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Singular Band Behavior of the Extended Emery Model with O-O hopping for High-Tc Superconductors

The three band structure of the extended Emery model for the copper-oxide layered materials is analyzed for all the values of the effective tight-binding parameters. The model is characterized by the Cu-O site energy splitting, the Cu-O first neighbor hopping and the O-O second neighbor hopping. For the sufficiently large O-O hoppings, two bands can come together at one point on the diagonal of the square Brillouin zone, but it is rigorously shown that they cannot cross. The full range of the parameters for which the band touching occurs is also determined here. For the first time it is shown that the band touching at the bottom of the two bands is accompanied by the appearance of the extended, one-dimensional-like van Hove singularity at the lower edge of the density of states. With $1+\delta$ holes ($\delta$ small) the extended van Hove singularity can thus occur close to the Fermi level only if the latter cuts two bands. The topology of the Fermi surfaces observed by ARPES in the high-T$_c$ superconductors eliminates such possibility. The Fermi surfaces in LSCO, Bi2212 and Y123 are then fitted with the one of the three bands at the Fermi level. The agreement is excellent considering in particular the fact that the fits use only two parameters. This limit corresponds to the possibly large electron fluctuations among oxygen sites and it is at variance with the proposals that the Hubbard model alone can account for the behavior of the high-T$_c$ superconductors. The departure of the measured band structure from the three band prediction found on the small energy scales away from the Fermi level is attributed to the effects of the fluctuations not included into the energy scales which define the three band structure.

high temperature superconductivity; extended Emery model; copper-oxides; charge fluctuations

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