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Charge equilibration between quantum-Hall edge states can be studied toreveal geometric structure of edge channels not only in the integer quantumHall (IQH) regime but also in the fractional quantum Hall (FQH) regimeparticularly for hole-conjugate states. Here we report on a systematic study ofcharge equilibration in both IQH and FQH regimes by using a generalized Hallbar, in which a quantum Hall state is nested in another quantum Hall state withdifferent Landau filling factors. This provides a feasible way to evaluateequilibration in various conditions even in the presence of scattering in thebulk region. The validity of the analysis is tested in the IQH regime byconfirming consistency with previous works. In the FQH regime, we find that theequilibration length for counter-propagating $\delta \nu $ = 1 and $\delta \nu$ = -1/3 channels along a hole-conjugate state at Landau filling factor $\nu $= 2/3 is much shorter than that for co-propagating $\delta \nu $ = 1 and$\delta \nu $ = 1/3 channels along a particle state at $\nu $ = 4/3. Thedifference can be associated to the distinct geometric structures of the edgechannels. Our analysis with generalized Hall bar devices would be useful instudying edge equilibration and edge structures.

Charge equilibration in integer and fractional quantum Hall edge channels in a generalized Hall-bar device