Enhancement of the Metallic Behavior of Graphene due to Coulomb Interaction in the Paramagnetic Limit: A Tight-Binding Study

Abstract

The pristine graphene is a zero band gap semiconductor with valence and conduction bands touching each other at Dirac points. The graphene-on-substrate exhibits a small gap at the Dirac points. The microscopic Hamiltonian describes the nearest-neighbor [Formula: see text]-electron hopping with tight-binding approach. Graphene-on-substrate exhibits a gap at the Dirac points where the energy at A sublattice is raised by [Formula: see text] and the energy at B sublattice is lowered by energy [Formula: see text] leading to asymmetry in the two sublattices. Further, we have introduced impurities at both the sublattices. The Coulomb interaction in graphene-on-substrate is described by Hubbard-type Coulomb interaction with energy U. The Coulomb interaction is treated in the calculation within the mean-field approximation in the paramagnetic limit. The temperature-dependent site-independent electron occupancies at both the sublattices are calculated and computed self-consistently. The difference between the electron occupancies of both the sublattices introduces a charge gap. The effect of charge gap on the electronic band dispersion in graphene-on-substrate is investigated by varying different model parameters of the system like Coulomb energy, substrate-induced gap, temperature, total band filling and impurity concentrations. It is observed that both the valence and conduction bands are shifted above the Fermi level exhibiting a charge gap between the bands. As a result, the partially filled valence band exhibits metallic behavior.