Exact Long-Range Dielectric Screening and Interatomic Force Constants in Quasi-Two-Dimensional Crystals

• Published in: Physical review. X Vol. 11; no. 4; p. 041027
• Main Authors: Royo, Miquel, Stengel, Massimiliano
• Format: Journal Article
• Language: English
• Published: College Park American Physical Society 01-11-2021
• Subjects: Couplings; Crystal structure; Dipole interactions; Electric fields; Electrostatics; Exact solutions; Hyperbolic functions; Insulation; Interatomic forces; Material properties; Phonons; Quadrupoles; Screening; Tin disulfide; Trigonometric functions; Two dimensional models
• ISSN: 2160-3308; 2160-3308
• DOI: 10.1103/PhysRevX.11.041027

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 by2×2matrices, with nonuniform macroscopic potentials that are two-component hyperbolic functions of the out-of-plane coordinatez. 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,SnS2, andBaTiO3membranes, 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.