Fractional Quantum Hall Effect with Unconventional Pairing in Monolayer Graphene

Motivated by the observation of even denominator fractional quantum Hall effect in the n = 3 Landau level of monolayer graphene [Kim et al., Nat. Phys. 15, 154 (2019)], we consider a Bardeen-Cooper-Schrieffer variational state for composite fermions and find that the composite-fermion Fermi sea in this Landau level is unstable to an f -wave pairing. Analogous calculation suggests the possibility of a p -wave pairing of composite fermions at half filling in the n = 2 graphene Landau level, whereas no pairing instability is found at half filling in the n = 0 and n = 1 graphene Landau levels. The relevance of these results to experiments is discussed.