Fractional Quantum Hall Effect at ν=2+6/13: The Parton Paradigm for the Second Landau Level.

The unexpected appearance of a fractional quantum Hall effect (FQHE) plateau at ν=2+6/13 [A. Kumar et al., Phys.

Anomalously low magnetoroton energies of the unconventional fractional quantum Hall States of composite fermions.

We show a generic formation of the primary magnetorotons in the collective modes of the observed "unconventional" fractional quantum Hall effect states of the composite fermions at the filling factors 4/11, 4/13, 5/13, 5/17, and 3/8 at very low wave vectors with anomalously low energies which do not have any analog to the conventional fractional quantum Hall states. Rather slow decay of the oscillations of the pair-correlation functions in these states is responsible for the low-energy magnetorotons. This is a manifestation of the distinct topology predicted previously for these fractional quantum Hall effect states.

Enigmatic 4/11 state: a prototype for unconventional fractional quantum Hall effect.

The origin of the fractional quantum Hall effect (FQHE) at 4/11 and 5/13 has remained controversial. We make a compelling case that the FQHE is possible here for fully spin polarized composite fermions, but with an unconventional underlying physics. Thanks to a rather unusual interaction between composite fermions, the FQHE here results from the suppression of pairs with a relative angular momentum of three rather than one, confirming the exotic mechanism proposed by Wójs, Yi, and Quinn [Phys.

Possible anti-Pfaffian pairing of composite fermions at ν = 3/8.

We predict that an incompressible fractional quantum Hall state is likely to form at ν = 3/8 as a result of a chiral p-wave pairing of fully spin polarized composite fermions carrying four quantized vortices, and that the pairing is of the anti-Pfaffian kind. Experimental ramifications include quasiparticles with non-Abelian braid statistics and upstream neutral edge modes.