Abstract
To determine the topological quantum numbers of fractional quantum Hall (FQH) states hosting counter-propagating (CP) downstream (N_d) and upstream (N_u) edge modes, it is pivotal to study quantized transport both in the presence and absence of edge mode equilibration. While reaching the non-equilibrated regime is challenging for charge transport, we target here the thermal Hall conductance G_Q, which is purely governed by edge quantum numbers N_d and N_u. Our experimental setup is realized with a hBN encapsulated graphite gated monolayer graphene device. For temperatures up to 35mK, our measured G_Q at ν = 2/3 and 3/5 (with CP modes) match the quantized values of non-equilibrated regime (N_d + N_u)κ₀T, where κ₀T is a quanta of G_Q. With increasing temperature, G_Q decreases and eventually takes the value of equilibrated regime |N_d - N_u|κ₀T. By contrast, at ν = 1/3 and 2/5 (without CP modes), G_Q remains robustly quantized at N_dκ₀T independent of the temperature. Thus, measuring the quantized values of G_Q at two regimes, we determine the edge quantum numbers, which opens a new route for finding the topological order of exotic non-Abelian FQH states.