The nature of interactions in layered two-dimensional transition metal dichalcogenides - Anomalous frequency trends and surface effects

MoS$_{2}$ is a prototypical layered dichalcogenide material, with interlayer interactions dominated by weak van der Waals (vdW) interactions. Recent Raman experiments reported an anomalous blue-shift of the $E_{2g}^{1} $ mode with decreasing thickness, a trend that is not understood by simply relating frequencies to the restoring force in the system. Here, we combine experimental and theoretical studies to clarify and explain this trend.[1] We show that although interlayer interactions are weak in these materials, removing layers to form a surface in thin film MoS$_{2}$ can lead to larger Mo-S force constants at the surface (``surface effect''), which in turn accounts for the observed anomalous frequency trend. We predict the same anomalous trends for other modes in layered WSe$_{2}$, which are confirmed by experiments [2]. We find that most of the important interactions responsible for this ``surface effect'' occur within $\sim$ 1.5 {\AA} of the equilibrium interlayer distance. Our results have significant implications on the nature of interactions in vdW layered transition metal dichalcogenides. \\[4pt] [1] PRB 88, 075320 (2013);\\[0pt] [2] PRB accepted (2013)