Impact of dynamical screening on the phonon dynamics of metallic La2CuO4

It is shown within a quantitative calculation that poor dynamical screening of the long-ranged Coulomb interaction due to the slow charge dynamics around the c axis leads in metallic La2CuO4 to low-energy electronic collective excitations in a small region around this axis, strongly mixing with certain interlayer phonons. The manifestation of such a phonon-plasmon scenario in layered systems based on a nonadiabatic charge response recently proposed on a qualitative level is quantitatively investigated by a realistic calculation of the frequency and wave-vector-dependent irreducible polarization part of the density response function. Our calculation corrects for a generic deficit of LDA calculations which as a rule predict a too large electronic c-axis dispersion insufficient to describe the c-axis charge response in general and in particular the phonons along this axis in the cuprates. As shown in this work, the latter are highly sensitive with respect to the interlayer coupling and thus a very accurate electronic dispersion along the c axis is crucial. Linear response theory is used 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 phononlike and plasmonlike modes. The corresponding mode induced orbital averaged changes in the self-consistent 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. On the other hand, modes inside this sector have to be determined nonadiabatically. In particular, the relevance of a strongly coupling nonadiabatic phononlike apex oxygen Z-point breathing mode O-z(Z) at about 40 meV is emphasized whose mode energy decreases with less doping.