Determination of topological edge quantum numbers of fractional quantum Hall phases

Understand

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 $\nu = $ 2/3 and 3/5 (with CP modes) match the quantized values of non-equilibrated regime $(N_d + N_u)\kappa_{0}T$, where $\kappa_{0}T$ is a quanta of $G_{Q}$.