Massless Dirac Fermions in Graphene under an External Periodic Magnetic Field

By solving two-component spinor equation for massless Dirac Fermions, we show that graphene under a periodic external magnetic field exhibits a unique energy spectrum: At low energies, Dirac Fermions are localized inside the magnetic region with discrete Landau energy levels, while at higher energies, Dirac Fermions are mainly found in non-magnetic regions with continuous energy bands originating from wavefunctions analogous to particle-in-box states of electrons. These findings offer a new methodology for the control and tuning of massless Dirac Fermions in graphene.