Abstract
The effect of electron-impurity and electron-electron interactions on the energy spectrum of electrons moving in graphene is investigated in the presence of a high magnetic field. We find that the width of the broadened Landau levels exhibits an approximate $1/B$ dependence near half filling for charged impurity scattering. The Landau-level width, the density of states, and the Fermi energy exhibit an oscillatory behavior as a function of magnetic field. Comparison with experiment shows that scattering with charged impurities cannot be the main scattering mechanism that determines the width of the Landau levels.
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