Model study of the effect of Coulomb interaction on band gap of graphene-on-substrates

Graphene develops modulated gap, when it is placed on different substrates. In order to study the effect of Coulomb interaction on the gaps, we propose here a tight-binding model taking nearest-neighbor hopping integrals in the presence of Coulomb interactions on two inequivalent sublattices of honeycomb lattice of graphene. Here Coulomb interaction is treated within a Hartree–Fock mean-field approximation and difference in electron occupation numbers is computed numerically and self-consistently. It is observed that the system develops ferromagnetism at A-site atoms as well as B-site atoms. However this ferromagnetisms in two sub-lattices are antiferromagnetically ordered. The Coulomb interaction develops a gap near ’K’ point in reciprocal space. The evolution of this gap is investigated in the electron density of states, energy band dispersion and electron specific heat of graphene.