@article{6ad265803d8b4224ba1808bab4058235,
title = "De Haas–van Alphen spectroscopy and magnetic breakdown in moir{\'e} graphene",
abstract = "Quantum oscillations originating from the quantization of electron cyclotron orbits provide sensitive diagnostics of electron bands and interactions. We report on nanoscale imaging of the thermodynamic magnetization oscillations caused by the de Haas-van Alphen effect in moir{\'e} graphene. Scanning by means of superconducting quantum interference device (SQUID)-on-tip in Bernal bilayer graphene crystal axis-aligned to hexagonal boron nitride reveals large magnetization oscillations with amplitudes reaching 500 Bohr magneton per electron in weak magnetic fields, unexpectedly low frequencies, and high sensitivity to superlattice filling fraction. The oscillations allow us to reconstruct the complex band structure, revealing narrow moir{\'e} bands with multiple overlapping Fermi surfaces separated by unusually small momentum gaps. We identified sets of oscillations that violate the textbook Onsager Fermi surface sum rule, signaling formation of broad-band particle-hole superposition states induced by coherent magnetic breakdown.",
author = "Matan Bocarsly and Matan Uzan and Indranil Roy and Sameer Grover and Jiewen Xiao and Zhiyu Dong and Mikhail Labendik and Aviram Uri and Huber, {Martin E.} and Yuri Myasoedov and Kenji Watanabe and Takashi Taniguchi and Binghai Yan and Levitov, {Leonid S.} and Eli Zeldov",
note = "The authors thank E. Berg, A. Stern, I. Rozhansky, and N. Avraham Tayar for useful discussions. Funding: This work was supported by the European Union (ERC, MoireMultiProbe – 101089714): Views and opinions expressed are however those of the author(s) only and do not necessarily reflect those of the European Union or the European Research Council. Neither the European Union nor the granting authority can be held responsible for them (to E.Z.); the Minerva Foundation, with funding from the Federal German Ministry of Education and Research Grant 140687 (to E.Z.); United States–Israel Binational Science Foundation (BSF) Grant 2022013 (to E.Z. and L.S.L.); Andre Deloro Prize for Scientific Research and Leona M. and Harry B. Helmsley Charitable Trust grant 2112-04911 (to E.Z.); Goldfield Family Charitable Trust (to E.Z.); Science and Technology Center for Integrated Quantum Materials, NSF grant DMR1231319, and Army Research Office Grant W911NF-18-1-0116 (to L.S.L.); Sagol Weizmann-MIT Bridge Program (to E.Z. and L.S.L.); European Research Council (ERC Consolidator Grant “NonlinearTopo,” 815869) (to B.Y.); Israel Science Foundation ISF grant 2932/21 (to B.Y.); JSPS KAKENHI grants 21H05233 and 23H02052 (to K.W. and T.T.); World Premier International Research Center Initiative (WPI), MEXT, Japan (to K.W. and T.T.); MIT Pappalardo Fellowship (to A.U.); VATAT Outstanding Postdoctoral Fellowship in Quantum Science and Technology (to A.U.); and a VATAT Outstanding PhD Fellowship in Quantum Science and Technology (to M.B.) Author contributions: Local magnetization measurements: M.B., I.R., and S.G. Sample fabrication and transport measurements: M.U. SOT fabrication and tuning fork feedback: I.R., M.L., and Y.M. Development of experimental setup: A.U. Design and building of the SOT readout system: M.E.H. BS calculations: J.X., B.Y., and M.B. Development of theoretical model (CMB): M.B., E.Z., L.S.L., and Z.D. Data analysis: M.B., I.R., M.U., and S.G. hBN crystals: K.W. and T.T. Writing of original manuscript: M.B., E.Z., L.S.L., J.X., M.U., I.R., and Z.D. Editing and review of manuscript: all authors.",
year = "2024",
month = jan,
day = "1",
doi = "https://doi.org/10.1126/science.adh3499",
language = "الإنجليزيّة",
volume = "383",
pages = "42--48",
journal = "Science",
issn = "0036-8075",
publisher = "American Association for the Advancement of Science",
number = "6678",
}