Phonons in single-layer and few-layer MoS2and WS2

We report ab-initio calculations of the phonon dispersion relations of the single-layer and bulk dichalcogenides MoS2 and WS2. We explore in detail the behavior of the Raman active modes, A1g and E2g as a function of the number of layers. In agreement with recent Raman spectroscopy measurements [C. Lee et. al., ACS Nano Vol. 4, 2695 (2010)] we find that the A1g mode increases in frequency with increasing layer number while the E2g mode decreases. We explain this decrease by an enhancement of the dielectric screening of the long-range Coulomb interaction between the effective charges with growing number of layers. This decrease in the long-range part over-compensates the increase of the short-range interaction due to the weak inter-layer interaction.