@article{d92ce7d0883042aabee2f7132b1c455b,
title = "Correlated Hofstadter spectrum and flavour phase diagram in magic-angle twisted bilayer graphene",
abstract = "In magic-angle twisted bilayer graphene, the moir{\'e} superlattice potential gives rise to narrow electronic bands that support a multitude of many-body quantum phases. Further richness arises in the presence of a perpendicular magnetic field, where the interplay between moir{\'e} and magnetic length scales leads to fractal Hofstadter subbands. In this strongly correlated Hofstadter platform, multiple experiments have identified gapped topological and correlated states, but little is known about the phase transitions between them in the intervening compressible regimes. Here we simultaneously unveil sequences of broken-symmetry Chern insulators and resolve sharp phase transitions between competing states with different topological quantum numbers and different occupations of the spin-valley flavour. Our measurements determine the energy spectrum of interacting Hofstadter subbands in magic-angle twisted bilayer graphene and map out the phase diagram of flavour occupancy. In addition, we observe full lifting of the degeneracy of the zeroth Landau levels together with level crossings, indicating moir{\'e} valley splitting. We propose a unified flavour polarization mechanism to understand the intricate interplay of topology, interactions and symmetry breaking as a function of density and applied magnetic field in this system.",
author = "Jiachen Yu and Foutty, {Benjamin A.} and Zhaoyu Han and Barber, {Mark E.} and Yoni Schattner and Kenji Watanabe and Takashi Taniguchi and Philip Phillips and Shen, {Zhi Xun} and Kivelson, {Steven A.} and Feldman, {Benjamin E.}",
note = "Funding Information: We thank D. Goldhaber-Gordon and O. Vafek for helpful discussions. This work was supported by the QSQM, an Energy Frontier Research Center funded by the US Department of Energy (DOE), Office of Science, Basic Energy Sciences (BES), under award no. DE-SC0021238. B.E.F. acknowledges a Stanford University Terman Fellowship and an Alfred P. Sloan Foundation Fellowship. K.W. and T.T. acknowledge support from the Elemental Strategy Initiative conducted by MEXT, Japan (grant no. JPMXP0112101001) and JSPS KAKENHI (grant no. JP20H00354). S.A.K. acknowledges support from the Department of Energy, Office of Basic Energy Sciences, under contract no. DEAC02-76SF00515. B.A.F. acknowledges a Stanford Graduate Fellowship. M.E.B. acknowledges support from the Marvin Chodorow Postdoctoral Fellowship of the Applied Physics Department, Stanford University. Y.S. was supported by the Gordon and Betty Moore Foundation{\textquoteright}s EPiQS Initiative through grants GBMF 4302 and GBMF 8686. P.P. acknowledges partial support from NSF grant DMR-2111379. Part of this work was performed at the Stanford Nano Shared Facilities (SNSF), supported by the National Science Foundation under award ECCS-2026822. Publisher Copyright: {\textcopyright} 2022, The Author(s), under exclusive licence to Springer Nature Limited.",
year = "2022",
month = jul,
doi = "10.1038/s41567-022-01589-w",
language = "English (US)",
volume = "18",
pages = "825--831",
journal = "Nature Physics",
issn = "1745-2473",
publisher = "Nature Publishing Group",
number = "7",
}