General invariance and equilibrium conditions for lattice dynamics in 1D, 2D, and 3D materials

• Published in: npj computational materials Vol. 8; no. 1; pp. 1 - 11
• Main Authors: Lin, Changpeng, Poncé, Samuel, Marzari, Nicola
• Format: Journal Article
• Language: English
• Published: London Nature Publishing Group UK 15.11.2022; Nature Publishing Group; Nature Portfolio
• Subjects: 639/301/1034; 639/301/357/1018; 639/766/119; Acoustics; Bending; Carrier transport; Characterization and Evaluation of Materials; Chemistry and Materials Science; Computational Intelligence; Crystals; Dipole interactions; Dispersions; Equilibrium; Equilibrium conditions; Invariance; Lattice vibration; Linear polarization; Material properties; Materials Science; Mathematical and Computational Engineering; Mathematical and Computational Physics; Mathematical Modeling and Industrial Mathematics; Optical properties; Phonons; Superconductivity; Tensors; Theoretical; Thermoelectric materials; Thermomechanical properties; Two dimensional materials; Vibration mode; Wavelength
• ISSN: 2057-3960; 2057-3960
• DOI: 10.1038/s41524-022-00920-6

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.