  We study the electronic structure of two Dirac electron gazes coupled by a
periodic Hamiltonian such as it appears in rotated graphene bilayers. Ab initio
and tight-binding approaches are combined and show that the spatially periodic
coupling between the two Dirac electron gazes can renormalize strongly their
velocity. We investigate in particular small angles of rotation and show that
the velocity tends to zero in this limit. The localization is confirmed by an
analysis of the eigenstates which are localized essentially in the AA zones of
the Moire patterns.
