Employing the random phase approximation we investigate the binding energy and Van der Waals (vdW) interlayer spacing between the two layers of bilayer transition metal dichalcogenides ${\mathrm{MoS}}_2$, ${\mathrm{MoSe}}_2$, ${\mathrm{WS}}_2$, and ${\mathrm{WSe}}_2$ for five different stacking patterns, and examine the stacking-induced modifications on the electronic and optical/excitonic properties within the GW approximation with a priori inclusion of spin-orbit coupling and by solving the two-particle Bethe-Salpeter equation. Our results show that for all cases, the most stable stacking order is the high symmetry $A{A}^{\prime }$ type, distinctive of the bulklike $2H$ symmetry, followed by the $AB$ stacking fault, typical of the $3R$ polytypism, which is by only 5 meV/formula unit less stable. The conduction band minimum is always located in the midpoint between K and $\Gamma$, regardless of the stacking and chemical composition. All $M{X}_2$ undergo an direct-to-indirect optical gap transition going from the monolayer to the bilayer regime. The stacking and the characteristic vdW interlayer distance mainly influence the valence band splitting at K and its relative energy with respect to $\Gamma$, as well as, the electron-hole binding energy and the values of the optical excitations.

• Received 26 November 2013
• Revised 26 January 2014

DOI:https://doi.org/10.1103/PhysRevB.89.075409