Continuity of phonon dispersion curves in layered ionic materials

The coupling of lattice vibrations with macroscopic electric fields in ionic crystals is examined from first principles based on density functional theory and density functional perturbation theory. Our analyses show that the coupled optical phonon-photon modes are well represented by using the pure phonon modes evaluated at as a basis. In addition, we find that apparent 'discontinuities' and mode 'disappearances' in the phonon dispersion curves of ionic materials for in hexagonal and other anisotropic materials are caused by the directional dependence of the Born effective charge tensor which is responsible for this coupling. The full dispersion curves, including the phonon-photon transverse modes are shown to be continuous functions of wavevector. Our work in this report provides a promising tool for first principles evaluation of phonon polaritons that may be accessible to experiment. Explicit examples are explored for cubic and hexagonal BN; the calculated results are in good agreement with previous computational values and available experimental measurements.