Phonons, electronic charge response and electron-phonon interaction in the high-temperature superconductors

We investigate the complete phonon dispersion, the phonon induced electronic charge response and the corresponding self-consistent change of the crystal potential an electron feels as a direct measure of the electron-phonon interaction in the high-temperature superconductors within a microscopic model in the framework of linear response theory. Moreover, dielectric and infrared properties are calculated. The experimentally observed strong renormalization of the in-plane oxygen bond-stretching modes which appears upon doping in the high-temperature superconductors is discussed. It is shown that the characteristic softening, indicating a strong nonlocal electron-phonon interaction, is most likely a generic effect of the CuO plane and is driven by a nonlocal coupling of the displaced ions to the localized charge-fluctuations at the Cu and the O-xy ions. At hand of the oxygen bond-stretching modes it is illustrated how lattice-, charge- and spin-degrees of freedom may act synergetically for anisotropic pairing in the high-temperature superconductors. The different behaviour of these modes during the insulator-metal transition via the underdoped phase is calculated and from a comparison of these generic modes in the different phases conclusions about the electronic state are drawn. For the non-cuprate potassium doped high-temperature superconductor Ba-Bi-O also a very strong and anisotropic renormalization of the oxygen bond-stretching modes is predicted. In another investigation c-axis polarized infrared- and Raman-active modes of the HTSC's are calculated in terms of charge fluctuations and anisotropic dipole-fluctuations. Mode assignments discussed controversially in the literature are proposed. Finally, interlayer phonons propagating along the c-axis and their accompanying charge response are investigated. Depending on the strength of the interlayer coupling calculations are performed ranging from the static, adiabatic response regime to the non-adiabatic regime where dynamical screening of the bare Coulomb interaction and phonon-plasmon coupling becomes relevant within a certain region around the direction of the c-axis. A comparison with the experimental situation is given. Both, the oxygen bond-stretching modes calculated in adiabatic approximation and the non-adiabatic coupled c-axis phonon-plasmon modes are found to be important for pairing via lattice- and charge-degrees of freedom. Favouring aspects to achieve high-temperature superconductivity are also discussed. (C) 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.