Static structure factor and pair correlation function of graphene

Abstract

We report our theoretical investigations on the static structure factor and pair correlationfunction using both the density–density and spin-density response functions of a dopedsingle graphene sheet based on the random phase approximation and on graphene’smassless Dirac fermions concept. The static structure factor and pair correlation functionare obtained by regularizing the dynamical polarization function, which otherwise is clearlydivergent due to the interaction energy of the infinite Dirac sea of negative energy states.The local field effects have been considered in the simplistic Hubbard approximation. Wefind the structure factor to be dependent on the dimensionless coupling constantα, and for high values of coupling constant the magnetic structure factor indicatesparamagnetic instability which is also corroborated from other theoretical investigations.The spin symmetric pair correlation function computed in the simplistic Hubbardapproximation begins from zero at zero separation only at very high densities but theresults for parallel spin and anti-parallel spin pair correlation functions expose theshortcoming of this local field approximation. This work should stimulate moreinvestigations testing various other local field schemes and also quantum Monte Carlobased simulations.