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 2×2 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, SnS2, and BaTiO3 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.1 MoreReceived 14 December 2020Revised 27 July 2021Accepted 8 September 2021DOI:https://doi.org/10.1103/PhysRevX.11.041027Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasLattice dynamicsOptical phononsPhononsPhysical Systems2-dimensional systemsThin filmsTransition metal dichalcogenidesTechniquesDensity functional theoryFirst-principles calculationsCondensed Matter, Materials & Applied Physics
Highlights
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
The separation of the interatomic force constants (IFCs) into short-range and long-range contributions has been a mainstay of lattice dynamics theory since the early 1950s [1]
The advantages of a rigorous derivation are numerous: On one hand, it paved the way for modern first-principles lattice dynamics, within the framework of density-functional perturbation theory (DFPT) [4,5,6,7,8,9,10]; on the other hand, it set the stage for further developments in linear-response methods, including higher-order generalizations of the CochranCowley formula [11,12]
Summary
The separation of the interatomic force constants (IFCs) into short-range and long-range contributions has been a mainstay of lattice dynamics theory since the early 1950s [1]. The Dyson equation for the screened Coulomb interaction reduces to a linear-algebra problem involving 2 × 2 matrices, i.e., is only marginally more complex than the scalar (1 × 1) inverse dielectric function that is characteristic of the 3D case This result allows for a natural separation of the long-range electrostatic potentials into even and odd components with respect to z → −z reflection and provides a unified description of both the intralayer couplings as well as the interaction with external sources. III) is dedicated to the numerical implementation and tests of the formalism and, of its performance in the Fourier interpolation of phonon bands
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