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

Integer Quantum Hall Effect of Interacting Electrons in Graphene