Coherent-Incoherent Crossover of Charge and Neutral Mode Transport as Evidence for the Disorder-Dominated Fractional Edge Phase

Couplings between topological edge channels open electronic phases possessing nontrivial eigenmodes far beyond the noninteracting-edge picture. However, inelastic scatterings mask the eigenmodes' inherent features, often preventing us from identifying the phases, as is the case for the quintessential Landau-level filling factor v = 2/3 edge composed of the counterpropagating v = 1/3 and 1 (1/3-1) channels. Here, we study the coherent-incoherent crossover of the 1/3-1 channels by tuning the channel length in situ using a new device architecture comprising a junction of v = 1/3 and 1 systems, the particle-hole conjugate of the 2/3 edge. We successfully observed the concurrence of the fluctuating electrical conductance and the quantized thermal conductance in the crossover regime, the definitive hallmark of the eigenmodes in the disorder-dominated edge phase left experimentally unverified.