A single particle Hamiltonian for electro-magnetic properties of graphene nanoribbons

Graphene zigzag edges are known to show the spin polarized ferromagnetic states, which are well described by the mean field treatment of Hubbard model. The parameter of onsite Coulomb interaction U is estimated to be comparable to the kinetic hopping parameter t so as to fit the electronic band structures obtained by the spin–polarized density functional theory (DFT). In this paper, we propose a simple way to transfer the electronic band structures obtained by DFT onto the mean-field Hubbard Hamiltonian by adopting site-dependent U parameter, which is taken as the decaying function from the edge. This approach is applicable to both anti-ferromagnetic and ferromagnetic states between two edges of graphene nanoribbons and will serve to perform the further large-scale simulation of electro-magnetic transport properties of graphene-based nanodevices.