The electronic structures of graphene systems and topological insulators have
closely-related features, such as quantized Berry phase and zero-energy edge
states. The reason for these analogies is that in both systems there are two
relevant orbital bands, which generate the pseudo-spin degree of freedom, and,
less obviously, there is a correspondence between the valley degree of freedom
in graphene and electron spin in topological insulators. Despite the
similarities, there are also several important distinctions, both for the bulk
topological properties and for their implications for the edge states --
primarily due to the fundamental difference between valley and spin. In view of
their peculiar band structure features, gapped graphene systems should be
properly characterized as marginal topological insulators, distinct from either
the trivial insulators or the true topological insulators.Comment: This manuscript will be published on the Proceedings of the 2010
Nobel Symposium on Graphene and Quantum Matte
