Phonons in single-layer and few-layer MoS2 and 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 E12g as a function of the number of layers. In agreement with recent Raman spectroscopy measurements [C. Lee et al., ACS Nano 4, 2695 (2010)], we find that the A1g mode increases in frequency with an increasing number of layers while the E12g mode decreases. We explain this decrease by an enhancement of the dielectric screening of the long-range Coulomb interaction between the effective charges with a growing number of layers. This decrease in the long-range part overcompensates for the increase of the short-range interaction due to the weak interlayer interaction