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

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 2×2 matrices, with nonuniform macroscopic potentials th...

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Autores principales:	Miquel Royo, Massimiliano Stengel
Formato:	article
Lenguaje:	EN
Publicado:	American Physical Society 2021
Materias:	Physics QC1-999
Acceso en línea:	https://doaj.org/article/fddace73dd844105b25da7e6fbe4e692
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spelling	oai:doaj.org-article:fddace73dd844105b25da7e6fbe4e6922021-11-08T15:41:30ZExact Long-Range Dielectric Screening and Interatomic Force Constants in Quasi-Two-Dimensional Crystals10.1103/PhysRevX.11.0410272160-3308https://doaj.org/article/fddace73dd844105b25da7e6fbe4e6922021-11-01T00:00:00Zhttp://doi.org/10.1103/PhysRevX.11.041027http://doi.org/10.1103/PhysRevX.11.041027https://doaj.org/toc/2160-3308We 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 2×2 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.Miquel RoyoMassimiliano StengelAmerican Physical SocietyarticlePhysicsQC1-999ENPhysical Review X, Vol 11, Iss 4, p 041027 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Physics QC1-999
spellingShingle	Physics QC1-999 Miquel Royo Massimiliano Stengel Exact Long-Range Dielectric Screening and Interatomic Force Constants in Quasi-Two-Dimensional Crystals
description	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 2×2 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.
format	article
author	Miquel Royo Massimiliano Stengel
author_facet	Miquel Royo Massimiliano Stengel
author_sort	Miquel Royo
title	Exact Long-Range Dielectric Screening and Interatomic Force Constants in Quasi-Two-Dimensional Crystals
title_short	Exact Long-Range Dielectric Screening and Interatomic Force Constants in Quasi-Two-Dimensional Crystals
title_full	Exact Long-Range Dielectric Screening and Interatomic Force Constants in Quasi-Two-Dimensional Crystals
title_fullStr	Exact Long-Range Dielectric Screening and Interatomic Force Constants in Quasi-Two-Dimensional Crystals
title_full_unstemmed	Exact Long-Range Dielectric Screening and Interatomic Force Constants in Quasi-Two-Dimensional Crystals
title_sort	exact long-range dielectric screening and interatomic force constants in quasi-two-dimensional crystals
publisher	American Physical Society
publishDate	2021
url	https://doaj.org/article/fddace73dd844105b25da7e6fbe4e692
work_keys_str_mv	AT miquelroyo exactlongrangedielectricscreeningandinteratomicforceconstantsinquasitwodimensionalcrystals AT massimilianostengel exactlongrangedielectricscreeningandinteratomicforceconstantsinquasitwodimensionalcrystals
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Exact Long-Range Dielectric Screening and Interatomic Force Constants in Quasi-Two-Dimensional Crystals

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