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.

• Received 30 August 2022
• Accepted 24 February 2023

DOI:https://doi.org/10.1103/PhysRevLett.130.126201