From Graphite to Graphene: The Confinement of the Fermi Surface to the Line KH

The graphite structure is self-consistently calculated by use of the all electron Modified Augmented Plane Wave (MAPW) scheme with lattice constants considerably enlarged above the experimental value of graphite. Overall, the band structures of the series are found to be quite similar: the energy levels of the highly symmetric states K and H almost coincide, essentially fixing the Fermi level of the semimetallic solid. The dispersion along lines parallel to the atomic planes, already small in graphite at the experimental value of , continues to flatten with increasing value of . The structure with an interlayer distance enlarged by the factor 3 over the experimental value provides a good approximation of the behaviour of a monoatomic sheet. In this context, the unusual behaviour of graphene appears in a new light. 1. Introduction Because of its layered structure with relatively large separation between the layers, graphite has been modelled as a two-dimensional solid in the first theoretical investigations based on various methods [1]. In the following decade, the full three-dimensional crystal structure has been investigated by all modern band structure schemes: pseudo-potential [2–5], full-potential linearised augmented plane wave [6, 7], full-potential linear muffin-tin-orbital [8], full-potential linear combination of Gaussian-type orbitals fitting-function technique (LCGTO-FF) [9] which all, due to inherent systematic restrictions, produce different degrees of accuracy. To understand the extraordinary behaviour of graphene we use the reverse strategy and study how the electronic structure of the graphite structure changes with increasing interlayer distance. We find that the semimetallic behaviour is drastically reduced as the Fermi surface shrinks to the surrounding of the KH line accompanied with a loss of the dispersion in the relevant bands. Only highly accurate schemes can properly describe this phenomenon. By a proper choice of the intrinsic parameters and with some specific care the MAPW method [10, 11] satisfies this criterion. The present investigations raise doubts on previous investigations of graphite and graphene based on the tight binding scheme with the nearest and second nearest neighbours couplings [12–14]. The outline of the paper is as follows: in Section 2 some issues of the crystallography of graphite and graphene are described. Then we sketch some features and the proper choice of intrinsic parameters of MAPW as well as further details of the calculation. Section 3 reports the results of self-consistent calculations done with