Quantum transport of Dirac electrons in graphene in the presence of a spatially modulated magnetic field

We have investigated the electrical transport properties of Dirac electrons in a monolayer graphene sheet in the presence of a perpendicular magnetic field that is weakly and periodically modulated along one direction. We find that the Landau levels broaden into bands and their width oscillates as a function of the band index and the magnetic field. We determine the sigma(yy) component of the magnetoconductivity tensor for this system, which is shown to exhibit Weiss oscillations. We also analytically determine the asymptotic expressions for sigma(yy). We compare these results to recently obtained results for electrically modulated graphene, as well as those for a magnetically modulated conventional two-dimensional electron gas (2DEG) system. We find that in the magnetically modulated graphene system considered in this work, Weiss oscillations in sigma(yy) have a reduced amplitude compared to that in the 2DEG but are less damped by temperature, while they have a higher amplitude than in the electrically modulated graphene system. We also find that these oscillations are out of phase by pi with those of the electrically modulated system while they are in phase with those in the 2DEG system.