Bias-voltage induced phase-transition in bilayer quantum Hall ferromagnets

We consider bilayer quantum Hall systems at total filling factor $\nu =1$ in presence of a bias voltage ${\mathrm{\Delta }}_v$ which 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 $\nu =1$ phase-coherent state {\it with charge imbalance}. We present simple analytical expressions for bias-dependent renormalized charge imbalance and pseudospin stiffness which are sensitive to the softening of collective modes.