CDW quantum critical point under pressure in 2$H$-TaSe$_2$

Suppressing of an ordered state that competes with superconductivity is one route to enhance superconducting transition temperatures. Whereas the effect of suppressing magnetic states is still not fully understood, materials featuring charge-density waves and superconductivity offer a clearer scenario as both states can be associated with electron-phonon coupling. Metallic transition-metal dichalcogenides are prime examples for such intertwined electron-phonon-driven phases, yet, various compounds do not show the expected interrelation or feature additional mechanisms which make an unambiguous interpretation difficult. Here, we report high-pressure X-ray diffraction and inelastic X-ray scattering measurements of the prototypical transition-metal dichalcogenide 2H-TaSe2 and determine the evolution of the charge-density-wave state and its lattice dynamics up to and beyond its suppression at the critical pressure pc = 19.9(1) GPa and at low temperatures. The high quality of our data allows the full refinement of the commensurate CDW superstructure at low pressure and we find the quantum critical point of the CDW to be in close vicinity to the reported maximum superconducting transition temperature Tsc = 8.2 K. Ab-initio calculations corroborate that 2H-TaSe2 is a reference example of order-suppressed enhanced superconductivity and can serve as a textbook case to investigate superconductivity near a charge-density-wave quantum critical point.