Abstract

Motivated by recent studies that reported the successful synthesis of monolayer $\mathrm{Mg}{(\mathrm{OH})}_{2}$ [Suslu et al., Sci. Rep. 6, 20525 (2016)] and hexagonal $(h\text{\ensuremath{-}})\text{AlN}$ [Tsipas et al., Appl. Phys. Lett. 103, 251605 (2013)], we investigate structural, electronic, and optical properties of vertically stacked $h$-AlN and $\mathrm{Mg}{(\mathrm{OH})}_{2}$, through ab initio density-functional theory (DFT), many-body quasiparticle calculations within the GW approximation and the Bethe-Salpeter equation (BSE). It is obtained that the bilayer heterostructure prefers the $A{B}^{\ensuremath{'}}$ stacking having direct band gap at the $\mathrm{\ensuremath{\Gamma}}$ 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 heterobilayer are investigated. The heterobilayer possesses excitonic peaks, which appear only after the construction of the heterobilayer. The lowest three exciton peaks are analyzed in detail by means of band decomposed charge density and the oscillator strength. Furthermore, the wave function calculation shows that the first peak of the heterobilayer originates from spatially indirect exciton where the electron and hole localized at $h$-AlN and $\mathrm{Mg}{(\mathrm{OH})}_{2}$, respectively, which is important for the light harvesting applications.

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