Phonons in single-layer and few-layer MoS 2 and WS 2

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 E2g¹ 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 E2g¹ 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.