Moire patterns in graphene bilayers: electronic structure*

Moire patterns, resulting from a small angle rotation of the top layer have been observed in graphite [1]. We consider a similar situation in a graphene bilayer. We determine the angles for which the resulting structure is periodic and study its symmetries. We develop a general formalism for the calculation of the electronic properties at low energies (close to the Dirac points of the uncoupled bilayers) and for small rotation angles, based on a continuum approximation for the uncoupled layers. We discuss the resulting electronic structure and possible consequences for transport properties. [1] Z. Rong and P Kuiper, Phys. Rev B. 48, 17427, (1993)