Determination of topological edge quantum numbers of fractional quantum Hall phases

TL;DR

This study measures thermal Hall conductance in fractional quantum Hall states to identify topological edge quantum numbers, distinguishing between equilibrated and non-equilibrated regimes, and providing insights into the topological order of these states.

Contribution

It demonstrates a method to determine topological edge quantum numbers of FQH states by measuring thermal Hall conductance in different regimes, revealing new ways to identify non-Abelian topological order.

Findings

Thermal Hall conductance quantization matches non-equilibrated regime values at low temperatures.

G_Q decreases with temperature and reaches equilibrated regime values.

G_Q remains quantized at certain values for states without counter-propagating modes.

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.