Exchange-driven re-entrant layer-occupancy transitions in biased bilayer systems

Hamilton \textit{et al.} showed experimentally that an externally biased double-quantum-well system in zero magnetic field could exhibit an exchange-driven bilayer-to-monolayer (``2-1'') transition as the total carrier density was increased. This transition is due to the combined effects of the negative compressibility of the low-density carriers and the layer imbalance produced by external gate biases. We give an approximate criterion for observing a re-entrant ``2-1-2'' transition that repopulates the emptied layer as the total carrier density is further increased. The gate voltages required for repopulation are shown to be impractically high for $p$-type GaAs bilayer devices with hole carriers. We show, however, that it may be possible to observe a ``2-1-2'' transition in low-density $n$-type electron bilayer systems with very small layer separations.