Determination of topological edge quantum numbers of fractional quantum Hall phases

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 $\nu =$ 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 $G_Q$. With increasing temperature, $G_Q$ decreases and eventually takes the value of equilibrated regime $|N_d-N_u|{\kappa }_{0}T$. By contrast, at $\nu =$1/3 and 2/5 (without CP modes), $G_Q$ remains robustly quantized at $N_d{\kappa }_{0}T$ 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.

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• Coherent-Incoherent Crossover of Charge and Neutral Mode Transport as Evidence for the Disorder-Dominated Fractional Edge Phase
• Fingerprints of anti-Pfaffian topological order in quantum point contact transport
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• Quantized Thermal Hall Conductance and the Topological Phase Diagram of a Superconducting Bismuth Bilayer
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