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The purpose of this thesis is to understand the quantum Hall effect in graphene. In particular, we investigate the occurrence of various crystalline phases in the first three Landau levels; we determine which crystalline structure is energetically favorable as the filling factor is varied. In this thesis, we begin with a review of the quantum Hall effect in the two-dimensional electron gas (2DEG); we review and discuss the Hartree-Fock method which has been successfully used to investigate various aspects of the quantum Hall effect in the 2DEG. We then utilize the Hartree-Fock method to investigate the quantum Hall effect in graphene and, in particular, the occurrence of crystalline phases in the first three Landau levels.
Komeilizadeh, Nazanin, "Investigations of the quantum Hall effect in graphene" (2007). Electronic Theses and Dissertations. 4666.