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Broken symmetries and excitation spectra of interacting electrons in partially filled Landau levels

Nature Physics volume 19, pages 1482–1488 (2023)Cite this article

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Abstract

Interacting electrons in flat bands give rise to a variety of quantum phases. One fundamental aspect of such states is the ordering of the various flavours—such as spin or valley—that the electrons can possess and the excitation spectrum of the broken-symmetry states that they form. These properties cannot be probed directly with electrical transport measurements. The zeroth Landau level of monolayer graphene with fourfold spin–valley degeneracy is a model system for such investigations, but the nature of its broken-symmetry states—particularly at partial fillings—is still not understood. Here we demonstrate a non-invasive spectroscopic technique with a scanning tunnelling microscope and use it to perform measurements of the valley polarization of the electronic wavefunctions and their excitation spectrum in the partially filled zeroth Landau level of graphene. We can extract information such as the strength of the Haldane pseudopotentials that characterize the repulsive interactions underlying the fractional quantum states. Our experiments also demonstrate that fractional quantum Hall phases are built upon broken-symmetry states that persist at partial filling. Our experimental approach quantifies the valley phase diagram of the partially filled Landau level as a model flat-band platform, which is applicable to other graphene-based electronic systems.

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Fig. 1: Influence of the STM tip on LL spectra.
Fig. 2: Point spectroscopy of the ZLL with a charge-neutral tip.
Fig. 3: Fourier analysis of constant-height maps at representative fillings.
Fig. 4: Evolution of valley texture of the excitations with gate and bias.

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Data availability

The data that support the findings of this study are available at Figshare (https://doi.org/10.6084/m9.figshare.22807172).

Code availability

The code that supports the findings of this study is available at Figshare (https://doi.org/10.6084/m9.figshare.22807172).

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Acknowledgements

We thank S. S. Hegde and I. S. Villadiego for helpful discussions. This work was supported by the ARO MURI (W911NF-21-2-0147), ONR N00012-21-1-2592, Gordon and Betty Moore Foundation’s EPiQS initiative grant GBMF9469 and DOE-BES grant DE-FG02-07ER46419 to A.Y. Other support for the experimental work was provided by NSF-MRSEC through the Princeton Center for Complex Materials NSF-DMR-1420541, NSF-DMR-1904442. Z.P. acknowledges funding by the Leverhulme Trust Research Leadership Award RL-2019-015. M.P.Z. acknowledges support from the US Department of Energy, Office of Science, Office of Basic Energy Sciences, Materials Sciences and Engineering Division, under contract DE-AC02-05CH11231, within the van der Waals Heterostructures Program (KCWF16). K.W. and T.T. acknowledge support from the Elemental Strategy Initiative conducted by MEXT, Japan, grant JPMXP0112101001, JSPS KAKENHI grant JP20H00354 and CREST (JPMJCR15F3), JST.

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Author notes

  1. These authors contributed equally: Gelareh Farahi, Cheng-Li Chiu, Xiaomeng Liu.

Authors and Affiliations

  1. Joseph Henry Laboratories and Department of Physics, Princeton University, Princeton, NJ, USA

    Gelareh Farahi, Cheng-Li Chiu, Xiaomeng Liu & Ali Yazdani

  2. School of Physics and Astronomy, University of Leeds, Leeds, UK

    Zlatko Papic

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

    Kenji Watanabe

  4. International Center for Materials Nanoarchitectonics, National Institute for Materials Science, Tsukuba, Japan

    Takashi Taniguchi

  5. Department of Physics, University of California at Berkeley, Berkeley, CA, USA

    Michael P. Zaletel

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  1. Gelareh Farahi
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Contributions

G.F., C.-L.C., X.L. and A.Y. designed the experiment. G.F. and C.-L.C. fabricated the sample. G.F., C.-L.C. and X.L. performed the measurements and analysed the data. M.P.Z., Z.P. and X.L. conducted the theoretical analysis. G.F., C.-L.C., X.L., A.Y. and M.P.Z. wrote the manuscript with input from all authors.

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Correspondence to Ali Yazdani.

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Nature Physics thanks Raymond Ashoori and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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Supplementary Figs. 1–9 and Discussion.

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Farahi, G., Chiu, CL., Liu, X. et al. Broken symmetries and excitation spectra of interacting electrons in partially filled Landau levels. Nat. Phys. 19, 1482–1488 (2023). https://doi.org/10.1038/s41567-023-02126-z

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