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To determine the topological quantum numbers of quantum Hall (QH) states hosting counter-propagating (CP) downstream (Nd) and upstream (Nu) 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 conductance GQ, which is governed by quantum numbers Nd and Nu. Our experimental setup, realized with a hBN encapsulated graphite gated monolayer graphene device, facilitates experimental control over GQ quantization: For temperatures up to 35mK, our measured GQ at ν = 2/3 and 3/5 (with CP modes) match the quantized values of non-equilibrated regime (Nd + Nu)κ0T, where κ0T is a quanta of GQ. With increasing temperature, GQ decreases and even- tually takes the value of equilibrated regime |Nd − Nu|κ0T. By contrast, at ν =1/3 and 2/5 (no CP modes), GQ remains robustly quantized at Ndκ0T independent of the temperature. Our work opens a new route for finding the topological order of non-Abelian QH states and for accurately characterizing reconstructed edges.

Rights:

• Creative Commons BY Attribution 4.0 International
  

Keyword: Topological quantum numbers, fractional quantum Hall, thermal Hall conductance

Date published: 2022-09-03

Publisher: Springer Science and Business Media LLC

Journal:

• Nature Communications (ISSN: 20411723) vol. 13 issue. 1 5185

Funding:

Manuscript type: Publisher's version (Version of record)

MDR DOI:

First published URL: https://doi.org/10.1038/s41467-022-32956-z

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Updated at: 2025-02-27 16:31:13 +0900

Published on MDR: 2025-02-27 16:31:13 +0900