Incoherent transport on the ν=2/3 quantum Hall edge

We study edge state transport for the nu(bulk) = 2/3 edge in the fully incoherent transport regime. To do so, we use a hydrodynamic approximation for the calculation of voltage and temperature profiles along the edge of the sample. Within this formalism, we study two different bare mode structures with tunneling: the edge model (1) consisting of two counterpropagating modes with filling factor discontinuities (from the bulk to the edge) delta nu = -1 /3 and delta nu = +1, and the more complicated model (2) consisting of four modes with delta nu = 1/3, +1, -1/3, and +1/3. We find that the topological characteristics of transport (quantized electrical and heat conductance) within these models are intact, with finite-size corrections which are determined by the extent of equilibration. In particular, our calculation of conductance for edge model (2) in a double quantum point contact geometry reproduces conductance results of a recent experiment [R. Sabo et al., Edge reconstruction in factional quantum Hall states, Nat. Phys. 13, 491 (2017)], which are inconsistent with the edge model (1). Our results can be explained in the charge/neutral mode picture, with incoherent analogs of the renormalization fixed points of the edge models. Additionally, we find diffusive (similar to 1/L) conductivity corrections to the heat conductance in the fully incoherent regime for both models of the edge.