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In two-dimensional hole systems confined to wide GaAs quantum wells, where the heavy- and light- hole states are close in energy, we observe a very unusual crossing of the lowest two Landau levels as the sample is tilted in magnetic field. At a magic tilt angle $��\simeq 34^{\circ}$, which surprisingly is independent of the well-width or hole density, in a large filling factor range near $��=1$ the lowest two levels are nearly degenerate as evinced by the presence of two-component quantum Hall states. Remarkably, a quantum Hall state is seen at $��=1$, consistent with a \textit{correlated} $��_{111}$ state.

We observe geometric resonance features of composite fermions on the flanks of the even denominator �� = 1/2 fractional quantum Hall state in high-mobility two-dimensional electron and hole systems confined to wide GaAs quantum wells and subjected to a weak, strain-induced, unidirectional periodic potential modulation. The features provide a measure of how close to �� = 1/2 the system stays single-component and supports a composite fermion Fermi sea before transitioning into a �� = 1/2 fractional quantum Hall state, presumably the two-component ��331 state.

In two-dimensional electron systems confined to GaAs quantum wells, as a function of either tilting the sample in magnetic field or increasing density, we observe multiple transitions of the fractional quantum Hall states (FQHSs) near filling factors $\nu=3/4$ and 5/4. The data reveal that these are spin-polarization transitions of interacting two-flux composite Fermions, which form their own FQHSs at these fillings. The fact that the reentrant integer quantum Hall effect near $\nu=4/5$ always develops following the transition to full spin polarization of the $\nu=4/5$ FQHS strongly links the reentrant phase to a pinned \emph{ferromagnetic} Wigner crystal of two-flux composite Fermions.

We observe fractional quantum Hall effect (FQHE) at the even-denominator Landau level filling factor $��=1/2$ in two-dimensional hole systems confined to GaAs quantum wells of width 30 to 50 nm and having bilayer-like charge distributions. The $��=1/2$ FQHE is stable when the charge distribution is symmetric and only in a range of intermediate densities, qualitatively similar to what is seen in two-dimensional electron systems confined to approximately twice wider GaAs quantum wells. Despite the complexity of the hole Landau level structure, originating from the coexistence and mixing of the heavy- and light-hole states, we find the hole $��=1/2$ FQHE to be consistent with a two-component, Halperin-Laughlin ($��_{331}$) state.

We report magneto-transport measurements for the fractional quantum Hall state at filling factor $��=$ 5/2 as a function of applied parallel magnetic field ($B_{||}$). As $B_{||}$ is increased, the 5/2 state becomes increasingly anisotropic, with the in-plane resistance along the direction of $B_{||}$ becoming more than 30 times larger than in the perpendicular direction. Remarkably, the resistance anisotropy ratio remains constant over a relatively large temperature range, yielding an energy gap which is the same for both directions. Our data are qualitatively consistent with a fractional quantum Hall \textit{nematic} phase.