  Transition metal dichalcogenides (TMD) monolayers, holding potential as good
sunlight absorbers, are promising materials for next-generation optoelectronic
devices. They may enable ultrathin photovoltaic(PV) devices thanks to their
semiconducting character. In addition, heterocombinations of AlN and GaN sheets
with MoS$_2$ monolayers have been suggested to be efficient water-splitting
devices. Following these promising findings and motivated by the small lattice
mismatch, we take up the idea of coupling a semiconducting WS$_2$ TMD monolayer
with a AlN monolayer in a vdW heterostructure which is, as well, promising for
photo-catalysis or photo-voltaic devices. We study this heterostructure by
means of first principles calculations, and we show that many-body effects
change the heterostructure band alignment from type II to I, demonstrating how
their inclusion is compulsory for a correct prediction of the electronic and
optical properties of 2D materials.
