2D Vanadium Sulfides: Synthesis, Atomic Structure Engineering, and Charge Density Waves.

Two ultimately thin vanadium-rich 2D materials based on VS2 are created via molecular beam epitaxy and investigated using scanning tunneling microscopy, X-ray photoemission spectroscopy, and density functional theory (DFT) calculations. The controlled synthesis of stoichiometric single-layer VS2 or either of the two vanadium-rich materials is achieved by varying the sample coverage and sulfur pressure during annealing. Through annealing of small stoichiometric single-layer VS2 islands without S pressure, S-vacancies spontaneously order in 1D arrays, giving rise to patterned adsorption. Via the comparison of DFT calculations with scanning tunneling microscopy data, the atomic structure of the S-depleted phase, with a stoichiometry of V4S7, is determined. By depositing larger amounts of vanadium and sulfur, which are subsequently annealed in a S-rich atmosphere, self-intercalated ultimately thin V5S8-derived layers are obtained, which host 2 × 2 V-layers between sheets of VS2. We provide atomic models for the thinnest V5S8-derived structures. Finally, we use scanning tunneling spectroscopy to investigate the charge density wave observed in the 2D V5S8-derived islands.

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.

Band Bending and Valence Band Quantization at Line Defects in MoS2.

The variation of the electronic structure normal to 1D defects in quasi-freestanding MoS2, grown by molecular beam epitaxy, is investigated through high resolution scanning tunneling spectroscopy at 5 K. Strong upward bending of valence and conduction bands toward the line defects is found for the 4|4E mirror twin boundary and island edges but not for the 4|4P mirror twin boundary. Quantized energy levels in the valence band are observed wherever upward band bending takes place. Focusing on the common 4|4E mirror twin boundary, density functional theory calculations give an estimate of its charging, which agrees well with electrostatic modeling. We show that the line charge can also be assessed from the filling of the boundary-localized electronic band, whereby we provide a measurement of the theoretically predicted quantized polarization charge at MoS2 mirror twin boundaries. These calculations elucidate the origin of band bending and charging at these 1D defects in MoS2. The 4|4E mirror twin boundary not only impairs charge transport of electrons and holes due to band bending, but holes are additionally subject to a potential barrier, which is inferred from the independence of the quantized energy landscape on either side of the boundary.

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.