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We study the electronic structure of a heterojunction made of two monolayers of MoS2 and WS2. 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 MoS2 and WS2 single layers. We find that 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 portrait the MoS2-WS2 bilayer as a prototypical example for band-gap engineering of atomically thin two-dimensional semiconducting heterostructures.

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