  Different stacking sequences of graphene are investigated using a combination
of experimental and theoretical methods. The high-resolution transmission
electron microscopy (HRTEM) of the stacking sequence of several layers of
graphene, formed on the C-terminated 4H-SiC(0001) surface, was used to
determine the stacking sequence and the interlayer distances. These data prove
that the three metastable configurations exist: ABAB, AAAA, ABCA. In accordance
to these, findings those three cases were considered theoretically, using
Density Functional Theory calculations comparing graphene sheets, freestanding
and positioned on the SiC(0001) substrate. The total energies were calculated,
the most stable structure was identified and the electronic band structure was
obtained. The four graphene layer electron band structure depends crucially on
the stacking: for the ABAB and ABCA stacking, the bands, close to the K point,
are characterized by the hyperbolic dispersion relation while the AA stacking
the dispersion in this region is linear, similar to that of a single graphene
layer. It was also shown that the linear dispersion relation is preserved in
the presence of the SiC substrate, and also for different distances between
adjacent carbon layers.
