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

TL;DR

This paper investigates various fractional quantum Hall states, finding that some are conventional while others exhibit unconventional behavior, and provides detailed analysis of their spin states and excitation gaps.

Contribution

It clarifies the nature of specific fractional quantum Hall states, showing which are conventional and analyzing spin polarization effects and excitation gaps.

Findings

States at 4/5, 5/7, 6/7, and 6/17 are mostly conventional.

Interaction depends on the number and direction of attached vortices.

Predicted critical Zeeman energies for spin transitions.

Abstract

Numerical studies by W\'ojs, 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.