Slave boson mean-field approximation is carried out analytically for weakly doped CuO_2 conduction planes, characterized by Cu-O charge transfer energy \Delta_{pd}, Cu-O hopping t_0, O-O hopping t' ...and repulsion U_d between holes on Cu site taken as infinite. At zero doping \delta, finite negative t',|t'|<t_0/2, expands the range of stability of the covalent, conducting state on the expense of the insulating state which, however, remains stable at larger \Delta_{pd}. For sufficiently large \Delta_{pd} the renormalized charge transfer energy saturates at 4|t'| instead of decreasing to zero, as at t'=0 case. In contrast to t', finite \delta suppresses the insulating state nearly symmetrically with respect to the sign of \delta. The regime with charge transfer energy renormalized close to 4|t'| fits remarkably well the ARPES spectra of Bi2212 and LSCO, and, in the latter case, explains the observed strong doping dependence of the Cu-O hopping.
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 they cannot cross. The range of the parameters for which the band touching occurs is determined. The model relates the band touching at the bottom of the two bands to 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-Tc superconductors elliminates such possibility. The Fermi surfaces in LSCO, Bi1221 and Y123 are than 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. 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.
The strong, electronically induced anomaly in the spectrum of the
longitudinal optical (LO) phonons propagating along the main axes of the
CuO$_2$ plane is tentatively attributed to the oxygen-oxygen ...charge transfer
between the two oxygens in the plane. It is argued that this charge transfer
can be large and that it is strongly coupled to the zone boundary LO phonons.
The corresponding negative contribution to the free energy is quartic in the LO
phonon amplitude, making the LO phonon unstable through the first order phase
transition, with a concomitant domain structure.
The strong, electronically induced anomaly in the spectrum of the longitudinal optical (LO) phonons propagating along the main axes of the CuO\(_2\) plane is tentatively attributed to the ...oxygen-oxygen charge transfer between the two oxygens in the plane. It is argued that this charge transfer can be large and that it is strongly coupled to the zone boundary LO phonons. The corresponding negative contribution to the free energy is quartic in the LO phonon amplitude, making the LO phonon unstable through the first order phase transition, with a concomitant domain structure.
