  Friedel oscillations of the graphene-like materials are investigated
theoretically beyond the Dirac point-approximation. Numerical calculations have
been performed within the random phase approximation (RPA). For intra-valley
transitions it was demonstrated that the contribution of the different Dirac
points in the wave-number dependent quantities, such as dielectric function
$\epsilon(q)$, has been determined by the orientation of the wave-number with
respect to the Dirac point position vector in $k$-space. Therefore identical
contribution of the different 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 ($E_F=0$). This means that
the Dirac point approximation based studies give the correct physics only at
high wave length limit. The anisotropy of the static dielectric function
reveals different contribution of the each Dirac point. Additionally, the
anisotropic $k$-space dielectric function results in anisotropic Friedel
oscillations in graphene-like materials. Calculations have also been performed
in the presence of the Rashba interaction. It was shown that increasing the
Rashba interaction strength slightly modifies the Friedel oscillations in
graphene-like materials. Therefore the anisotropic dielectric function in
$k$-space is the clear manifestation of band anisotropy in the graphene-like
systems.
