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

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.

14 pages, 7 figures for main text, 52 pages with supplementary information

References in corpus (5)

• Quantum ESPRESSO: a modular and open-source software project for quantum simulations of materials
• Restoring the density-gradient expansion for exchange in solids and surfaces
• Generalized gradient approximation for solids and their surfaces
• First-principles predictions of Hall and drift mobilities in semiconductors
• Lattice-mediated bulk flexoelectricity from first principles

Cited by in corpus (10)

• Superconductivity and strain-enhanced phase stability of Janus tungsten chalcogenide hydride monolayers
• On-site and inter-site Hubbard corrections in magnetic monolayers: The case of FePS${}_3$ and CrI${}_3$
• Self-consistent electron lifetimes for electron-phonon scattering
• Stability-superconductivity map for compressed Na-intercalated graphite
• Charting the landscape of Bardeen-Cooper-Schrieffer superconductors in experimentally known compounds
• Second-order topological insulator in Bilayer borophene
• Extreme anharmonicity and thermal contraction of 1D wires
• A Framework for Identifying Non-van der Waals 2D Materials
• Engineering correlated Dirac fermions and flat bands on SiC with transition-metal adatom lattices
• Elastic Constants and Bending Rigidities from Long-Wavelength Perturbation Expansions