For quasi-freestanding 2H-TaS 2 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 TaS 2 monolayer possible. As hybridization with substrate bands is absent, the fit yields a precise value for the doping of the TaS 2 layer. Additional Li doping shifts the charge density wave to a 2 × 2 periodicity. Unexpectedly, the bilayer of TaS 2 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 TaS 2 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.

In the standard model of charge density wave (CDW) transitions, the displacement along a single phonon mode lowers the total electronic energy by creating a gap at the Fermi level, making the CDW a metal–insulator transition. Here, using scanning tunneling microscopy and spectroscopy and ab initio calculations, we show that VS2 realizes a CDW which stands out of this standard model. There is a full CDW gap residing in the unoccupied states of monolayer VS2. At the Fermi level, the CDW induces a topological metal-metal (Lifshitz) transition. Non-linear coupling of transverse and longitudinal phonons is essential for the formation of the CDW and the full gap above the Fermi level. Additionally, x-ray magnetic circular dichroism reveals the absence of net magnetization in this phase, pointing to coexisting charge and spin density waves in the ground state.

We present an ab-initio approach for the calculation of phonon self-energies and their fluctuation diagnostics, which allows us to identify the electronic processes behind phonon anomalies. Application to the prototypical transition-metal dichalcogenide 1H-TaS2 reveals that coupling between the longitudinal-acoustic phonons and the electrons from an isolated low-energy metallic band is entirely responsible for phonon anomalies like mode softening and associated charge-density waves observed in this material. Our analysis allows to distinguish between different mode-softening mechanisms including matrix-element effects, Fermi-surface nesting, and Van Hove scenarios. We find that matrix-element effects originating from a peculiar type of Dirac pseudospin textures control the charge-density-wave physics in 1H-TaS2 and similar transition-metal dichalcogenides. arXiv:1911.02450v1 [cond-mat.str-el]

Using ab initio calculations we reveal the nature of the insulating phase recently found experimentally in monolayer 1T-NbSe. We find soft phonon modes in a large part of the Brillouin zone indicating the strong-coupling nature of a charge-density-wave instability. Structural relaxation of a [Formula: see text] supercell reveals a Star-of-David reconstruction with an energy gain of 60 meV per primitive unit cell. The band structure of the distorted phase exhibits a half-filled flat band which is associated with orbitals that are delocalized over several atoms in each Star of David. By including many-body corrections through a combined GW, hybrid-functional, and DMFT treatment, we find the flat band to split into narrow Hubbard bands. The lowest energy excitation across the gap turns out to be between itinerant Se-p states and the upper Hubbard band, determining the system to be a charge-transfer insulator. Combined hybrid-functional and GW calculations show that long-range interactions shift the Se-p states to lower energies. Thus, a delicate interplay of local and long-range correlations determines the gap nature and its size in this distorted phase of the monolayer 1T-NbSe.

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