Graphene in a magnetic field and a superlattice potential

The problem of electrons in a periodic potential in the presence of a magnetic field is revisited here in the context of graphene, by considering a superlattice periodic perturbation on the Dirac-Weyl equation for massless fermions. We solve the problem of a periodic potential for massless Dirac Fermions in a magnetic field. The relevance for graphene physics arises from the possibility of a superlattice modulation, both in single-layer graphene, due to the substrate, and in few layer graphene due to rotational stacking faults, which give rise to long wavelength moire patterns [1,2]. \par\noindent [1] J. Hass. \emph{et. al} arXiv:0706.2134v1 [cond-mat.mtrl-sci]\par\noindent [2] JMB Lopes dos Santos, NMR Peres and AH Castro Neto,arXiv:0704.2128v1 [cond-mat.mtrl-sci]