Dirac Fermion Confinement in Graphene

We study the problem of Dirac fermion confinement in graphene in the presence of a perpendicular magnetic field B. We show, analytically and numerically, that confinement leads to anomalies in the electronic spectrum and to a magnetic field dependent crossover from \sqrt{B}, characteristic of Dirac-Landau level behavior, to linear in B behavior, characteristic of confinement. This crossover occurs when the radius of the Landau level becomes of the order of the width of the system. As a result, we show that the Shubnikov-de Haas oscillations also change as a function of field, and lead to a singular Landau plot. We show that our theory is in excellent agreement with the experimental data.