Two-dimensional (2D) transition metal dichalcogenide (TMD) nanosheets exhibit remarkable electronic and optical properties. The 2D features, sizable bandgaps, and recent advances in the synthesis, characterization, and device fabrication of the representative MoS2, WS2, WSe2, and MoSe2 TMDs make TMDs very attractive in nanoelectronics and optoelectronics. Similar to graphite and graphene, the atoms within each layer in 2D TMDs are joined together by covalent bonds, while van der Waals interactions keep the layers together. This makes the physical and chemical properties of 2D TMDs layer dependent. In this review, we discuss the basic lattice vibrations of monolayer, multilayer, and bulk TMDs, including high-frequency optical phonons, interlayer shear and layer breathing phonons, the Raman selection rule, layer-number evolution of phonons, multiple phonon replica, and phonons at the edge of the Brillouin zone. The extensive capabilities of Raman spectroscopy in investigating the properties of TMDs are discussed, such as interlayer coupling, spin-orbit splitting, and external perturbations. The interlayer vibrational modes are used in rapid and substrate-free characterization of the layer number of multilayer TMDs and in probing interface coupling in TMD heterostructures. The success of Raman spectroscopy in investigating TMD nanosheets paves the way for experiments on other 2D crystals and related van der Waals heterostructures.

Thickness is one of the fundamental parameters that define the electronic, optical, and thermal properties of two-dimensional (2D) crystals. Phonons in molybdenum disulfide (MoS2) were recently found to exhibit unique thickness dependence due to the interplay between short and long range interactions. Here we report Raman spectra of atomically thin sheets of WS2 and WSe2, isoelectronic compounds of MoS2, in the mono- to few-layer thickness regime. We show that, similar to the case of MoS2, the characteristic A1g and E2g(1) modes exhibit stiffening and softening with increasing number of layers, respectively, with a small shift of less than 3 cm(-1) due to large mass of the atoms. Thickness dependence is also observed in a series of multiphonon bands arising from overtone, combination, and zone edge phonons, whose intensity exhibit significant enhancement in excitonic resonance conditions. Some of these multiphonon peaks are found to be absent only in monolayers. These features provide a unique fingerprint and rapid identification for monolayer flakes.

We study by Raman scattering the shear and layer breathing modes in multilayer MoS2. These are identified by polarization measurements and symmetry analysis. Their positions change with the number of layers, with different scaling for odd and even layers. A chain model explains the results, with general applicability to any layered material, and allows one to monitor their thickness.