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<h4> 
Continuity of phonon dispersion curves in layered ionic materials
</h4> <p>
  Yan Li, W. C. Kerr, and N. A. W. Holzwarth </br />
 <a href="https://iopscience.iop.org/article/10.1088/1361-648X/ab4cc1/">
 <i> Journal of Physics: Condensed Matter</i> (2019)  </a> &nbsp;
  <a href="./papers/polariton/Li_2020_J._Phys.__Condens._Matter_32_055402.pdf"> (local copy) </a> <p>
<hr></p>


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 q = 0 as a 
basis. In addition, we find that apparent "discontinuities" and mode 
"disappearances" in the phonon dispersion curves of ionic materials for 
q --> 0 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. <p> 


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