Unusual Landau Level Pinning and Correlated $\nu=1$ Quantum Hall Effect in Hole Systems Confined to Wide GaAs Quantum Wells

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 $\theta\simeq 34^{\circ}$, which surprisingly is independent of the well-width or hole density, in a large filling factor range near $\nu=1$ 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 $\nu=1$, consistent with a \textit{correlated} $\Psi_{111}$ state.