Calculated effects of charge fluctuations on the phonon dispersion of YBa2Cu3O6 and YBa2Cu3O7. II. Results

Using the model presented in the preceding paper we investigate the effects of charge fluctuations (CF) on the phonon dispersion of YBa₂Cu₃O₆ (O₆) and YBa₂Cu₃O₇ (O₇). Starting from an ab-initio rigid-ion model as a reference system, CF are allowed for at the copper- and oxygen ions. The CF are treated as adiabatic electronic degrees of freedom. Within the rigid-ion model (RIM) the structural parameters are calculated by minimization of the energy. The results agree reasonably well with the experiment, indicating the suitability of the ionic model as a starting point and the importance of ionic forces for the properties of the high-temperature superconductors (HTSC) in general. Next, the phonon dispersion is calculated in the RIM as well as including CF additionally and the renormalization of the individual modes is discussed. By restricting the CF optionally to the planes, effects arising specifically from CF in the planes on the one hand and from CF in the chain as well as at the axial bridging oxygens (O4) on the other hand can be separated. We find the oxygen axial modes at the γ- and Z point (A_1g/A_2μ in O₆, A_g/B_1μ in O₇) particularly interesting. Most of these modes show considerable renormalizations. Moreover, the γ/Z-axial modes are characterized by the possibility of having CF of the same sign in the whole CuO planes what distinguishes them from the modes at other symmetry points. In particular, the Z-point axial modes are singular in having CF of alternating sign in consecutive structural units in c direction. Such a “c-direction-charge-transfer” has been shown previously to be an effective screening mechanism in La₂CuO₄. Indeed, we find a drastic renormalization of the plane-oxygen A_g mode at the Z point (A_g(O23;Z)) in O₇ (oxygen ions in neighboring planes vibrating in-phase), at least in the adiabatic approximation used here. In the insulating phase this mode exhibits, on the other hand, very large changes of the potential at the ion sites, whereas its renormalization is moderate only. The reason for this behaviour is that in the insulating phase in case of a two-dimensional electronic structure the charge transfer (screening) is restricted locally in the structural unit and long-range charge transfer is not possible as in the metal. However, a strong suppression of screening for this mode can also be expected for the metallic phase in O₇ in case non-adiabatic electron-phonon coupling would be important. The A_g (O23;Z)-mode thus seems to be by far the most interesting mode in O₇. These features are directly related to the layered structure of the HTSC compounds considered here. The O4-axial-breathing modes show significant renormalizations too, and are characterized by plane-chain charge transfer. Moreover, besides the O23- and O4-modes, the yttrium modes appear to be important too. In addition to the phonon-dispersion curves, we present values for the CF amplitudes and screened site-potential changes at the copper-and oxygen ions. Finally, we give transverse effective charges and dielectric constants for the insulating phase (O₆) as calculated within our formalism.