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We explore the interplay of electron-electron correlations and surfaceeffects in the prototypical correlated insulating material, NiO. In particular,we compute the electronic structure, magnetic properties, and surface energiesof the $(001)$ and $(110)$ surfaces of paramagnetic NiO using a fully chargeself-consistent DFT+DMFT method. Our results reveal a complex interplay betweenelectronic correlations and surface effects in NiO, with the electronicstructure of the $(001)$ and $(110)$ NiO surfaces being significantly differentfrom that in bulk NiO. We obtain a sizeable reduction of the band gap at thesurface of NiO, which is most significant for the $(110)$ NiO surface. Thissuggests a higher catalytic activity of the $(110)$ NiO surface than that ofthe $(001)$ NiO one. Our results reveal a charge-transfer character of the$(001)$ and $(110)$ surfaces of NiO. Most notably, for the $(110)$ NiO surfacewe observe a remarkable electronic state characterized by an alternatingcharge-transfer and Mott-Hubbard character of the band gap in the surface andsubsurface NiO layers, respectively. This novel form of electronic orderstabilized by strong correlations is not driven by lattice reconstructions butof purely electronic origin. We notice the importance oforbital-differentiation of the Ni $e_g$ states to characterize the Mott-Hubbardinsulating state of the $(001)$ and $(110)$ NiO surfaces. The unoccupied Ni$e_g$ surface states are seen to split from the lower edge of the conductionband to form strongly localized states in the fundamental gap of bulk NiO. Ourresults for the surface energies of the $(001)$ and $(110)$ NiO surfaces showthat the $(001)$ facet of NiO has significantly lower energy. This implies thatthe relative stability of different surfaces, at least from a purely energeticpoint of view, does not depend on the presence or absence of magnetic order inNiO.

physical review. b./physical review. b

Electronic correlations at paramagnetic $(001)$ and $(110)$ NiO  surfaces: Charge-transfer and Mott-Hubbard-type gaps at the surface and  subsurface of $(110)$ NiO