The impact of dynamical screening on the phonon dynamics of LaCuO
  It is shown that dynamical screening of the Coulomb interaction in LaCuO leads to low-energy electronic collective excitations in a small region around the c-axis, strongly mixing with interlayer phonons. The manifestation of such a phonon-plasmon scenario based on a nonadiabatic charge response is quantitatively supported by a realistic calculation of the frequency and wavevector dependent irreducible polarization part of the density response function. The latter is used within linear response theory to calculate the coupled mode dispersion in the main symmetry directions of the Brillouin zone and the charge density redistributions excited by certain strongly coupling phonon-like and plasmon-like modes. Moreover, the corresponding mode induced orbital averaged changes of the selfconsistent potential felt by the electrons are assessed. Our analysis should be representative for the optimally to overdoped state of the cuprates where experimental evidence of a coherent three-dimensional Fermi surface and a coherent c-axis charge transport is given. It is demonstrated that modes from the outside of a small region around the c-axis can reliably be calculated within the adiabatic limit. Only a minor nonadiabatic correction is found for these modes in form of stiffening of the high-frequency oxygen-bond-stretching mode at the X-point which is attributed to dynamical reduced nesting. On the other hand, modes inside the nonadiabatic sector of the BZ have to be determined nonadiabatically owing to the poor dynamical screening of the long-ranged Coulomb interaction around the c-axis by the slow charge dynamics. In particular, the relevance of the strongly coupling phonon-like apex oxygen $Z$-point breathing mode at about 40 meV is emphasized whose mode energy decreases with less doping. 
Thomas Bauer and Claus Falter