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

Abstract

Transition metal dichalcogenides (TMDs) are an exciting family of 2D materials; a member of this family, MoS₂, became the first studied monolayer semiconductor. In this paper, a generalized phenomenological continuum approach for the optical vibrations of the monolayer TMDs valid in the long-wavelength limit is developed. The equation of motions for nonpolar and polar oscillations include the phonon dispersion up to a quadratic approximation in the phonon wave vector. On the other hand, the polar modes satisfy coupled equations for the displacement vector and the inner electric field. The two-dimensional phonon dispersion curves for in-plane and out-of-plane oscillations are thoroughly analyzed. The model parameters are fitted from density functional perturbation theory calculations. The current formalism provides an effective tool to describe the phonon dispersion curves around the Γ point of the Brillouin zone for a large group of members of the TMD monolayers. A detailed evaluation of the intravalley Pekar-Fröhlich and the A₁-homopolar mode deformation potential coupling mechanisms is performed. The effects of metal ions and chalcogen atoms on polaron mass and binding energy are studied. It is argued that both mechanisms should be considered for a correct analysis of the properties of the polaron or of any process that involves the intraband transitions assisted by the electron-phonon interaction.