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Detection of fractional quantum Hall states by entropy-sensitive measurements

Nature Physics volume 21, pages 724–731 (2025)Cite this article

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Abstract

The thermopower of a clean two-dimensional electron system is directly proportional to the entropy per charge carrier and can probe strongly interacting quantum phases such as fractional quantum Hall liquids. In particular, thermopower is a valuable parameter to probe the quasiparticle statistics that give rise to excess entropy in certain even-denominator fractional quantum Hall states. Here we demonstrate that the magneto-thermopower detection of fractional quantum Hall states is more sensitive than resistivity measurements. We do this in the context of Bernal-stacked bilayer graphene and highlight several even-denominator states at a relatively low magnetic field. These capabilities of thermopower measurements support the interest in fractional quantum Hall states for finding quasiparticles with non-Abelian statistics and elevate bilayer graphene as a promising platform for achieving this.

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Fig. 1: Thermopower measurements in the IQH regime.
Fig. 2: Thermopower measurements in the FQH regime.
Fig. 3: Energy gaps of even-denominator FQH states.
Fig. 4: Excess entropy of even-denominator FQH states.

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Data availability

The data that support the findings of this study are available from the George Mason University Dataverse at https://doi.org/10.13021/orc2020/681UPS (ref. 42). Source data are provided with this paper.

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Acknowledgements

We thank Y. Barlas and F. Mahfouzi for useful discussions. N.S. acknowledges funding from the National Science foundation (NSF) under award no. 2337497. F.G. thanks J. Schnur for inspiring discussions and support. F.G. acknowledges funding from the National Institute of Standards and Technology (NIST) under grant no. 70NANB23H012. T.T. and K.W. acknowledge support from the Japan Society for the Promotion of Science KAKENHI under grant nos. 21H05233 and 23H02052 and World Premier International Research Center Initiative (WPI), Ministry of Education, Culture, Sports, Science and Technology (MEXT), Japan. D.E.F. was supported in part by the NSF under grant no. DMR-2204635.

Author information

Authors and Affiliations

  1. Department of Physics and Astronomy, George Mason University, Fairfax, VA, USA

    Nishat Sultana, Robert W. Rienstra & Fereshte Ghahari

  2. Research Center for Electronic and Optical Materials, National Institute for Materials Science, Tsukuba, Japan

    Kenji Watanabe

  3. Research Center for Materials Nanoarchitectonics, National Institute for Materials Science, Tsukuba, Japan

    Takashi Taniguchi

  4. Physical Measurement Laboratory, National Institute of Standards and Technology, Gaithersburg, MD, USA

    Joseph A. Stroscio & Nikolai B. Zhitenev

  5. Theoretical Physics Center and Physics Department, Brown University, Providence, RI, USA

    D. E. Feldman

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  1. Nishat Sultana
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Contributions

F.G. conceptualized and designed the experiment. N.S. fabricated the devices. N.S. performed measurements and analysed the experimental data, under the supervision of F.G. R.W.R. assisted with data acquisition and cryostat maintenance. D.E.F. provided theoretical support of the experimental data. T.T. and K.W. grew the hexagonal boron nitride crystals. F.G., J.A.S. and N.B.Z. wrote the paper with input from all co-authors.

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Correspondence to Fereshte Ghahari.

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Extended data

Extended Data Fig. 1 Thermopower measurements in the fractional quantum Hall regime in device no. 3.

a, The longitudinal thermal voltage Vxx (left axis) and Rxx (right axis) vs filling factor ν measured at B = 9 T and T = 1.64 K between pair 1 in device no. 3 (see e). While FQH states appear around filling factors 5/2 and 7/5 in Rxx, more FQH states are observable in Vxx. The temperature gradient was not calculated in this device due to a broken thermometer contact at base temperature. Therefore, the thermal voltage Vxx is plotted instead of thermopower. b, Landau fan of Vxx as a function of filling factor ν and magnetic field B at T = 300 mK measured between pair 1 in device no. 3 see e). In this plot the QH states appear as vertical lines at specific filling factors. In addition to integer QH states, FQH states at fractional fillings of 1/2, 4/5, 7/5, 5/2 and 8/3 are observable consistent with minima observed in a. c, Thermal voltage Vxx vs ν measured at B = −7.85 T and T = 300 mK between pair 2 in device no. 3 (see e). d, Landau fan of Vxx as a function of filling factor ν and magnetic field B measured at T = 300 mK between pair 2 showing vertical lines at fractional fillings including strong even denominator FQH states at 1/2 and 5/2 and odd denominator states consistent with those labeled in c. e, Optical image of a bilayer graphene thermopower device no. 3. Arrows show local thermometers and various electrode pairs used in measurements. f, Vxx and Vxy vs magnetic field B measured at fixed density of n = 0.99 × 1011 cm−2 at T = 300 mK between pair 1 showing a strong FQH state at ν = 5/2 specified by a minimum in Vxx (left axis) and a linear slope in Vxy (right axis) at this filling factor (see blue oval region). Only the strongest features are labeled.

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Supplementary Information

Supplementary Sections A–C, Figs. 1–21 and References.

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Source data for Fig. 1c,d,f.

Source Data Fig. 2

Source data for Fig. 2a–d,f,g.

Source Data Fig. 3

Source data for Fig. 3a–e.

Source Data Fig. 4

Source data for Fig. 4a,b.

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Sultana, N., Rienstra, R.W., Watanabe, K. et al. Detection of fractional quantum Hall states by entropy-sensitive measurements. Nat. Phys. 21, 724–731 (2025). https://doi.org/10.1038/s41567-025-02813-z

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