Figure 1

The comparison of a 1/3 fractional Hall state for a monolayer graphene (a) and a typical 2DEG (b). The pink colour symbolizes filled (with electrons) parts of subsequent sublevels of the LLL. In a classical two-dimensional semiconductor the filling factor ν_semi is measured in relation to the empty lowest Landau level. However, in graphene, since a half of the lowest Landau level is placed in the VB (due to the Berry phase), the filling factor ν is not counted with respect to the empty LLL, but with respect to the first empty sublevel of the LLL placed in the CB (third spin-valley branch of the LLL called ). Thus, such filling in graphene , unlike in a traditional semiconductor, is accompanied by two completely filled sublevels of the LLL located in the VB^22,25. The relation between graphene and typical semiconductor filling factor can be expressed in a form ν = ν_semi − 2.