Abstract: Based on the elementary concepts of quantum mechanics, the Landau levels of the two-dimensional massless Dirac electron in monolayer graphene are calculated analytically within the Landau gauge and the symmetric gauge by means of special functions theory. The results show that the Landau level spectrum in the system is distinctive from that in the conventional two-dimensional electron gas.

Key words: monolayer graphene, two-dimensional Dirac electron, Landau level