Electronic structure of graphene: (nearly) free electrons bands vs. tight-binding bands

In our previous paper (Phys. Rev. B {\bf 89}, 165430 (2014)) we have found that in graphene, in distinction to the four occupied bands, which can be described by the simple tight-binding model (TBM) with four atomic orbitals per atom, the two lowest lying at the $\Gamma$-point unoccupied bands (one of them of a $\sigma$ type and the other of a $\pi$ type) can not be described by such model. In the present work we suggest a minimalistic model for these two bands, based on (nearly) free electrons model (FEM), which correctly describes the symmetry of these bands, their dispersion law and their localization with respect to the graphene plane.

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