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Tunability of the Fractional Quantum Hall States in Buckled Dirac Materials

We report on the fractional quantum Hall states of germanene and silicene where one expects a strong spin-orbit interaction. This interaction causes an enhancement of the electron-electron interaction strength in one of the Landau levels corresponding to the valence band of the system. This enhancement manifests itself as an increase of the fractional quantum Hall effect gaps compared to that in graphene and is due to the spin-orbit induced coupling of the Landau levels of the conduction and valence bands, which modifies the corresponding wave functions and the interaction within a single level. Due to the buckled structure, a perpendicular electric field lifts the valley degeneracy and strongly modifies the interaction effects within a single Landau level: in one valley the perpendicular electric field enhances the interaction strength in the conduction band Landau level, while in another valley, the electric field strongly suppresses the interaction effects.