When is the fractional quantum Hall effect stable

The fractional quantum Hall (FQH) effect, signaled by the vanishing of the longitudinal resistance and the quantization of the Hall resistance, is the hallmark of interacting two-dimensional electrons in a large perpendicular magnetic field. The effect is most prominently observed at low Landau level (LL) filling factors ($\nu$) and is conspicuously absent for $\nu>4$. We examine the stability of the FQH states at high fillings in a 2D electron system in a wide GaAs quantum well which we can tune the Fermi energy ($E_F$) to lie, at a given filling factor, in different LLs of two electric subbands. The data provide direct and definitive evidence that the stability of the FQH states is linked to the LL where $E_F$ resides. We observe FQH states at high filling factors such as 13/3, 14/3, 16/3, and 17/3, but only when $E_F$ lies in the ground state ($N=0$) orbital LLs of either of the two electric subbands, regardless of the underlying, fully occupied levels.