Model Study of the Role of Impurity on the Ferromagnetic Order in Graphene-on-Substrate

We report here a tight-binding calculation to investigate the effect of doping on the ferromagnetism in graphene supported by different substrates. The Hamiltonian consists of electron hoppings in the graphene upto third-nearest-neighbors. The substrate introduces in-equivalence in the two sub-lattices of carbon in the honey-comb lattice. The strong Coulomb correlation between electrons at the sub-lattices produces ferromagnetic order in the system. The doping introduces further in-equivalence in the sub-lattices and is expected to stabilize the ferromagnetic order. The Green’s functions are calculated by using Zubarev’s Green’s function technique. Finally the ferromagnetic magnetizations and hence the ferromagnetic gap are calculated from the electron correlations obtained from the corresponding electron Green’s functions. The ferromagnetic gap equation is computed numerically and self-consistently by using 100 × 100 grid points of the electron momentum. The effect of doping on the temperature dependent ferromagnetic gap is investigated by varying different doping concentrations, impurity potential and Coulomb energy.