Effects of Landau level mixing on the fractional quantum Hall effect in monolayer graphene.

We report results of exact diagonalization studies of the spin- and valley-polarized fractional quantum Hall effect in the N = 0 and N = 1 Landau levels in graphene. We use an effective model that incorporates Landau level mixing to lowest order in the parameter κ = ((e(2)/εℓ)/(ħv(F)/ℓ)) = (e(2)/εv(F)ħ), which is magnetic field independent and can only be varied through the choice of substrate. We find Landau level mixing effects are negligible in the N = 0 Landau level for κ ≲ 2. In fact, the lowest Landau level projected Coulomb Hamiltonian is a better approximation to the real Hamiltonian for graphene than it is for semiconductor based quantum wells. Consequently, the principal fractional quantum Hall states are expected in the N = 0 Landau level over this range of κ. In the N = 1 Landau level, fractional quantum Hall states are expected for a smaller range of κ and Landau level mixing strongly breaks particle-hole symmetry, producing qualitatively different results compared to the N = 0 Landau level. At half filling of the N = 1 Landau level, we predict the anti-Pfaffian state will occur for κ ∼ 0.25-0.75.