Charge equilibration between quantum-Hall edge states can be studied to reveal geometric structure of edge channels not only in the integer quantum Hall (IQH) regime but also in the fractional quantum Hall (FQH) regime particularly for hole-conjugate states. Here we report on a systematic study of charge equilibration in both IQH and FQH regimes by using a generalized Hall bar, in which a quantum Hall state is nested in another quantum Hall state with different Landau filling factors. This provides a feasible way to evaluate equilibration in various conditions even in the presence of scattering in the bulk region. The validity of the analysis is tested in the IQH regime by confirming consistency with previous works. In the FQH regime, we find that the equilibration length for counter-propagating δν = 1 and δν = -1/3 channels along a hole-conjugate state at Landau filling factor ν = 2/3 is much shorter than that for co-propagating δν = 1 and δν = 1/3 channels along a particle state at ν = 4/3. The difference can be associated to the distinct geometric structures of the edge channels. Our analysis with generalized Hall bar devices would be useful in studying edge equilibration and edge structures.

We demonstrate a quantum antidot (QAD) formed with an airbridge gate on an AlGaAs/GaAs heterostructure, where a sub-micron pillar-shaped surface gate is biased via the bridge. We study transport through the QAD in the two regimes; one with a fully depleted region and the other with a partially depleted region at the center of the QAD. While standard Coulomb blockade (CB) oscillations with discrete levels are observed in the fully depleted region, short-period CB oscillations and more complicated patterns with multiple QADs are seen in the partially depleted region. The device is promising for investigating the few-particle regime.

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