Charge density wave collapse of ${\mathrm{NbSe}}_2$ in the (LaSe)${}_{1.14}$(${\mathrm{NbSe}}_2{)}_2$ misfit layer compound

Misfit layer compounds, heterostructures composed of a regular alternating stacking of rocksalt monochalcogenide bilayers and few-layer transition-metal dichalcogenides, are an emergent platform to investigate highly doped transition-metal dichalcogenides. Among them, (LaSe)${}_{1.14}{\left({\mathrm{NbSe}}_2\right)}_2$ displays Ising superconductivity, while the presence of a charge density wave (CDW) in the material is still under debate. Here, by using polarized Raman spectroscopy and first-principles calculations, we show that ${\mathrm{NbSe}}_2$ undergoes a doping-driven collapse of the CDW ordering within the misfit, and no signature of the CDW is detected down to 8 K. We provide a complete experimental and theoretical description of the lattice dynamics of this misfit compound. We show that the vibrational properties are obtained from those of the two subunits, namely, the LaSe unit and the ${\mathrm{NbSe}}_2$ bilayer, in the presence of a suitable field-effect doping, and then highlight the two-dimensional nature of the lattice dynamics of ${\mathrm{NbSe}}_2$ within the (LaSe)${}_{1.14}{\left({\mathrm{NbSe}}_2\right)}_2$ three-dimensional structure.