Fractional charges and quantum phase transitions in imbalanced bilayer quantum Hall systems

We extend the Composite Boson theory to study slightly im-balanced bi-layer Quantum Hall systems. In the global $U(1)$ symmetry breaking excitonic superfluid side, as the imbalance increases, the system supports continuously changing fractional charges. In the translational symmetry breaking pseudo-spin density wave (PSDW) side, there are two quantum phase transitions from the commensurate PSDW to an in-commensurate PSDW and then to the excitonic superfluid state. We compare our theory with experimental data and also the previous microscopic calculations.

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