Local compressibility measurement of the vtot=1 quantum Hall state in a bilayer electron system

The filling v(tot) = 1 quantum Hall state under charge imbalance is investigated through both transport and thermodynamicmeasurements on a high- mobility low- density GaAs bilayer samplewith negligible single particle tunneling. The v(tot) = 1 state demonstrates its robustness against imbalance by evolving continuously from the single layer regime (v(upper) = 1, v(lower) = 0) to the bilayer regime with fillings v(upper) = 1/3 and v(lower) = 2/3 for the separate layers. The energy gap of the v(tot) = 1 state obtained from compressibility measurements using single electron transistors depends on position, i.e., the local disorder potential. Nevertheless, compressibility and thermal activation measurements yield comparable values for the energy gap under imbalance.