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 [Y. Kim $\mathit{\text{et}}\mathit{\text{al.}}$, Nature Physics $\mathbf{\text{15}}$, 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 $1$ graphene Landau levels. The relevance of these results to experiments is discussed.