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sp$^{2}$/sp$^{3}$ bonding controlling mechanism at the $α$-Al$_{2}$O$_{3}|$graphene interface

First-principles calculations reported here illuminate the effects of the interfacial properties of $α$-Al$_{2}$O$_{3}$ and graphene, with emphasis on the structural and electronic properties. Various contact interfaces and different $α$-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 $sp^{3}$ 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 $α$-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 $sp^{3}$ bond between oxygen and carbon atoms at the interface. We discuss the potential of utilizing this sensitivity for practical applications.