Azimuthal dependence of Γ-point LO-TO phonons in polar semiconductors

The longitudinal optical (LO) and transverse optical (TO) frequencies at the Brillouin-zone Γ point of polar crystalline materials are used to construct the infrared dielectric function that underpins light-lattice interactions, particularly through phonon polaritons (PhPs). In low-symmetry materials, anisotropic LO-TO splittings enable novel phenomena, such as hyperbolic PhPs with azimuthal dependence. Conventional investigations rely on solving Maxwell's equations by rotating bulk dielectric-function tensors, a process that does not reveal the nature of phonons that propagate along azimuthal angles. Here, we incorporate density functional theory (DFT)-based calculations to develop a phonon-centered understanding of PhPs. By analyzing Γ-point phonons in cubic (NaCl), uniaxial (h-BN), and biaxial (MoO₃) systems, we elucidate the interplay between crystal symmetry and charge-induced LO-TO splittings. In particular, we find that the LO-TO splittings are functions of the azimuthal angle in which the phonons propagate. Furthermore, the frequencies at which ε(ω) = 0 do not necessarily correspond to a LO phonon.