The importance of electron correlation in graphene and hydrogenated graphene

Local density approximation (LDA) and Green function effective Coulomb (GW) calculations are performed to investigate the effect of electronic correlations on the electronic properties of both graphene and graphane. The size of band gap in graphane increases from 3.7 eV in LDA to 4.9 eV in GW approximation. By calculating maximally localized Wannier wave functions, we evaluate the necessary integrals to get the Hubbard U and the exchange J interaction from first principles for both graphene and graphane. Our ab-initio estimates indicate that in the case of graphene, in addition to the hopping amplitude t ∼ 2.8 eV giving rise to the Dirac nature of low lying excitations, the Hubbard U value of ∼8.7 eV gives rise to a super-exchange strength of J AFM ∼ 3.5 eV. This value dominates over the direct (ferromagnetic) exchange value of J FM ∼ 1.6 eV. This brings substantial Mott-Heisenberg aspects into the problem of graphene. Moreover, similarly large values of the Hubbard and super-exchange strength in graphane suggests that the nature of gap in graphane has substantial Mott character. Copyright EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2015