Theoretical Tight-Binding Study of Electronic Band Dispersion in Ferromagnetically Ordered Graphene-on-Substrate

Abstract

The graphene-on-substrate in the presence of impurity exhibits ferromagnetism. In the present paper, we propose a tight-binding Hamiltonian model which consists of electron hopping upto-third-nearest-neighbors. The graphene-on-substrate develops a gap of few meV. This Hamiltonian incorporates a gap of energy [Formula: see text] at A sub-lattice and a gap of energy [Formula: see text] at B sub-lattice. The Hamiltonian describes the impurity effect at A and B sub-lattices with the impurity potential describing hole and/or electron doping. The on-site Coulomb interaction at A and B sub-lattices is described by Hubbard type repulsive Coulomb interaction which is considered within the mean-field approximation having ferromagnetic magnetization of two different magnitudes at the sub-lattices. The total Hamiltonian is solved by Zubarev’s Green’s function technique. The temperature-dependent ferromagnetic magnetizations are solved self-consistently taking [Formula: see text] grid points of the electron momentum. The electron band dispersion splits into four for A site and four for B site and the combined band dispersion exhibits eight bands for up/down spin orientations. The evolution of the band dispersion is investigated by varying different model parameters of graphene.