Motivated by recent studies that reported the successful synthesis of
monolayer Mg(OH)2 [Suslu \textit{et al.}, Sci. Rep. \textbf{6}, 20525
(2016)] and hexagonal (\textit{h}-)AlN [Tsipas \textit{et al}., Appl. Phys.
Lett. \textbf{103}, 251605 (2013)], we investigate structural, electronic, and
optical properties of vertically stacked h-AlN and Mg(OH)2, through
\textit{ab initio} density-functional theory (DFT), many-body quasi-particle
calculations within the GW approximation, and the Bethe-Salpeter equation
(BSE). It is obtained that the bilayer heterostructure prefers the
AB′ stacking having direct band gap at the Γ with Type-II band
alignment in which the valance band maximum and conduction band minimum
originate from different layer. Regarding the optical properties, the imaginary
part of the dielectric function of the individual layers and hetero-bilayer are
investigated. The hetero-bilayer possesses excitonic peaks which appear only
after the construction of the hetero-bilayer. The lowest three exciton peaks
are detailedly analyzed by means of band decomposed charge density and the
oscillator strength. Furthermore, the wave function calculation shows that the
first peak of the hetero-bilayer originates from spatially indirect exciton
where the electron and hole localized at h-AlN and Mg(OH)2,
respectively, which is important for the light harvesting applications.Comment: Accepted by Physical Review