  Two-dimensional (2D) InSe and WS$_2$ exhibit promising characteristics for
optoelectronic and photoelectrochemical applications, e.g. photodetection and
photocatalytic water splitting. However, both of them have poor absorption of
visible light due to wide band gaps. 2D InSe has high electron mobility but low
hole mobility, while 2D WS$_2$ is on the opposite. Here, we design a 2D
heterostructure composed of their monolayers and study its optoelectronic
properties by first-principles calculations. Our results show that the
heterostructure has a direct band gap of 2.19 eV, which is much smaller than
those of the monolayers mainly due to a type-II band alignment: the valence
band maximum and the conduction band minimum of monolayer InSe are lower than
those of monolayer WS$_2$, respectively. The visible-light absorption is
enhanced considerably, e.g. about fivefold (threefold) increase at the
wavelength of 490 nm in comparison to monolayer InSe (WS$_2$). The type-II band
alignment also facilitates the spatial separation of photogenerated
electron-hole pairs, i.e., electrons (holes) reside preferably in the InSe
(WS$_2$) layer. The two layers complement each other in carrier mobilities of
the heterostructure: the photogenerated electrons and holes inherit the large
mobilities from the InSe and WS$_2$ monolayers, respectively.
