Interacting composite fermions: Nature of the 4/5, 5/7, 6/7, and 6/17 fractional quantum Hall states

Numerical studies by Wojs, Yi, and Quinn have suggested that an unconventional fractional quantum Hall effect is plausible at filling factors nu = 1/3 and 1/5, provided the interparticle interaction has an unusual form for which the energy of two fermions in the relative angular momentum three channel dominates. The interaction between composite fermions in the second Lambda level (composite fermion analog of the electronic Landau level) satisfies this property, and recent studies have supported unconventional fractional quantum Hall effect of composite fermions at nu* = 4/3 and 5/3, which manifests as fractional quantum Hall effect of electrons at nu = 4/11, 4/13, 5/13, and 5/17. I investigate in this article the nature of the fractional quantum Hall states at nu = 4/5, 5/7, 6/17, and 6/7, which correspond to composite fermions at nu* = 4/3, 5/3, and 6/5, and find that all these fractional quantum Hall states are conventional. The underlying reason is that the interaction between composite fermions depends substantially on both the number and the direction of the vortices attached to the electrons. I also study in detail the states with different spin polarizations at 6/17 and 6/7 and predict the critical Zeeman energies for the spin phase transitions between them. I calculate the excitation gaps at 4/5, 5/7, 6/7, and 6/17 and compare them against recent experiments.