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Entropy of Strongly Correlated Electrons in a Partially Filled Landau Level

Alexandre Assouline1,2,*, Taige Wang3,4,*, Heun Mo Yoo1,*, Ruihua Fan3, Fangyuan Yang1, Ruining Zhang1, Takashi Taniguchi5, Kenji Watanabe6, Michael P. Zaletel3,4 et al.

Andrea F. Young1,†

  • *These authors contributed equally to this work.
  • †Contact author: andrea@physics.ucsb.edu
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Phys. Rev. X 16, 021016 – Published 17 April, 2026

DOI: https://doi.org/10.1103/jpf1-4zdk

Abstract

We use high-resolution chemical potential measurements to extract the entropy of monolayer and bilayer graphene in the quantum Hall regime via the Maxwell relation [(dμ)/(dT)]|N=−[(dS)/(dN)]|T. Measuring the entropy from T=300  K down to T=200  mK, we identify the sequential emergence of quantum Hall ferromagnetism, fractional quantum Hall states, and various charge orders by comparing the measured entropy in different temperature regimes with theoretical models. At the lowest temperature of T≈200  mK we perform a detailed study of the entropy near even-denominator fractional quantum Hall states in bilayer graphene, and comment on the possible topological origin of the observed excess entropy.

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Measuring entropy in strongly interacting electron systems is a central challenge because it requires capturing the precise number of active degrees of freedom as the temperature approaches absolute zero. We investigated the entropy of electrons in quantum Hall phases of both monolayer and bilayer graphene, covering more than 3 orders of magnitude in temperature. With high detection sensitivity, we reveal the intricate interplay between motional and spin degrees of freedom, which successively freeze out in succession to form low-temperature Wigner crystals or fractionalized phases. These results provide a thermodynamic signature of emergent particles and place new constraints on the conditions required to observe non-Abelian statistics in fractionalized phases. Overall, our work offers a practical road map for using entropy as a probe to identify and characterize exotic topological states.

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Phys. Rev. X 16, 021016– Published 17 April, 2026
  • Received 20 March 2025
  • Revised 4 January 2026
  • Accepted 5 February 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

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