Nonadiabatic and nonlocal electron-phonon interaction and phonon-plasmon mixing in the high-temperature superconductors.

Abstract

Within the framework of an electronic density response approach, recently worked out to describe screening, lattice dynamics, and the electron-phonon interaction in the high-temperature superconductors, it is shown, using ${\mathrm{La}}_{2}$${\mathrm{CuO}}_{4}$ as an example, that the already large (nonlocal) electron-phonon coupling as calculated in the adiabatic approximation is further strongly enhanced for certain phonons in the high-temperature superconductors (HTSC's) in the nonadiabatic regime where dynamical screening comes into play. At the same time, a low-lying plasma mode of the electronic system appears for wave vectors in the (0,0,1) direction which mixes strongly with the phonons of appropriate symmetry and leads in addition to the phonons to very large changes of the crystal potential. Such a coexistence of phononlike and plasmonlike modes in the same frequency range is argued to be a specific feature of the HTSC's related to their layered structure and weak screening of the strong ionic forces in the c direction. It leads to a significant increase of the retarded attractive interaction and provides, at least in part, an understanding of the reduction of the oxygen isotope effect in these materials, which is difficult to explain for a pure (harmonic) electron-phonon superconductor.