BCS pairing of composite fermions in wide quantum wells

There is evidence for fractional quantum Hall effect at $\nu = 1/4$ in wide GaAs quantum wells [1].  This state has been predicted, in variational studies, to be topologically distinct from the Pfaffian state [2]. We investigate the problem by constructing BCS wave functions of composite fermions for different pairing channels. We minimize the Coulomb interaction energy by varying two variational parameters of the wave function, namely the gap parameter and a momentum cutoff analogous to the Debye frequency in BCS formalism. We search for a pairing instability as a function of the well width and electron density. 

[1] D. R. Luhman, W. Pan, D. C. Tsui, L. N. Pfeiffer, K. W. Baldwin and K. W. West, Phys. Rev. Lett. 101, 266804 (2008) 

[2] W. N. Faugno, A. C. Balram, M. Barkeshli and J. K. Jain, Phys. Rev. Lett. 123, 016802 (2019)