Phonon dispersion in high temperature superconductors by LAPW calculation

Lattice vibrations in high temperature superconductors have been the topic of many investigations over the last years. Though the critical temperature can hardly be explained only by phonoic contributions, they might be involved in the pairing mechanism. Furthermore there are many fascinating physical question related to phones even in the normal state. One of them is the temperature dependence of the vibrational frequencies, life-times, Roman intensities, and the multi-phonon Roman signal. Inelastic neutron scattering has mostly resolved the dispersion relation of the phonons branches but there are stillinvonsistencies in the interpretation concerning some regions within the Brillouin zone. Thus a detailed knowledge based on first-principles calculations of the phonic dispersion and the electron-phonon interaction is highly desirable for a better understanding of these materials. So far, ab-initio methods like LAPW calculations have succeeded in calculating phonon frequencies and eigenvectors for q=0. Recently, a linear response formalism has been developed for fist-principles calculations allowing the determination of phonon dispersion by perturbation theory. With this method the extremely time- consuming supercell calculations can be avoided and even complex systems like the HTc compounds can be investigated. There are three main goals of the present project towards a theoretical understanding of lattice vibration in HTc materials starting from first-principles calculations. These are the calculation of the phonon dispersion using the linear response theory within the LAPW method, the application of the dispersion relations to the overtone Roman spectra as a further development of the accuracy of LDA phonon freing, and a detailed analysis and improvement of the accuracy of LDA phonon frequencies.