Fellows,
I have been investigating layered materials based on graphene and hexagonal boron nitride. Recently, when using Virtual NanoLab 2008.10, I examined effects of conformation and composition on the band structures of these layered materials. I created a lattice-matched model for both layer materials to be used in the same unit cell, assuming that they relax to form the interface. These materials differ by less than 1.8% in their lattice constants, so little strain is expected for the interface formation. One consistent tendency I found was misalignment of the Fermi energy level of the graphene or carbon band structure. The individual graphene bands rarely line up with the Fermi energy level at the K and H points of the Brillouin zone (where the Dirac intersection point should be). Since band structure is calculated relative to the Fermi energy level, the misalignment is quite visible in band structure diagrams, because it is not placing the Dirac intersection point right at zero energy (should be the Fermi energy) of the diagram. What factors can cause misalignment of the Fermi energy level, as in these examples?
I had found that boron nitride layers were causing the graphene layers to experience loss of degeneracy at the K and H points, turning graphene sheets into indirect band gap conductors. The misalignment is not making it difficult to understand the K-H line behavior, but is making it tricky to look at carrier concentration in the line. We do know that a band gap opens in graphene when it is covered with boron nitride layers, regardless of orientation. This finding seems to be very similar to the discovery that electric fields cause degeneracy lifting in graphene or bilayer graphene (Nature, June 11, 2009), as the boron nitride layers have intrinsic electric fields of their own. I have included four examples of the misaligned K-H lines, computed at DZDP basis level with LDA for exchange correlation.
