Exact long-range dielectric screening and interatomic force constants in quasi-2D crystals

Abstract

We develop a fundamental theory of the long-range electrostatic interactions in two-dimensional crystals by performing a rigorous study of the nonanalyticities of the Coulomb kernel. We find that the dielectric functions are best represented by $2\times 2$ matrices, with nonuniform macroscopic potentials that are two-component hyperbolic functions of the out-of-plane coordinate, $z$. We demonstrate our arguments by deriving the long-range interatomic forces in the adiabatic regime, where we identify a formerly overlooked dipolar coupling involving the out-of-plane components of the dynamical charges. The resulting formula is exact up to an arbitrary multipolar order, which we illustrate in practice via the explicit inclusion of dynamical quadrupoles. By performing numerical tests on monolayer BN, SnS${}_2$ and BaTiO${}_3$ membranes, we show that our method allows for a drastic improvement in the description of the long-range electrostatic interactions, with comparable benefits to the quality of the interpolated phonon band structure.

References in corpus (6)

• Quantum ESPRESSO: a modular and open-source software project for quantum simulations of materials
• Truncation of Periodic Image Interactions for Confined Systems
• Screening in 2D: GW calculations for surfaces and thin films using the repeated-slab approach
• Plasmons on the edge of MoS2 nanostructures
• Ab initio dipolar electron-phonon interactions in two-dimensional materials
• Experimental demonstration of the suppression of optical phonon splitting in 2D materials by Raman spectroscopy