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

Changpeng Lin1,2*, Samuel Poncé3,1*, Nicola Marzari1,2*

1 Theory and Simulation of Materials (THEOS), École Polytechnique Fédérale de Lausanne, CH-1015 Lausanne, Switzerland

2 National Centre for Computational Design and Discovery of Novel Materials (MARVEL), École Polytechnique Fédérale de Lausanne, CH-1015 Lausanne, Switzerland

3 European Theoretical Spectroscopy Facility, Institute of Condensed Matter and Nanosciences, Université catholique de Louvain, Chemin des Étoiles 8, bte L07.03.01, B-1348 Louvain-la-Neuve, Belgium

* Corresponding authors emails: changpeng.lin@epfl.ch, samuel.ponce@uclouvain.be, nicola.marzari@epfl.ch
DOI10.24435/materialscloud:gf-3n [version v1]

Publication date: Sep 12, 2022

How to cite this record

Changpeng Lin, Samuel Poncé, Nicola Marzari, General invariance and equilibrium conditions for lattice dynamics in 1D, 2D, and 3D materials, Materials Cloud Archive 2022.111 (2022), doi: 10.24435/materialscloud:gf-3n.


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 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 the invariance conditions in crystals with non-vanishing Born effective charges where the long-range dipole-dipole interactions induce a contribution to the stress tensor. Our approach has been successfully applied to the phonon dispersions of 158 two-dimensional materials, opening new avenues for the studies of phonon-mediated properties of low-dimensional materials. The dataset uploaded here contains an AiiDA database for new phonon dispersions of all 245 two-dimensional materials produced in this work and essential data for reproducing the main results of this work. These data include the modified q2r and matdyn code of Quantum ESPRESSO distribution, pseudopotentials used in this work, optimized crystal structures, interatomic force constants and phonon dispersions.

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File name Size Description
1.5 KiB A description of each file uploaded
Open this AiiDA archive on renkulab.io (https://renkulab.io/)
52.5 MiB An AiiDA database for new phonon dispersions of 245 2D materials
45.7 KiB Modified q2r and matdyn code
5.3 MiB Essential data for reproducing main results of this work


Files and data are licensed under the terms of the following license: Creative Commons Attribution Non Commercial Share Alike 4.0 International.
Metadata, except for email addresses, are licensed under the Creative Commons Attribution Share-Alike 4.0 International license.

External references

C. Lin, S. Poncé, N. Marzari, arXiv (2022)


2D materials phonons lattice dynamics acoustic sum rule AiiDA SNSF F.R.S.-FNRS.

Version history:

2022.111 (version v1) [This version] Sep 12, 2022 DOI10.24435/materialscloud:gf-3n