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

摘要

We report an experimental investigation of fractional quantum Hall effect(FQHE) at the even-denominator Landau level filling factor $\nu$ = 1/2 in veryhigh quality wide GaAs quantum wells, and at very high magnetic fields up to 45T. The quasi-two-dimensional electron systems we study are confined to GaAsquantum wells with widths $W$ ranging from 41 to 96 nm and have variabledensities in the range of $\simeq 4 \times 10^{11}$ to $\simeq 4 \times10^{10}$ cm$^{-2}$. We present several experimental phase diagrams for thestability 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 whereit has a bilayer-like charge distribution; it makes a transition to acompressible phase at low densities and to an insulating phase at highdensities. The densities at which the $\nu=1/2$ FQHE is stable are larger fornarrower quantum wells. Moreover, even a slight charge distribution asymmetrydestabilizes the $\nu=1/2$ FQHE and turns the electron system into acompressible state. We also present a plot of the symmetric-to-antisymmetricsubband separation ($\Delta_{SAS}$), which characterizes the inter-layertunneling, vs density for various $W$. This plot reveals that $\Delta_{SAS}$ atthe boundary between the compressible and FQHE phases increases\textit{linearly} with density for all the samples. Finally, we summarize theexperimental data in a diagram that takes into account the relative strengthsof the inter-layer and intra-layer Coulomb interactions and $\Delta_{SAS}$. Weconclude that, consistent with the conclusions of some of the previous studies,the $\nu=1/2$ FQHE observed in wide GaAs quantum wells with symmetric chargedistribution is stabilized by a delicate balance between the inter-layer andintra-layer interactions, and is very likely described by a two-component($\Psi_{311}$) state.