Role of density imbalance in an interacting bilayer hole system

We study interacting GaAs hole bilayers in the limit of zero interlayer tunneling. When the layers have equal density, we observe a phase-coherent bilayer quantum Hall state (QHS) at a total filling factor nu=1, flanked by a reentrant insulating phase at nearby fillings which suggests the formation of a pinned, bilayer Wigner crystal. As we transfer charge from one layer to another, the phase-coherent QHS becomes stronger, evincing its robustness against charge imbalance, but the insulating phase disappears, suggesting that its stability requires the commensurability of the two layers.