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

TL;DR

This paper presents a rigorous theory for long-range electrostatic interactions in 2D crystals, improving the accuracy of interatomic force calculations and phonon band structure modeling by incorporating matrix dielectric functions and multipolar effects.

Contribution

It introduces a novel matrix-based representation of dielectric functions and derives an exact formula for long-range forces including multipolar contributions in 2D materials.

Findings

Enhanced accuracy in modeling long-range electrostatics in 2D materials.

Significant improvement in phonon band structure predictions.

Validation on monolayer BN, SnS₂, and BaTiO₃ membranes.

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.