Activation energy gap of the layer-imbalanced bilayer image quantum Hall states

We investigate the bilayer fractional quantum Hall state (FQHS) in layer-imbalanced configurations at the total Landau level filling factor View the MathML source, which is interpreted as the bilayer ν=1 integer quantum Hall state (IQHS) of composite fermions (CFs). We carried out detailed magnetotransport experiments, especially focused on measurements of the activation energy gap Δ in the bilayer View the MathML source FQHS under tilted magnetic fields. We observed Δ as a function of in-plane magnetic field for various layer density imbalance parameters σ, which is compared with the reported data of the bilayer ν=1 IQHS. At small σ, the FQHSs collapse by applying large in-plane fields. This behavior is interpreted as the transition from the commensurate (C)-like phase to no-FQHS. At large σ, Δ stays finite even in large in-plane field, which means the incommensurate (IC)-like phase appears also in the View the MathML source layer-imbalanced bilayer FQHS. We discuss the interactions among CFs from the phase transition point between the C-like and the IC-like phases in the layer-imbalanced View the MathML source FQHS.