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20 CHAPTER 1. INTRODUCTION
local Coulomb correlations. To incorporate electronic correlations, one has to
map the complicated band structure onto effective microscopic models which
treat in a better way the electron-electron interactions.
The importance of the strong correlations in these materials is corroborated
by the vicinity of the metal-insulator transitions, of the antiferromagnetism instability,
and also by the presence of superconductivity in this phase diagram. These
phases are frequently attributed to electron interaction effects in the context of
doped Mott insulators.
Indeed, the low-energy charge and spin dynamics of the cuprates displays
many features which defy an interpretation in terms of normal Fermi-liquid theory.
In the compounds, most noteworthy are the unconventional temperature
and frequency dependencies of various scattering rates and cross sections, which
allow to think that strong correlation might be responsible for these unconventional
electronic behaviors. Various theoretical scenari have been proposed which
speculate on the complete breakdown of Fermi-liquid theory including new and
exotic quantum ground states of the spin and charge carriers.
Nevertheless, despite many unexpected features and unconventional behaviors
in the high T c compounds, a number of electronic properties remain which are
quite conventional and thereby constrain possible theories. In particular, the
angular resolved photo-emission (ARPES) reveals the presence of a normal Fermi
surface in the metallic compounds [5]. Moreover, photoemission data identifies
dispersive single-particle states which seem related to the predictions of the LDA
although they exhibit significant mass enhancement [6].
In conclusion, the compounds are expected to be highly correlated, with an
effective bandwidth roughly equal to the effective local Coulomb interaction. The
undoped materials are antiferromagnetic charge transfer insulators at half-filling,
and upon doping the antiferromagnetism is destroyed and the system becomes
superconducting. At small doping, in the proximity of the antiferromagnetic
phase, the normal state physics cannot be described in terms of Fermi liquid
theory and is characterized by the presence of a pseudo-gap.
An essential requirement of any successful theory is to capture all these fundamental
features at the same time.
1.4 Microscopic models for the cuprates
1.4.1 Three band Hubbard model
The electronic properties of oxide high-Tc superconductors have been extensively
investigated over the last decade. The mechanism of superconductivity (SC) has
been studied using various two-dimensional (2D) models of electronic interactions.
One of the models proposed to describe the physics of high Tc materials was the
so-called three-band Hubbard model introduced by Varma et al. [7] and Emery