Coulomb bare interactions in inhomogeneous 4-layer graphene structures

Abstract

We investigate Coulomb bare interactions in 4-layer graphene systems, taking into account the inhomogeneity of dielectric environment. By solving Poisson equation in momentum space, 16 elements of Coulomb potential tensor have been formed with analytical expressions. The formulae illustrate that Coulomb bare interactions in inhomogeneous 4-layer graphene system differ noticeably from those in homogeneous one. Nevertheless, both intra- and interlayer Coulomb potentials become independent with dielectric constants of contacting media, but they are decided by those of dielectric layer surrounding the system in long wavelength approximation. Besides, numerical results demonstrate that Coulomb bare interactions decrease considerably with the increase in carrier density in graphene sheets as well as their separated distance. In all investigations, the inhomogeneity of dielectric background should not be neglected for improvement in the model.