Phonon dispersion in the (110) direction: a testing ground for phenomenological models of germanium

Dispersion of eigenfrequencies and eigenvectors of lattice vibrations in Ge along the (110) direction is calculated from planar force constants, which are evaluated ab initio using the local density-functional theory and the pseudopotential scheme. The particularity of these vibrations is in the harmonic coupling between the longitudinal and transverse modes which is not predicted by group theory, even in high-symmetry crystals such as Ge. The formalism of lattice dynamics is systematically built in terms of the vibrating (110) planar sublattices-the form suitable for the ab initio determination of force constants-and it is shown how the coupled modes are to be treated in the planar representation. Particular attention is paid to anharmonicity of the vibrations, which the first-principles calculations provide as well. The results are used for comparison with predictions offered by different phenomenological models (i.e. shell model and bond-charge model) and for judging the physical realism of the latter.