Coulomb potentials in 5-layer graphene structures: inhomogeneity effects

We analytically calculate the Coulomb bare interactions in a 5-layer graphene structure consisting of five graphene sheets assembled in an inhomogeneous background dielectric. By solving the Poisson equation, we obtained the analytical expressions for 25 elements of the Coulomb potential tensor in the system. Our calculations demonstrate that the intra- and the interlayer Coulomb bare interactions are significantly affected by the inhomogeneity of the dielectric environment. This factor creates noticeable differences in values between Coulomb potentials in inhomogeneous systems and those in the homogeneous ones at critical momentum despite they behave as decreasing functions of wave vector. In the long-wavelength limit, the interactions between charged particles in the structure depend only on the dielectric constant of the outermost layers. The Coulomb bare interactions are applied to calculate the dynamical dielectric function of 5-layer graphene structures, and the results show significant differences, compared to those in the homogeneous case. (author)