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

Charge equilibration between quantum Hall edge states can be studied to reveal the 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 counterpropagating 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 copropagating delta nu = 1 and delta nu = 1/3 channels along a particle state at nu = 4/3. The difference can be associated with 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.