Stability of the q/3 fractional quantum Hall states

Magnetotransport measurements in a wide GaAs quantum well in which we can tune the Fermi energy (E_F) to lie in different Landau levels of the two occupied electric subbands reveal a remarkable pattern for the appearance and disappearance of fractional quantum Hall states at ν=10/3, 11/3, 13/3, 14/3, 16/3, and 17/3. The data provide direct evidence that the q/3 states are stable and strong even at such high fillings as long as E_F lies in a ground-state (N=0) Landau level of either of the two electric subbands, regardless of whether that level belongs to the symmetric or the antisymmetric subband. Evidently, the node in the out-of-plane direction of the antisymmetric subband does not destabilize the q/3 fractional states. On the other hand, when E_F lies in an excited (N>0) Landau level of either subband, the wave function node(s) in the in-plane direction weaken or completely destabilize the q/3 fractional quantum Hall states. Our data also reveal that the strength of the q/3 fractional states near the crossing of two Landau levels belonging to the two subbands depends on the relative spin polarization of the levels; specifically, the states remain stable very near the crossing if the two levels have parallel spins.