Fractional quantum Hall effect with unconventional pairing in monolayer graphene

There is experimental evidence for fractional quantum Hall effect at half-filling in the n=3 Landau level of monolayer graphene [1]. To understand its origin, we construct BCS wave functions of composite fermions [2] for different pairing channels and minimize the Coulomb interaction energy by varying two variational parameters of the wave function. We search for pairing instability as a function of the variational parameters and find that the composite fermion Fermi sea is unstable to an f-wave pairing [3].

[1] Y. Kim, A. C. Balram, T. Taniguchi, K. Watanabe, J. K. Jain, and J. H. Smet, Even denominator fractional quantum Hall states in higher Landau levels of graphene, Nature Physics 15, 154 (2019).

[2] Anirban Sharma, Songyang Pu, Ajit C. Balram, Jainendra K. Jain, Bardeen-Cooper-Schrieffer pairing of composite fermions, Physical Review B 104, 205303 (2021).

[3] Anirban Sharma, Songyang Pu, Ajit C. Balram, Jainendra K. Jain, Fractional quantum Hall effect with unconventional pairing in monolayer graphene, submitted (2022).