Modeling of the electronic state of the High-Temperature Superconductor   LaCuO: Phonon dynamics and charge response
  A modeling of the normal state of the p-doped high-temperature superconductors (HTSC's) is presented. This is achieved starting from a more conventional metallic phase for optimal- and overdoping and passing via the underdoped to the insulating state by consecutive orbital selective compressibility-incompressibility transitions in terms of sum rules for the charge response. The modeling is substantiated by corresponding phonon calculations. Extending investigations of the full dispersion and in particular of the strongly doping dependent anomalous phonon modes in LaCuO, which so far underpin our treatment of the density response of the electrons in the p-doped HTSC's, gives additional support for the modeling of the electronic state, compares well with recent experimental data and predicts the dispersion for the overdoped regime. Moreover, phonon densities of states have been calculated and compared for the insulating, underdoped, optimally doped and overdoped state of LaCuO. From our modeling of the normal state a consistent picture of the superconducting phase also can be extracted qualitatively pointing in the underdoped regime to a phase ordering transition. On the other hand, the modeling of the optimal and overdoped state is consistent with a quasi-particle picture with a well defined Fermi surface. Thus, in the latter case a Fermi surface instability with an evolution of pairs of well defined quasiparticles is possible and can lead to a BCS-type ordering. So, it is tempting to speculate that optimal $T_C$ in the HTSC's marks a crossover region between these two forms of ordering. 
Claus Falter, Thomas Bauer and Frank Schnetgoeke