where the plus sign applies to the upper * and the
minus sign the lower band. It is clear from Eq. 6
that the spectrum is symmetric around zero energy if t
= 0. For finite values of t, the electron-hole symmetry is
broken and the and * bands become asymmetric. In
Fig. 3, we show the full band structure of graphene with
both t and t. In the same figure, we also show a zoom in
of the band structure close to one of the Dirac points at
the K or K point in the BZ. This dispersion can be
obtained by expanding the full band structure, Eq. 6,
close to the K or K vector, Eq. 3, as k=K+q, with
q K Wallace,