Unconventional Charge-Density-Wave Gap in Monolayer NbS2.

Using scanning tunneling microscopy and spectroscopy, for a monolayer of transition metal dichalcogenide H-NbS2 grown by molecular beam epitaxy on graphene, we provide unambiguous evidence for a charge density wave (CDW) with a 3 × 3 superstructure, which is not present in bulk NbS2. Local spectroscopy displays a pronounced gap on the order of 20 meV at the Fermi level. Within the gap, low-energy features are present. The gap structure with its low-energy features is at variance with the expectation for a gap opening in the electronic band structure due to a CDW. Instead, comparison with ab initio calculations indicates that the observed gap structure must be attributed to combined electron-phonon quasiparticles. The phonons in question are the elusive amplitude and phase collective modes of the CDW transition. Our findings advance the understanding of CDW mechanisms in 2D materials and their spectroscopic signatures.

A full gap above the Fermi level: the charge density wave of monolayer VS2.

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.

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.