CONSPECTUS: After the discovery of graphene and the development of powerful exfoliation techniques, experimental preparation of two-dimensional (2D) crystals can be expected for any layered material that is known to chemistry. Besides graphene and hexagonal boron nitride (h-BN), transition metal chalcogenides (TMC) are among the most studied ultrathin materials. In particular, single-layer MoS2, a direct band gap semiconductor with ∼1.9 eV energy gap, is popular in physics and nanoelectronics, because it nicely complements semimetallic graphene and insulating h-BN monolayer as a construction component for flexible 2D electronics and because it was already successfully applied in the laboratory as basis material for transistors and other electronic and optoelectronic devices. Two-dimensional crystals are subject to significant quantum confinement: compared with their parent layered 3D material, they show different structural, electronic, and optical properties, such as spontaneous rippling as free-standing monolayer, significant changes of the electronic band structure, giant spin-orbit splitting, and enhanced photoluminescence. Most of those properties are intrinsic for the monolayer and already absent for two-layer stacks of the same 2D crystal. For example, single-layer MoS2 is a direct band gap semiconductor with spin-orbit splitting of 150 meV in the valence band, while the bilayer of the same material is an indirect band gap semiconductor without observable spin-orbit splitting. All these properties have been observed experimentally and are in excellent agreement with calculations based on density-functional theory. This Account reports theoretical studies of a subgroup of transition metal dichalcogenides with the composition MX2, with M = Mo, or W and X = Se or S, also referred to as "MoWSeS materials ". Results on the electronic structure, quantum confinement, spin-orbit coupling, spontaneous monolayer rippling, and change of electronic properties in the presence of an external electric field are reported. While all materials of the MoWSeS family share the same qualitative properties, their individual values can differ strongly, for example, the spin-orbit splitting in WSe2 reaches the value of 428 meV, nearly three times that of MoS2. Further, we discuss the effect of strain on the electronic properties (straintronics). While MoWSeS single layers are very robust against external electric fields, bilayers show a linear reduction of the band gap, even reaching a semiconductor-metal phase transition, and an increase of the spin-orbit splitting from zero to the monolayer value at rather small fields. Strain is yet another possibility to control the band gap in a linear way, and MoWSeS monolayers become metallic at strain values of ∼10%. The density-functional based tight-binding model is a useful tool to investigate the electronic and structural properties, including electron conductance, of large MoS2 structures, which show spontaneous rippling in finite-temperature molecular dynamics simulations. Structural defects in MoS2 result in anisotropy of the electric conductivity. Finally, DFT predictions on the properties of noble metal dichalcogenides are presented. Most strikingly, 1T PdS2 is an indirect band gap semiconductor in its monolayer form but becomes metallic as a bilayer. (Figure Presented).
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