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

J. Shabani, Y. Liu, M. Shayegan, L. N. Pfeiffer, K. W. West, K. W. Baldwin

Published 2013-06-22, updated 2013-11-29Version 2

We report an experimental investigation of fractional quantum Hall effect (FQHE) at the even-denominator Landau level filling factor $\nu$ = 1/2 in very high quality wide GaAs quantum wells, and at very high magnetic fields up to 45 T. 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 $\simeq 4 \times 10^{11}$ to $\simeq 4 \times 10^{10}$ cm$^{-2}$. We present several experimental phase diagrams for the stability of the $\nu=1/2$ FQHE in these quantum wells. In general, for a given $W$, the 1/2 FQHE is stable in a limited range of intermediate densities where it has a bilayer-like charge distribution; it makes a transition to a compressible phase at low densities and to an insulating phase at high densities. 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 symmetric-to-antisymmetric subband separation ($\Delta_{SAS}$), which characterizes the inter-layer tunneling, vs density for various $W$. This plot reveals that $\Delta_{SAS}$ at the boundary between the compressible and FQHE phases increases \textit{linearly} with density for all the samples. 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 conclude that, consistent with the conclusions of some of the previous studies, the $\nu=1/2$ FQHE observed in wide GaAs quantum wells with symmetric charge distribution is stabilized by a delicate balance between the inter-layer and intra-layer interactions, and is very likely described by a two-component ($\Psi_{311}$) state.