Integer quantum Hall effect of interacting electrons in graphene

By taking into account the charge and spin orderings and the exchange interactions between all the Landau levels, we investigate the integer quantum Hall effect of electrons in graphene using the mean-field theory. At the fillings $\nu = 4n+2$ with $n = 0, 1, \cdots$, the system is in the high-symmetry state with the Landau levels four-fold degenerated. We show that with doping the degenerated lowest empty levels can be sequentially filled one level by one level, the filled level is lower than the empty ones because of the symmetry breaking. This result explains the step $\Delta\nu$ = 1 in the integer quantized Hall conductivity of the experimental observations. We also present in the supplemental material a high efficient method for dealing with huge number of the Coulomb couplings between all the levels.