Phase Diagrams for the $\nu$ = 1/2 Fractional Quantum Hall Effect in Electron Systems Confined to Symmetric, Wide GaAs Quantum Wells

We report an experimental investigation of fractional quantum Hall effect (FQHE) at the even-denominator Landau level filling factor $\nu$ = 1/2 in high quality wide GaAs quantum wells. The quasi-two-dimensional electron systems we study are confined to GaAs quantum wells with widths, W, ranging from 41 to 96 nm and have variable densities in the range of $4 \times 10^{10}$ to $4 \times 10^{11} cm^{-2}$. We present several experimental phase diagrams for the stability of the $\nu$ = 1/2 FQHE in these quantum wells. We find that the densities at which the $\nu$ = 1/2 FQHE is stable are larger for narrower quantum wells. Moreover, even a slight charge distribution asymmetry destabilizes the $\nu$ = 1/2 FQHE and turns the electron system into a compressible state. We also present a plot of the subband separation ($\Delta_{SAS}$), which characterizes the interlayer tunneling, vs density for various W. Finally, we summarize the experimental data in a diagram that takes into account the relative strengths of the inter-layer and intra-layer Coulomb interactions and $\Delta_{SAS}$. We compare this experimental phase diagram of normalized inter-layer distance vs tunneling to recent theoretical calculations which have been used to conclude a two-component origin for the $\nu$ = 1/2 FQHE.