  We have used scanning tunneling microscopy and spectroscopy to resolve the
spatial variation of the density of states of twisted graphene layers on top of
a highly oriented pyrolytic graphite substrate. Owing to the twist a moire
pattern develops with a periodicity that is substantially larger than the
periodicity of a single layer graphene. The twisted graphene layer has
electronic properties that are distinctly different from that of a single layer
graphene due to the nonzero interlayer coupling. For small twist angles (about
1-3.5 degree) the integrated differential conductivity spectrum exhibits two
well-defined Van Hove singularities. Spatial maps of the differential
conductivity that are recorded at energies near the Fermi level exhibit a
honeycomb structure that is comprised of two inequivalent hexagonal
sub-lattices. For energies |E-E_F|>0.3 eV the hexagonal structure in the
differential conductivity maps vanishes. We have performed tight-binding
calculations of the twisted graphene system using the propagation method, in
which a third graphene layer is added to mimic the substrate. This third layer
lowers the symmetry and explains the development of the two hexagonal
sub-lattices in the moire pattern. Our experimental results are in excellent
agreement with the tight-binding calculations.
