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.

Superconductivity and electron self-energy in tungsten-sulfur-hydride monolayer

“…The elements of the phonon matrix of the irreducible wedge of points q were calculated in the QE package, based on the density functional perturbation theory [58] with 12 × 12 × 1 q-mesh grids. Then, the interatomic force constants (IFCs) are mapped onto a finer 120 × 120 × 1 q-mesh grids by the Fourier interpolation method associated with BH invariance and Huang conditions, as shown in [48], and implemented in QE. The BH invariance and the Huang conditions are constraints on IFCs to enforce the energy potential to be rotational invariant, and the equilibrium conditions of our 2D monolayer for vanishing stress tensors, respectively.…”

“…Furthermore, this binding must be strong enough to prevent the hydrogen from becoming a molecule, as the key ingredients for a high critical temperature are the hydrogen atom and its associated highfrequency phonons. To obtain high-quality results, we performed high-resolution calculations using the Fourier interpolation method together with Born-Huang invariance (BH) and the Huang conditions [44,45], which take into account the conservation of momentum and angular momentum in crystals [46,47] for translation and rotation, and for equilibrium stress-free conditions [48]. These effects guarantee the correct behaviors of the 2D phonons, especially at long wavelengths.…”

Phonon transport in Janus monolayer siblings: a comparison of 1T and 2H-ISbTe

“…Having 3 atoms in a primitive cell, the phonon dispersion of 1T-ISbTe consists of 3 acoustic and 6 optical phonon branches. The acoustic branch in the z-axis (ZA) is quadratic, which is typical of 2D materials, [48][49][50] whereas the LA and TA branches are linear in the vicinity of the G point.…”

Computationally Guided Synthesis of MXenes by Dry Selective Extraction

“…Phonon calculations were pre-and post-processed using YPHON [48] and Phonopy [49] codes. Phonon dispersion curves in Figure S2 (Supporting Information) were corrected according to the Born-Huang condition and Huang invariances [50] using the hiPhive package. [51] Prediction of Finite-Temperature thermodynamic Properties by quasi-Harmonic Approximation: Based on the QHA, Helmholtz free energy of a stoichiometric solid phase could be expressed as a function of volume and temperature,…”

“…Phonon calculations were pre‐ and post‐processed using YPHON [ 48 ] and Phonopy [ 49 ] codes. Phonon dispersion curves in Figure S2 (Supporting Information) were corrected according to the Born–Huang condition and Huang invariances [ 50 ] using the hiPhive package. [ 51 ]…”