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

TL;DR

This paper compares the free electrons and tight-binding models in graphene, proposing a minimal free electrons model for certain unoccupied bands that are not well-described by tight-binding.

Contribution

It introduces a minimal free electrons model to accurately describe specific unoccupied bands in graphene, complementing the tight-binding approach.

Findings

The free electrons model correctly describes the symmetry and dispersion of the unoccupied bands.

The tight-binding model fails to capture these two unoccupied bands.

The proposed model provides better insight into the localization of these bands.

Abstract

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.