Phonon dispersion and anomalies in one-layer high-temperature superconductors

Phonon dynamics, charge response and the phonon density of states are calculated for the high-temperature superconductors HgBa$_{2}$CuO$_{4}$ and Bi$_{2}$Sr$_{2}$CuO$_{6}$ within a microscopic model for the electronic density response. The results are compared with previous calculations for La$_{2}$CuO$_{4}$ and Nd$_{2}$CuO$_{4}$. Our main focus is on the phononanomalies which are connected with the high-frequency oxygen bond-stretching modes (OBSM) found before in our calculations for $p$-doped La$_{2}$CuO$_{4}$ and $n$-doped Nd$_{2}$CuO$_{4}$. We investigate the question if the characteristic softening of the OBSM and the related strong coupling to the electrons is also present in HgBa$_{2}$CuO$_{4}$ and Bi$_{2}$Sr$_{2}$CuO$_{6}$. In particular the importance of the contribution of the more delocalized Cu$4s$ state besides the localized Cu3d state on the softening is investigated and the different anticrossing behaviour due to the presence of several phonon modes with the same symmetry as the OBSM is studied making the identification of the anomalies quite complicate. Furthermore, the influence of electronic polarization processes at ions out of the CuO plane in the ionic layers on the phonon dynamics is calculated. In this context the qualitative type of charge response, i.e. the presence or not of possible metallic charge fluctuations at the Hg or Bi ion, respectively, linked via the apex oxygen to the CuO plane, proves to be very sensitive for certain phonon modes. All the calculations are compared to the experimental results available so far. The latter, however, are rather incomplete for the Hg and the Bi compound.