Phenomenological model for long wavelength optical modes in transition-metal dichalcogenide monolayer

TL;DR

This paper develops a continuum phenomenological model for long-wavelength optical modes in monolayer transition-metal dichalcogenides, enabling efficient phonon dispersion calculations and analysis of polaron properties.

Contribution

It introduces a generalized model for optical vibrations in TMD monolayers, fitting parameters from DFT calculations, and analyzes electron-phonon interactions affecting polarons.

Findings

Phonon dispersion curves are accurately modeled at the Γ-point.

Both deformation potential and Pekar-Fröhlich mechanisms significantly influence polaron properties.

The model provides a practical tool for studying vibrational and electronic interactions in TMD monolayers.

Abstract

Transition metal dichalcogenides (TMDs) are an exciting family of 2D materials; a member of this family, MoS$_2$, became the first measured monolayer semiconductor. In this article, a generalized phenomenological continuum model for the optical vibrations of the monolayer TMDs valid in the long-wavelength limit is developed. Non-polar oscillations involve differential equations for the phonon displacement vector that describe phonon dispersion up to a quadratic approximation. On the other hand, the polar modes satisfy coupled differential equations for the displacement vectors and the inner electric field. The two-dimensional phonon dispersion curves for in-plane and out-of-plane oscillations are thoroughly analyzed. This model provides an efficient approach to obtain the phonon dispersion curves at the $\Gamma$-point of the Brillouin zone of the whole family of TMD monolayers. The model parameters are fitted from density functional perturbation theory calculations. A detailed evaluation of the intravalley Pekar-Fr\"ohlich (P-F) and the $A_1$-homopolar mode deformation potential (Dp) coupling mechanisms is performed. The effects of metal ions and chalcogen atoms on polaron mass and binding energy are studied, considering these two contributions, the short-range Dp and P-F. It is argued that both mechanisms must be considered for a correct analysis of the polaron properties.