Multiple flat bands and topological Hofstadter butterfly in twisted bilayer graphene close to the second magic angle

Xiaobo Lu, Biao Lian, Gaurav Chaudhary, Benjamin A. Piot, Giulio Romagnoli, Kenji Watanabe, Takashi Taniguchi, Martino Poggio, Allan H. MacDonald, B. Andrei Bernevig, Dmitri K. Efetov

Research output: Contribution to journalArticlepeer-review

39 Scopus citations


Moiré 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 moiré system one of the most renowned condensed matter platforms. So far studies of tBLG have been mostly focused on the lowest two flat moiré bands at the first magic angle θm1 ∼ 1.1°, leaving high-order moiré bands and magic angles largely unexplored. Here we report an observation of multiple well-isolated flat moiré 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 moiré bands. Overall, our work provides a perspective for understanding the quantum phases in tBLG and the fractal Hofstadter spectra of multiple topological bands.

Original languageEnglish (US)
Article numbere2100006118
JournalProceedings of the National Academy of Sciences of the United States of America
Issue number30
StatePublished - Jul 27 2021

All Science Journal Classification (ASJC) codes

  • General


  • Materials
  • Moiré
  • Nanoelectronics
  • Two-dimensional
  • Van der Waals


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