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Aharonov–Bohm interference and statistical phase-jump evolution in fractional quantum Hall states in bilayer graphene

Nature Nanotechnology (2024)Cite this article

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Abstract

In the fractional quantum Hall effect, quasiparticles are collective excitations that have a fractional charge and show fractional statistics as they interchange positions. While the fractional charge affects semi-classical characteristics such as shot noise and charging energies, fractional statistics is most notable through quantum interference. Here we study fractional statistics in a bilayer graphene Fabry–Pérot interferometer. We tune the interferometer from the Coulomb-dominated regime to the Aharonov–Bohm regime, both for integer and fractional quantum Hall states. Focusing on the fractional quantum Hall state with a filling factor ν = 1/3, we follow the evolution of the Aharonov–Bohm interference of quasiparticles while varying the magnetic flux through an interference loop and the charge density within the loop independently. When their combined variation is such that the Landau filling remains 1/3, the charge density in the loop varies continuously. We then observe pristine Aharonov–Bohm oscillations with a period of three flux quanta, as expected for quasiparticles of one-third of the electron charge. Yet, when the combined variation leads to discrete events of quasiparticle addition or removal, phase jumps emerge and alter the phase evolution. Notably, across all cases with discrete and continuous charge variation, the average phase consistently increases by 2π with each addition of one electron to the loop, as expected for quasiparticles, obeying fractional statistics.

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Fig. 1: FPI based on bilayer graphene.
Fig. 2: Tunable IQHE interference regimes, from CD to AB regimes.
Fig. 3: AB interference at a 1/3 fractional filling.
Fig. 4: Tunability between constant filling and constant density.

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Data availability

The data shown in the main text are available from the online depository Zenodo at https://doi.org/10.5281/zenodo.12509248 (ref. 50).

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Acknowledgements

We thank M. Heiblum for the useful discussions and his support of the project. We also thank P. Kim, T. Werkmeister and J. Ehrest for fruitful discussions. This work was supported by the Quantum Science and Technology Program 2021 to Y.R., by a research grant from the Schwartz Reisman Collaborative Science Program, which is supported by the Gerald Schwartz and Heather Reisman Foundation to Y.R., by a research grant from the Center for New Scientists at the Weizmann Institute of Science to Y.R., by grants from the ERC under the European Union’s Horizon 2020 research and innovation programme (grant agreements LEGOTOP No. 788715 and HQMAT No. 817799) to A.S., the DFG (CRC/Transregio 183, EI 519/7-1) to A.S., and by the ISF Quantum Science and Technology (2074/19) to A.S.

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Authors and Affiliations

  1. Department of Condensed Matter Physics, Weizmann Institute of Science, Rehovot, Israel

    Jehyun Kim, Himanshu Dev, Ravi Kumar, Alexey Ilin, André Haug, Vishal Bhardwaj, Changki Hong, Ady Stern & Yuval Ronen

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

    Kenji Watanabe

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

    Takashi Taniguchi

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Contributions

J.K. and R.K. improved the quality of the stacks. J.K. and H.D. prepared the stacks. K.W. and T.T. grew the hBN crystals. J.K., A.I., V.B. and R.K. improved the quality of the device. J.K. fabricated the device. A.H. and C.H. developed the measurement circuit and a dilution refrigerator. J.K. performed the measurements. J.K., H.D., A.S. and Y.R. analysed the measured data. A.S. developed the theoretical aspect. J.K., H.D., A.S. and Y.R. wrote the paper with input from all authors. Y.R. supervised the overall work done on the project.

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Correspondence to Yuval Ronen.

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Supplementary Sections 1–11 with Figs. 1–21.

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Kim, J., Dev, H., Kumar, R. et al. Aharonov–Bohm interference and statistical phase-jump evolution in fractional quantum Hall states in bilayer graphene. Nat. Nanotechnol. (2024). https://doi.org/10.1038/s41565-024-01751-w

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