Theory of dielectric loss in Graphene-on-substrate: A tight- binding model study

Abstract

Graphene-on-substrate exhibits interesting dielectric behaviour due to screening of coulomb interaction induced by many body effects. In this communication we attempt to study the dielectric loss property of graphene within tight-binding model approach. The Hamiltonian consisting of electron hopping upto third-nearest-neighbour's with impurities in two in equivalent sub-lattices. The graphene-on-substrate raises the energy +Δ at one sub lattice and reduces energy -Δ at other sub lattice. Further we introduced coulomb interaction between π - electrons at the two sub lattices separately with the same effective coulomb interaction. We calculate polarization function Π(q, ω) which is a two particle Green's function arising due to charge-charge correlation by using Zubarev's Green's function technique. Finally we calculate dielectric function of graphene i.e. ε(q, ω) =1+Π(q,ω) at arbitrary wave vector q and frequency ra. The dielectric loss in graphene calculated from the imaginary part of dielectric function which is a measure of absorption spectrum. Only a few Fragmentary theoretical attempts have been made to utilize the full frequency and wave vector dependent dielectric function. We compute numerically the frequency dependent dielectric loss function for 100x100 momentum grid points. We observe a low energy Plasmon resonance peak and a high energy flat peak arising due to absorption of optical energy at substrate induced gap. With increase of small Plasmon wave vector, both low and high energy peaks approach each other. The dielectric loss at low energies exhibits a parabolic curve, but it exhibit a clear peak on introduction of higher order electron hopping's. The Coulomb interaction suppresses induced gap in graphene and decreases the optical energy absorption spectra. The increase of substrate induced gap shifts the high energy flat peak to higher energies and enhances the dielectric loss throughout the frequency range. Finally the effect of doping on dielectric loss is investigated and compared with the experimental results.