Within the tight-binding method the two-dimensional energy dispersion
relations of graphene can be calculated by solving the eigen-value problem for
a HAMILTONian
associated with the two carbon
atoms in the graphene unit cell [12]. In the
SLATER-KOSTER scheme one gets^{2.1}
(2.3)
where
and is the nearest
neighbor C-C tight binding overlap energy^{2.2} [29]. Solution of the
secular equation
leads to
(2.4)
where the
and
correspond to the
and the energy bands, respectively. Figure 2.6 shows the
electronic energy dispersion relations for graphene as a function of the
two-dimensional wave-vector in the hexagonal BRILLOUIN zone.
Figure 2.6:
The energy dispersion relations for graphene
are shown through the whole region of the BRILLOUIN zone.
The lower and the upper surfaces denote the valence and the
conduction energy bands, respectively. The
coordinates of high symmetry points are
,
, and
. The energy values at the
,
, and points are 0, , and , respectively.