Lattice dynamics in mono- and few-layer sheets of WS2 and WSe2.

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.