Effect of van der Waals Interactions on the Charge Density Wave Phase of 2H-TaSe$_{2}$.

Metallic transition metal dichalcogenides like tantalum diselenide (TaSe$_{2}$) exhibit exciting behaviors at low temperatures, including the emergence of charge density wave (CDW) states. In this work, density functional theory (DFT) is used to catalogue influences of van der Waals interactions and reduced dimensionality on the CDW atomic structures as a function of thickness, with the former effect being most strongly present between the layers of bulk TaSe$_{2}$, slightly reduced in few-layer TaS$_{2}$ and effectively absent in monolayer TaSe$_{2}$. Significant differences are found between monolayer and bulk results, with findings for the few-layer cases lying in-between, pointing out the role of van der Waals interactions in determining structural rearrangement. To support the validity of the DFT models, experimental Raman data is provided for monolayer, bilayer, and bulk TaSe$_{2}$ in the spectral range 165 cm$^{-1}$ to 215 cm$^{-1}$. The phonons seen in the experimental Raman spectra are compared with the results calculated from the DFT models as a function of temperature and layer number. The matching of data and calculations substantiates the model's description of the CDW structural formation as a function of thickness, which is shown in depth for 1L through 6L systems. These results highlight the importance of understanding interlayer interactions, which are pervasive in many quantum phenomena involving two-dimensional confinement.