Onset of interlayer phase coherence in a bilayer two-dimensional electron system: Effect of layer density imbalance

Tunneling and Coulomb drag are sensitive probes of spontaneous interlayer phase coherence in bilayer two-dimensional electron systems at total Landau level filling factor ${\nu }_T=1$. We find that the phase boundary between the interlayer phase coherent state and the weakly coupled compressible phase moves to larger layer separations as the electron density distribution in the bilayer is imbalanced. The critical layer separation increases quadratically with layer density difference.