LAUSR

The energy spectrum of massless Dirac fermions in graphene under two-dimensional periodic magnetic modulation with square-lattice symmetry is calculated. We show that the translation symmetry of the problem is similar to that of the Hofstadter or Thouless--Kohmoto--Nightingale--den Nijs problem, and in the weak-field limit the tight-binding energy eigenvalue equation is indeed given by the Harper-Hofstadter Hamiltonian. We show that due to its magnetic translational symmetry the Hall conductivity can be identified as a topological invariant and hence quantized. We thus extend the idea of topologically quantized Hall conductance to a two-dimensional electron system under periodic magnetic modulation. Finally, we indicate possible experimental systems where this may be verified.