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Determination of topological edge quantum numbers of fractional quantum Hall phases by thermal conductance measurements

Author

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  • Saurabh Kumar Srivastav

    (Indian Institute of Science)

  • Ravi Kumar

    (Indian Institute of Science)

  • Christian Spånslätt

    (Chalmers University of Technology)

  • K. Watanabe

    (National Institute of Material Science)

  • T. Taniguchi

    (National Institute of Material Science)

  • Alexander D. Mirlin

    (Karlsruhe Institute of Technology
    Karlsruhe Institute of Technology
    Petersburg Nuclear Physics Institute
    L. D. Landau Institute for Theoretical Physics RAS)

  • Yuval Gefen

    (Karlsruhe Institute of Technology
    Weizmann Institute of Science)

  • Anindya Das

    (Indian Institute of Science)

Abstract

To determine the topological quantum numbers of fractional quantum Hall (FQH) 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 Hall conductance GQ, which is purely governed by edge quantum numbers Nd and Nu. Our experimental setup is realized with a hexagonal boron nitride (hBN) encapsulated graphite gated single layer graphene device. For temperatures up to 35 mK, 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 eventually takes the value of the equilibrated regime ∣Nd − Nu∣κ0T. By contrast, at ν = 1/3 and 2/5 (without CP modes), GQ remains robustly quantized at Ndκ0T independent of the temperature. Thus, measuring the quantized values of GQ in two regimes, we determine the edge quantum numbers, which opens a new route for finding the topological order of exotic non-Abelian FQH states.

Suggested Citation

  • Saurabh Kumar Srivastav & Ravi Kumar & Christian Spånslätt & K. Watanabe & T. Taniguchi & Alexander D. Mirlin & Yuval Gefen & Anindya Das, 2022. "Determination of topological edge quantum numbers of fractional quantum Hall phases by thermal conductance measurements," Nature Communications, Nature, vol. 13(1), pages 1-8, December.
    • Handle: RePEc:nat:natcom:v:13:y:2022:i:1:d:10.1038_s41467-022-32956-z
    DOI: 10.1038/s41467-022-32956-z
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    References listed on IDEAS

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    1. Ravi Kumar & Saurabh Kumar Srivastav & Christian Spånslätt & K. Watanabe & T. Taniguchi & Yuval Gefen & Alexander D. Mirlin & Anindya Das, 2022. "Observation of ballistic upstream modes at fractional quantum Hall edges of graphene," Nature Communications, Nature, vol. 13(1), pages 1-7, December.
    2. Ron Aharon Melcer & Bivas Dutta & Christian Spånslätt & Jinhong Park & Alexander D. Mirlin & Vladimir Umansky, 2022. "Absent thermal equilibration on fractional quantum Hall edges over macroscopic scale," Nature Communications, Nature, vol. 13(1), pages 1-7, December.
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    5. Mitali Banerjee & Moty Heiblum & Vladimir Umansky & Dima E. Feldman & Yuval Oreg & Ady Stern, 2018. "Observation of half-integer thermal Hall conductance," Nature, Nature, vol. 559(7713), pages 205-210, July.
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    1. Ravi Kumar & Saurabh Kumar Srivastav & Ujjal Roy & Jinhong Park & Christian Spånslätt & K. Watanabe & T. Taniguchi & Yuval Gefen & Alexander D. Mirlin & Anindya Das, 2024. "Electrical noise spectroscopy of magnons in a quantum Hall ferromagnet," Nature Communications, Nature, vol. 15(1), pages 1-9, December.

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