Coulomb bare interactions in inhomogeneous 4-layer graphene structures

•Analytical expressions for 16 elements of Coulomb bare interaction tensor obtained.•The inhomogeneity of dielectric background makes significant influences to Coulomb potentials.•In long wavelength limit, intra- and interlayer potentials depend differently on dielectric constant.•Coulomb potentials are quickly decreasing functions of momentum and carrier density. 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.