New insights in the lattice dynamics of monolayers, bilayers, and trilayers of WSe₂ and unambiguous determination of few-layer-flakes' thickness

Among the most common few-layers transition metal dichalcogenides (TMDs), WSe₂ is the most challenging material from the lattice dynamics point of view. Indeed, for a long time the main two phonon modes (A _1g and) have been wrongly assigned. In the last few years, these two modes have been properly interpreted, and their quasi-degeneracy in the monolayer has been used for its identification. In this work, we show that this approach has a limited validity and we propose an alternative, more general approach, based on multi-phonon bands. Moreover, we show and interpret all the peaks (about 40) appearing in the Raman spectra of monolayers, bilayers, and trilayers of WSe₂ by combining experimental wavelength- and polarization-dependent Raman studies with density-functional theory calculations providing the phonon dispersions, the polarization-resolved first-order Raman spectra, and the two-phonon density of states. This complete study not only offers a method to distinguish between monolayers, bilayers, and trilayers with no need of optical images and atomic force microscopy, but it also sheds light on the interpretation of single and multi-phonon bands appearing in the inelastic light scattering experiments of layered WSe₂; some of these bands were never observed before, and some were observed and uncertainly assigned. We promote the full understanding of the lattice dynamics of this material that is crucial for the realization of optoelectronics devices and of novel phononic metamaterials, such as TMDs superlattices.