Bulk MoS2, a prototypical layered transition-metal dichalcogenide, is an indirect band gap semiconductor. Reducing its slab thickness to a monolayer, MoS2 undergoes a transition to the direct band semiconductor. We support this experimental observation by first-principle calculations and show that quantum confinement in layered d-electron dichalcogenides results in tuning the electronic structure. We further studied the properties of related TS2 nanolayers (T= W, Nb, Re) and show that the isotopological WS2 exhibits similar electronic properties, while NbS2 and ReS2 remain metallic independent of the slab thickness.

The stacking orders in layered hexagonal boron nitride bulk and bilayers are studied using high-level ab initio theory [local second-order M\o{}ller-Plesset perturbation theory (LMP2)]. Our results show that both electrostatic and London dispersion interactions are responsible for interlayer distance and stacking order, with $A{A}^{$'${}}$ being the most stable one. The minimum energy sliding path includes only the $A{A}^{$'${}}$ high-symmetry stacking, and the energy barrier is 3.4 meV per atom for the bilayer. State-of-the-art density functionals with and without London dispersion correction fail to correctly describe the interlayer energies with the exception of a Perdew-Burke-Ernzerhof functional intended for solid state and surface systems that agrees very well with our LMP2 results and experiment.

Quantum conductance calculations on the mechanically deformed monolayers of MoS${}_2$ and WS${}_2$ were performed using the nonequlibrium Green's functions method combined with the Landauer-Büttiker approach for ballistic transport together with the density-functional-based tight binding method. Tensile strain causes significant changes in the electronic structure of transition-metal dichalcogenide single layers and eventually the semiconductor-metal transition occurs for elongations as large as 11$\%$ for the 2D-isotropic deformations in the hexagonal structure. This transition enhances the electron transport in otherwise semiconducting materials.

Transition-metal dichalcogenides TX₂ (T = W, Mo; X = S, Se, Te) are layered materials that are available in ultrathin forms such as mono-, bi- and multilayers, which are commonly known as two-dimensional materials.