General invariance and equilibrium conditions for lattice dynamics in 1D, 2D, and 3D materials
(2022) npj Computational Materials — Vol. 8, n° 1, p. 236 (2022)
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- Authors
Lin, Changpeng 
Marzari, Nicola
- Abstract
- The long-wavelength behavior of vibrational modes plays a central role in carrier transport, phonon-assisted optical properties, superconductivity, and thermomechanical and thermoelectric properties of materials. Here, we present general invariance and equilibrium conditions of the lattice potential; these allow to recover the quadratic dispersions of flexural phonons in low-dimensional materials, in agreement with the phenomenological model for long-wavelength bending modes. We also prove that for any low-dimensional material the bending modes can have a purely out-of-plane polarization in the vacuum direction and a quadratic dispersion in the long-wavelength limit. In addition, we propose an effective approach to treat invariance conditions in crystals with non-vanishing Born effective charges where the long-range dipole-dipole interactions induce a contribution to the lattice potential and stress tensor. Our approach is successfully applied to the phonon dispersions of 158 two-dimensional materials, highlighting its critical relevance in the study of phonon-mediated properties of low-dimensional materials.
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Citations
Lin, C., Poncé, S., & Marzari, N. (2022). General invariance and equilibrium conditions for lattice dynamics in 1D, 2D, and 3D materials. npj Computational Materials, 8(1), 236. https://doi.org/10.1038/s41524-022-00920-6 (Original work published 2022)