@article{9e51fadc09774df6a27deff4e3a72f9f,
title = "Multiple flat bands and topological Hofstadter butterfly in twisted bilayer graphene close to the second magic angle",
abstract = "Moir{\'e} superlattices in two-dimensional van der Waals heterostructures provide an efficient way to engineer electron band properties. The recent discovery of exotic quantum phases and their interplay in twisted bilayer graphene (tBLG) has made this moir{\'e} system one of the most renowned condensed matter platforms. So far studies of tBLG have been mostly focused on the lowest two flat moir{\'e} bands at the first magic angle θm1 ∼ 1.1°, leaving high-order moir{\'e} bands and magic angles largely unexplored. Here we report an observation of multiple well-isolated flat moir{\'e} bands in tBLG close to the second magic angle θm2 ∼ 0.5°, which cannot be explained without considering electron–election interactions. With high magnetic field magnetotransport measurements we further reveal an energetically unbound Hofstadter butterfly spectrum in which continuously extended quantized Landau level gaps cross all trivial band gaps. The connected Hofstadter butterfly strongly evidences the topologically nontrivial textures of the multiple moir{\'e} bands. Overall, our work provides a perspective for understanding the quantum phases in tBLG and the fractal Hofstadter spectra of multiple topological bands.",
keywords = "Materials, Moir{\'e}, Nanoelectronics, Two-dimensional, Van der Waals",
author = "Xiaobo Lu and Biao Lian and Gaurav Chaudhary and Piot, {Benjamin A.} and Giulio Romagnoli and Kenji Watanabe and Takashi Taniguchi and Martino Poggio and MacDonald, {Allan H.} and Bernevig, {B. Andrei} and Efetov, {Dmitri K.}",
note = "Funding Information: of Excellence in R&D (SE5-0522), Fundaci{\'o} Privada Cellex, Fundaci{\'o} Privada Mir-Puig, the Generalitat de Catalunya through the CERCA program, the H2020 Programme under grant agreement 820378, Project: 2DSIPC, and the La Caixa Foundation. A.H.M. and G.C. acknowledge support from Department of Energy (DOE) grant DE-FG02-02ER45958 and Welch Foundation grant TBF1473. B.L. acknowledges support from the Princeton Center for Theoretical Science, Princeton University. B.A.B. was supported by DOE grant DE-SC0016239, the Schmidt Fund for Innovative Research, Simons Investigator grant 404513, and the Packard Foundation. Further support was provided by NSF EAGER grant DMR 1643312, NSF Materials Research Science and Engineering Centers grant DMR-1420541, United States–Israel Binational Science Foundation grant 2018226, Office of Naval Research grant N00014-20-1-2303, and Princeton Global Network Funds. M.P. thanks the Swiss National Science Foundation Sinergia network “Nanoskyrmionics” (grant CRSII5-171003). Funding Information: ACKNOWLEDGMENTS. We are grateful for fruitful discussions with Francisco Guinea. D.K.E. acknowledges support from the Ministry of Economy and Competitiveness of Spain through the “Severo Ochoa” program for Centres Publisher Copyright: {\textcopyright} 2021 National Academy of Sciences. All rights reserved.",
year = "2021",
month = jul,
day = "27",
doi = "10.1073/pnas.2100006118",
language = "English (US)",
volume = "118",
journal = "Proceedings of the National Academy of Sciences of the United States of America",
issn = "0027-8424",
publisher = "National Academy of Sciences",
number = "30",
}