We consider bilayer quantum Hall systems at total filling factor $\nu =1\mathrm{}$ in presence of a bias voltage ${\Delta }_v$ that leads to different filling factors in each layer. We use auxiliary field functional-integral approach to study mean-field solutions and collective excitations around them. We find that at large layer separation, the collective excitations soften at a finite wave vector leading to the collapse of quasiparticle gap. Our calculations predict that as the bias voltage is increased, bilayer systems undergo a phase transition from a compressible state to a $\nu =1\mathrm{}$ phase-coherent state with charge imbalance. We present simple analytical expressions for bias-dependent renormalized charge imbalance and pseudospin stiffness that are sensitive to the softening of collective modes.

• Received 4 November 2001

DOI:https://doi.org/10.1103/PhysRevB.65.235319