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Abstract
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Friedel oscillations of the graphene-like materials are investigated theoretically for low and
intermediate Fermi energies. Numerical calculations have been performed within the random phase
approximation. It was demonstrated that for intra-valley transitions the contribution of the diferent
Dirac points in the wave-number dependent quantities is determined by the orientation of the wavenumber in k-space. Therefore, identical contribution of the diferent Dirac points is not automatically
guaranteed by the degeneracy of the Hamiltonian at these points. Meanwhile, it was shown that the
contribution of the inter-valley transitions is always anisotropic even when the Dirac points coincide
with the Fermi level (EF = 0). This means that the Dirac point approximation based studies could give
the correct physics only at long wave length limit. The anisotropy of the static dielectric function reveals
diferent contribution of the each Dirac point. Additionally, the anisotropic k-space dielectric function
results in anisotropic Friedel oscillations in graphene-like materials. Increasing the Rashba interaction
strength slightly modifes the Friedel oscillations in this family of materials. Anisotropy of the dielectric
function in k-space is the clear manifestation of band anisotropy in the graphene-like systems.
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