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We study theoretically the electron–phonon interaction in NaxCoO2. For the A1g and E1g phonon modes found in Raman experiments, we calculate the matrix elements of the electron–phonon interaction. Analyzing the feedback effect of the conduction electrons on the phonon frequency ω, we investigate the doping dependence of these two phonon modes. Due to the momentum dependence of the electron–phonon interaction, we find the strongest renormalization of the E1g mode around the Brillouin zone boundary which should be observed in the neutron scattering. At the same time, the A1g mode shows the strongest coupling to the conducting electrons around the Γ point and reveals its doping dependence in the Raman experiments. Our results shed light on the possible importance of the electron–phonon interaction in the lamellar sodium cobaltates.

Double electron exchange between Cu4s and O2pσ orbitals is analyzed as mechanism which creates traditional cooper pairing in layered cuprates. The conductivity band is obtained in the oversimplified model which considers only hopping between O2pσ orbitals, and the amplitude of the Cu4s-O2pσ hybridization is accounted as perturbation. The proposed toy model possesses most of the distinguishable features of the experimental data: angle dependence of the superconducting gap, the shape of the Fermi surface, dispersion law for conductivity band and the electron spectrum of the superconducting phase. The influence of the Cu3dx2−y2 orbital, electron doping and disorder for transition to s-type superconducting gap is briefly discussed.

The Abrikosov-Gorkov equations for superconducting gap are numerically investigated for Heitler-London type valence bond interaction applied for layered cuprates. A transition between gaplessd—type, and nodelesss—type order parameter Δ(p) is observed upon increasing of disorder. The results are in agreement with those proposed by Pokrovsky and Pokrovsky. The well-known π-shift of the Josephson phase unambiguously observed by Mathaiet al. must disappear for irradiated samples.

It is demonstrated that in the framework of quantum field theory with non-Euclidean momentum space there exist several different equally acceptable expressions for the Dirac wave operator, which depend parametrically on the fundamental massM. As a result there appears the necessity to consider fermion fields of different types, includingexotic fields which increase in the flat limitM→∞ as √M. The description of all fermionic fields is made along the lines accepted in the previous article of this series. The main feature of the developed approach —the locality of the theory in configuration space of five dimensions— is conserved.