The ν=2/3 filling is the simplest paradigmatic example of a fractional
quantum Hall state, which contains counter-propagating edge modes. These modes
can be either in the coherent or equilibrated to different extents, on top of
the possible edge reconstruction. In the coherent regime, two distinct
renormalization group fixed points have been previously proposed, namely
Kane-Fischer-Polchinski and Wang-Meir-Gefen. In the equilibration regime,
different degree of thermal equilibration can exist, while charge is fully
equilibrated. Here, we show that these rich variety of models can give rise to
three possible conductance plateaus at e2/2h (recently observed in
experiments), 5e2/9h (we predict), and e2/3h (observed earlier in
experiments) in a quantum point contact geometry. We identify different
mechanisms for \emph{electrical shot noise} generation at these plateaus, which
provides an experimentally accessible venue for distinguishing among the
distinct models.Comment: 12 pages, 6 figure