Spatially resolved electronic structure of twisted graphene

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.