Dynamical polarizability of graphene with spatial dispersion

We perform a detailed analysis of electronic polarizability graphene with different theoretical approaches. From Kubo's linear response formalism, we give general expression frequency and wave-vector dependent within the random phase approximation. Four approaches have been applied to single-layer their differences are on band overlap wave functions. By comparing ab initio calculation, discuss validity methods used in literature. Our results show that tight-binding method is as good time-demanding approach calculating graphene. Moreover, due special Dirac-cone structure graphene, Dirac model reproduces for energy smaller than 3 eV. For doped intraband transitions dominate at low energies can be described by Lindhard formula two-dimensional electron gases. At zero temperature long-wavelength limit, relaxation time approximation, all reduce long-wave analytical contributions agree Drude Effects electrical doping also discussed. This work may provide solid reference researches applications screening effect