Theoretical study of even denominator fractions in graphene: Fermi sea versus paired states of composite fermions

The physics of the state at even denominator fractional fillings of Landau levels depends on the Coulomb pseudopotentials, and produces, in different GaAs Landau levels, a composite fermion Fermi sea, a stripe phase, or, possibly, a paired composite fermion state. We consider here even denominator fractions in graphene, which has different pseudopotentials as well as a possible fourfold degeneracy of each Landau level. We test various composite fermion (CF) Fermi sea wave functions [fully polarized, SU(2) singlet, SU(4) singlet] as well as the paired composite fermion states in the $n=0$ and 1 Landau levels and predict that (i) paired states are not favorable, (ii) CF Fermi seas occur in both Landau levels, and (iii) an SU(4) singlet composite fermion Fermi sea is stabilized in the appropriate limit. The results from detailed microscopic calculations are generally consistent with the predictions of the mean field model of composite fermions.

Figure 1

(Color online) Energy per particle, in units of $e^2∕ϵl$, for several wave functions (four CF Fermi sea states, the Pfaffian wave function, and the hollow-core wave functions) at ${\nu }^{\left(n\right)}=\frac{1}{2}$ and $\frac{1}{4}$ in the $n=0$ Landau level (top) and in the $\mid n\mid =1$ Landau level (bottom). Statistical error from Monte Carlo sampling is also shown. Here $ϵ$ is the background dielectric constant and $l$ is the magnetic length. Extrapolation to the thermodynamic limit is given, wherever possible; the thermodynamic energies are quoted in Table .