The theoretical study of the correlation between band filling and Coulomb interaction in the charge gap of graphene-on-substrate in paramagnetic limit

Abstract

A suitable substrate breaks the sub-lattice symmetry leading to generation of a gap at the Fermi level. We propose here a tight binding model Hamiltonian for graphene on a substrate with nearest neighbour-hopping in presence of symmetry breaking interaction due to substrate effect. The sub-lattice Coulomb interaction between the electrons which produces varieties of magnetic, non-magnetic and collective interactions is considered within mean-field approximation in the paramagnetic limit. The Hamiltonian is solved by Zubarev's double time Green's function technique. The electron occupancies of the two sub-lattices are calculated from the correlation functions. Finally, the expression for the temperature dependent charge gap is derived and calculated numerically. The evolution of the charge gap in graphene is investigated by varying the Coulomb interaction, electron-occupancy and substrate induced gap. The magnitude of the electron occupancy at A-site becomes larger than that at B-site indicating symmetry breaking of the two sub-lattices of graphene.