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Quasiparticle band structures and optical properties of MoS${}_{2}$, MoSe${}_{2}$, MoTe${}_{2}$, WS${}_{2}$, and WSe${}_{2}$ monolayers are studied using the GW approximation in conjunction with the Bethe-Salpeter equation (BSE). The inclusion of two-particle excitations in the BSE approach reveals the presence of two strongly bound excitons ($A$ and $B$) below the quasiparticle absorption onset arising from vertical transitions between a spin-orbit-split valence band and the conduction band at the $K$ point of the Brillouin zone. The transition energies for monolayer MoS${}_{2}$, in particular, are shown to be in excellent agreement with available absorption and photoluminescence measurements. Excitation energies for the remaining monolayers are predicted to lie in the range of 1--2 eV. Systematic trends are identified for quasiparticle band gaps, transition energies, and exciton binding energies within as well as across the Mo and W families of dichalcogenides. Overall, the results suggest that quantum confinement of carriers within monolayers can be exploited in conjunction with chemical composition to tune the optoelectronic properties of layered transition-metal dichalcogenides at the nanoscale.

Large excitonic effects in monolayers of molybdenum and tungsten dichalcogenides