Electronic structure, vibrational properties, and optical spectra of two- and three-dimensional hexagonal InSe: Layer-dependent ab initio calculations

We present a detailed study of the electronic properties and lattice dynamics of bulk and mono-, bi- and tri-tetralayer \ensuremath{\beta}-InSe by means of density functional and density functional perturbation theory. We show that the few-layers systems are semiconductors with an indirect nature of the fundamental band gap and a Mexican-hat-shape of the top valence band. The phonon branches analysis reveals the dynamical stability of a mono- and bi-tetralayer systems considered together with the longitudinal-optical--transverse-optical splitting breakdown toward one tetralayer. In-plane and out-of-plane zone-center lattice vibrations dominate the Raman and IR spectra. Small shifts of the peak positions but stronger variations of the peak intensities are observed as signatures of the number of layers.