Role of bonding, reduced screening, and structure in the high-temperature superconductors

In this paper we have studied the role of bonding, reduced screening, and structure in high-temperature superconductors (HTSC) using ${\mathrm{La}}_2$ ${\mathrm{CuO}}_4$ as a prototype material. In addition to the ionic and metallic component of bonding recently investigated, we estimate the influence of covalence effects on the structural parameters and the phonon spectrum. Also, the effect of a reduced dispersion of the electronic band structure on the polarizability and the phonon frequencies is considered and (hypothetical) mechanisms are investigated, which would favor ferroelectricity in the HTSC. In a further topic we deal with reduced screening, introduced by nonadiabatic effects related to the quasi-two-dimensional band structure and its consequence for the electron-phonon interaction, the phonon dispersion, and the pairing mechanism. We then focus our interest on features related to the tetragonal-to-orthorhombic phase transition in ${\mathrm{La}}_2$ ${\mathrm{CuO}}_4$. Structural parameters are calculated and the influence of the transition on the phonon dispersion as well as on the phonon-induced charge fluctuations is discussed. Finally, we present, on the basis of nonlocal electron-phonon interaction of the charge-fluctuation type, a theoretical interpretation of a universal relationship between ${\mathit{T}}_{\mathit{c}}$ and the hole content in the HTSC.