Lattice dynamics of the high-$T_c$ superconductor ${\mathrm{YBa}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{7-x}$

We present a lattice-dynamical calculation of the phonon dispersion curves and the one-phonon density of states of the high-$T_c$ superconductor ${\mathrm{YBa}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{7-x}$ in the framework of a shell model, which is based on a short-range overlap and long-range Coulomb potentials. The parameters of these potentials are obtained from best fits to the measured phonon dispersion curves of BaTi${\mathrm{O}}_3$ and appropriate metal oxides. The model for ${\mathrm{YBa}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{7-x}$ so obtained leads to rather satisfactory agreement with the available ir and Raman data without any major adjustments of the potential parameters. These results thus provide a solid basis for the discussion of the role of phonons for the high transition temperature and a guide for further experimental studies of the vibrational properties of this and related compounds.