sp${}^2$/sp${}^3$ bonding controlling mechanism at the $\alpha$-Al${}_2$O${}_3\mathrm{\mid }$graphene interface

First-principles calculations reported here illuminate the effects of the interfacial properties of $\alpha$-Al${}_2$O${}_3$ and graphene, with emphasis on the structural and electronic properties. Various contact interfaces and different $\alpha$-Al${}_2$O${}_3$ surface terminations are considered with on and slightly-off stoichiometric aluminium oxide. We show that depending on whether aluminium or oxygen is in contact with graphene, an $s{p}^3$ structural deformation and spontaneous spin-polarization may occur next to the interface contact. Interestingly, some cases cause a $p$-type doping in the graphene band structure, depending on the initial $\alpha$-Al${}_2$O${}_3$ geometry placed on graphene. The importance of leaving the surface dangling bonds of alumina saturated or not is also highlighted, and we show that it might be a control mechanism for opening a gap in graphene by the influence of the $s{p}^3$ bond between oxygen and carbon atoms at the interface. We discuss the potential of utilizing this sensitivity for practical applications.