Environmental Control of Charge Density Wave Order in Monolayer 2H-TaS₂

For quasi-freestanding 2H-TaS₂ in monolayer thickness grown by in situ molecular beam epitaxy on graphene on Ir(111), we find unambiguous evidence for a charge density wave close to a 3 × 3 periodicity. Using scanning tunneling spectroscopy, we determine the magnitude of the partial charge density wave gap. Angle-resolved photoemission spectroscopy, complemented by scanning tunneling spectroscopy for the unoccupied states, makes a tight-binding fit for the band structure of the TaS₂ monolayer possible. As hybridization with substrate bands is absent, the fit yields a precise value for the doping of the TaS₂ layer. Additional Li doping shifts the charge density wave to a 2 × 2 periodicity. Unexpectedly, the bilayer of TaS₂ also displays a disordered 2 × 2 charge density wave. Calculations of the phonon dispersions based on a combination of density-functional theory, density-functional perturbation theory, and many-body perturbation theory enable us to provide phase diagrams for the TaS₂ charge density wave as functions of doping, hybridization, and interlayer potentials, and offer insight into how they affect lattice dynamics and stability. Our theoretical considerations are consistent with the experimental work presented and shed light on previous experimental and theoretical investigations of related systems.