  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.
