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 (30)

• Quantum ESPRESSO: a modular and open-source software project for quantum simulations of materials
• Phonons and related properties of extended systems from density-functional perturbation theory
• Optimized norm-conserving Vanderbilt pseudopotentials
• The PseudoDojo: Training and grading a 85 element optimized norm-conserving pseudopotential table
• Electron-Electron Interactions in Graphene: Current Status and Perspectives
• Theory of Neutral and Charged Excitons in Monolayer Transition Metal Dichalcogenides
• Dielectric screening in two-dimensional insulators: Implications for excitonic and impurity states in graphane
• An exact Coulomb cutoff technique for supercell calculations
• Truncation of Periodic Image Interactions for Confined Systems
• Binding energies of exciton complexes in transition metal dichalcogenides and effect of dielectric environment
• Density functional perturbation theory for gated two-dimensional heterostructures: Theoretical developments and application to flexural phonons in graphene
• How dielectric screening in two-dimensional crystals affects the convergence of excited-state calculations: Monolayer MoS${}_2$
• Excitons in van der Waals heterostructures: The important role of dielectric screening
• The dielectric genome of van der Waals heterostructures
• Two-dimensional Fröhlich interaction in transition-metal dichalcogenide monolayers: Theoretical modeling and first-principles calculations
• Breakdown of optical phonons' splitting in two-dimensional materials
• Flexoelectricity from density-functional perturbation theory
• Vibrational properties of single-wall nanotubes and monolayers of hexagonal BN
• Electronic polarizability as the fundamental variable in the dielectric properties of two-dimensional materials
• Electron-Phonon Beyond Fröhlich: Dynamical Quadrupoles in Polar and Covalent Solids
• Plasmonics with two-dimensional semiconductors "beyond graphene": from basic research to technological applications
• Phonon-limited electron mobility in Si, GaAs and GaP with exact treatment of dynamical quadrupoles
• Piezoelectric Electron-Phonon Interaction from Ab Initio Dynamical Quadrupoles: Impact on Charge Transport in Wurtzite GaN
• Screening in 2D: GW calculations for surfaces and thin films using the repeated-slab approach
• Long-range quadrupole electron-phonon interaction from first principles
• Anisotropic plasmons, excitons and electron energy loss spectroscopy of phosphorene
• Plasmons on the edge of MoS2 nanostructures
• Ab initio dipolar electron-phonon interactions in two-dimensional materials
• Using high multipolar orders to reconstruct the sound velocity in piezoelectrics from lattice dynamics
• Experimental demonstration of the suppression of optical phonon splitting in 2D materials by Raman spectroscopy