Dielectric constant of graphene-on-polarized substrate: A tight-binding model study

Abstract

We report here a microscopic tight-binding theoretical study of the dynamic dielectric response of graphene-on-polarizable substrate with impurity. The Hamiltonian consists of first, second and third nearest-neighbour electron hopping interactions besides doping and substrate-induced effects on graphene. We have introduced electron–electron correlation effect at A and B sublattices of graphene which is considered within Hartree–Fock mean-field approximation. The electron occupancies at both sublattices are calculated and solved self-consistently and numerically for both up- and down-spin orientations. The polarization function appearing in the dielectric function is a two-particle Green’s function which is calculated by using Zubarev’s Green’s function technique. The temperature and optical frequency-dependent dielectric function is evaluated and compared with experimental data by varying Coulomb correlation energy, substrate-induced gap and impurity concentrations.