Continuity of phonon dispersion curves in layered ionic crystals

We investigate in detail the origin of apparent discontinuities and mode disappearances in phonon band diagrams of ionic materials having hexagonal and other anisotropic structures.¹ The phenomenon is due to the coupling of some of the vibrational modes to long wavelength electromagnetic waves within the material as described in 1951 by Huang.² Modern analyses by Giannozzi, Gonze, Baroni, and others, based on density functional theory and density functional perturbation theory, have been implemented in several first principles code packages such as ABINIT and QUANTUM ESPRESSO. These use the so-called non-analytic correction to the dynamical matrix to correctly represent the modified longitudinal optical vibrational modes. In this work, we extend the analysis to include the transverse phonon-photon modes as well. The combination of the longitudinal and transverse phonon-photon mode dispersions are continuous functions of the wavevector q. These effects are demonstrated for cubic and hexagonal BN.
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¹https://doi.org/10.1088/1361-648X/ab4cc1
²K. Huang, Proc. R. Soc. A A208, 352 (1951)