A two-dimensional periodic array of scatterers has been introduced to asingle layer of graphene in the presence of an external magnetic fieldperpendicular to the graphene layer. The eigenvalue equation for such a systemhas been solved numerically to display the structure of split Landau subbandsas functions of both wave number and magnetic flux. The effects of pseudo-spincoupling and Landau subbands mixing by a strong scattering potential have beendemonstrated. Additionally, we investigated the square barrier tunnelingproblem when magnetic field is present, as well as demonstrate the crucialdifference in the modulated band structure between graphene and thetwodimensional electron gas. The low-magnetic field regime is particularlyinteresting for Dirac fermions and has been discussed. Tunneling of Diracelectrons through a magnetic potential barrier has been investigated tocomplement the reported results on electrostatic potential scattering in thepresence of an ambient magnetic field.
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