Phonons in single-layer and few-layer MoS<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mrow/><mml:mn>2</mml:mn></mml:msub></mml:math>and WS<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mrow/><mml:mn>2</mml:mn></mml:msub></mml:math>

Abstract

We report ab initio calculations of the phonon dispersion relations of the single-layer and bulk dichalcogenides MoS${}_{2}$ and WS${}_{2}$. We explore in detail the behavior of the Raman-active modes ${A}_{1g}$ and ${E}_{2g}^{1}$ 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 ${A}_{1g}$ mode increases in frequency with an increasing number of layers while the ${E}_{2g}^{1}$ 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.