Fractional Quantum Hall States of Dirac Electrons in Graphene

We have investigated the fractional quantum Hall states of Dirac electrons in a graphene layer in different Landau levels. The relativistic nature of the energy dispersion relation of electrons in graphene significantly modifies the interelectron interactions. This results in a specific dependence of the ground state energy and the energy gaps for electrons on the Landau-level index. For the valley-polarized states, i.e., at $\nu =1/m$, $m$ being an odd integer, the energy gaps have the largest values in the $n=1$ Landau level. For the valley-unpolarized states, e.g., for the $2/3$ state, the energy gaps are suppressed for $n=1$ as compared to those at $n=0$. For both $n=1$ and $n=0$, the ground state of the $2/3$ system is fully valley-unpolarized.

Figure 1

The pseudopotentials [Eq. (4)] as a function of the relative angular momentum (a) for relativistic and for nonrelativistic 2D electrons in the first two Landau levels and (b) for relativistic electrons in various Landau levels.

Figure 2

Energy spectra of the eight-electron $\nu =1/3$-FQHE system, shown for different Landau levels: (a) $n=0$ (stars), $n=1$ (dots), and (b) $n=2$. The system is fully spin- and valley-polarized. The flux quanta is $2S=21$.

Figure 3

Energy spectra of the eight-electron $\nu =2/3$-FQHE system, shown for different Landau levels: $n=0$ (stars) and $n=1$ (dots). The system is valley-unpolarized and fully spin-polarized. The flux quanta is $2S=11$.