Microscopic tight-binding study of the interplay between on-site and inter-site Coulomb interactions in Graphene

Abstract

It is realized that the Coulomb interaction plays a vital role in describing the magnetic properties of graphene-on-substrate. We attempt here to study the competition between on-site and inter-site repulsive Coulomb interactions, with impurities at both the sub-lattices in graphene-on-substrate .The Hamiltonian describes the electron hopping up to third-nearest-neighbors within tight-binding approximation. Due to substrate effect, A-sub lattice is raised by energy and B-sub lattice acquired energy , besides impurity effects at both the sub lattices. The model consists of on-site repulsive Coulomb interaction at two sublattices with same on-site Coulomb energy U and nearest-neighbor inter-site Coulomb interactions between A and B sub lattice with inter site Coulomb energy . The Coulomb interaction is considered within Hartree-Fock type mean-field approximation. The Hamiltonian is solved by Zubarev's Green's function technique and an expression for temperature dependent difference in electron occupancies between two sub-lattices is calculated and solved self-consistency. Finally the charge gap and hence modified substrate induced gap is computed numerically by varying different physical parameters of the system like on-site and inter-site Coulomb interactions and substrate induced gap, impurity concentration and electron occupancy. It is observed that inter-site Coulomb interaction is smaller than on-site Coulomb interaction and plays an important role in describing the properties of graphene.