Theoretical and Experimental Study of Phonon Spectra of Bulk and Nano-Sized MoS₂ Layer Crystals

Theoretical analysis of Raman scattering spectra (RS) for single-crystal MoS₂ sample and atomically thin MoS₂ sample consisting from one to few layers was performed in order to explain the change of MoS₂ vibrations at transition from a monoatomic layer to a bulk crystal. Experiments have shown that changes of frequencies of the most intensive bands arising from the in-plane, [Formula: see text], and out-of-plane, A _1g , vibrations, as a function of number n of layers looks differently. Thus, the frequency of ω(A _1g ) is increasing with growth of n, whereas the frequency of [Formula: see text] is decreasing. Such a change of the [Formula: see text] frequency was explained as the effect of "strong increase of the dielectric tensor when going from single layer to the bulk" sample. In the present work, we show that the reason of different dependences of frequencies can be related to both the van der Waals (vdW) interlayer interaction and the anharmonic interaction of noted fundamental vibrations with the corresponding combination tones (CT) of layer that manifests itself due to Fermi resonance in the layer. Overjumping of these phonon pairs (s, s ') owing to interlayer interaction, [Formula: see text], to other layers at growth of number n, results in the change of frequencies for each interacting pair of A _1g or [Formula: see text] symmetry. The alteration of pair frequencies depends on the ratio of constants [Formula: see text] describing the interaction of studied states s and s '.