Electronic properties of the MoS<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mrow/><mml:mn>2</mml:mn></mml:msub></mml:math>-WS<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mrow/><mml:mn>2</mml:mn></mml:msub></mml:math>heterojunction

We study the electronic structure of a heterojunction made of two monolayers of MoS${}_{2}$ and WS${}_{2}$. Our first-principles density functional calculations show that, unlike in the homogeneous bilayers, the heterojunction has an optically active band gap, smaller than the ones of MoS${}_{2}$ and WS${}_{2}$ single layers. We find that the optically active states of the maximum valence and minimum conduction bands are localized on opposite monolayers, and thus the lowest energy electron-holes pairs are spatially separated. Our findings portray the MoS${}_{2}$-WS${}_{2}$ bilayer as a prototypical example for band-gap engineering of atomically thin two-dimensional semiconducting heterostructures.