Landau levels in graphene in crossed magnetic and electric fields: Quasi-classical approach

Within the framework of semi-classical approach, the Landau levels in the gapped and gapless graphene in crossed magnetic and electric fields are investigated. We showed that the Landau levels and the distance between them depend on an applied electric field. This is merely due to the non-quadratic electron spectrum and, therefore, it is a unique feature of graphene. At a first approximation, we investigated the effects of electron–electron interaction on the Landau levels. We obtained a general expression for the thermodynamic potential. We concluded that the magnetic properties of graphene can be controlled using the electric field. It is of great practical interest.