational studies of correlated electrons are briefly discussed.

DOI
10.1103/revmodphys.66.763

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This is a short review of the theoretical work on the two-dimensional Hubbard model performed in Sherbrooke in the last few years. It is written on the occasion of the twentieth anniversary of the discovery of high-temperature superconductivity. We discuss several approaches, how they were benchmarked and how they agree sufficiently with each other that we can trust that the results are accurate solutions of the Hubbard model. Then comparisons are made with experiment. We show that the Hubbard model does exhibit d-wave superconductivity and antiferromagnetism essentially where they are observed for both hole- and electron-doped cuprates. We also show that the pseudogap phenomenon comes out of these calculations. In the case of electron-doped high temperature superconductors, comparisons with angle-resolved photoemission experiments are nearly quantitative. The value of the pseudogap temperature observed for these compounds in recent photoemission experiments had been predicted by theory before it was observed experimentally. Additional experimental confirmation would be useful. The theoretical methods that are surveyed include mostly the two-particle self-consistent approach, variational cluster perturbation theory (or variational cluster approximation), and cellular dynamical mean-field theory.
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