Phase diagram of the ν=2 quantum Hall state in bilayer graphene

Udit Khanna, Ke Huang, Ganpathy Murthy, H. A. Fertig, Kenji Watanabe, Takashi Taniguchi, Jun Zhu, Efrat Shimshoni

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Bilayer graphene exhibits a rich phase diagram in the quantum Hall regime, arising from a multitude of internal degrees of freedom, including spin, valley, and orbital indices. The variety of fractional quantum Hall states between filling factors 1<ν≤2 suggests, among other things, a quantum phase transition between valley-unpolarized and polarized states at a perpendicular electric-field D∗. We find that the behavior of D∗ with ν changes markedly as B is reduced. At ν=2, D∗ may even vanish when B is sufficiently small. We present a theoretical model for lattice-scale interactions, which explains these observations; surprisingly, both repulsive and attractive components in the interactions are required. Within this model, we analyze the nature of the ν=2 state as a function of the magnetic and electric fields and predict that valley coherence may emerge for D∼D∗ in the high-B regime. This suggests the system supports Kekulé bond ordering, which could, in principle, be verified via scanning tunneling measurements.

Original languageEnglish
Article numberL041107
JournalPhysical Review B
Issue number4
StatePublished - 15 Jul 2023

Bibliographical note

Publisher Copyright:
© 2023 American Physical Society.


Acknowledgements. We thank C. Huang, R. Kaul, and B. Sacepe for useful discussions. E.S., H.A.F., and G.M. thank the Aspen Center for Physics (NSF Grant No. 1066293) for its hospitality, and financial support by the U.S.-Israel Binational Science Foundation through Award No. 2016130. U.K. and E.S. acknowledge support of the U.S.-Israel Binational Science Foundation through Award No. 2018726, and the Israel Science Foundation (ISF) Grant No. 993/19. H.A.F. acknowledges support of the NSF through Grants No. ECCS-1936406 and No. DMR-1914451. K.H. and J.Z. acknowledge support from the National Science Foundation through Grant No. NSF-DMR-1904986. The experiments were performed at the National High Magnetic Field Laboratory, which was supported by the National Science Foundation through Grant No. NSF-DMR-1644779 and the State of Florida. K.W. and T.T. acknowledge support from JSPS KAKENHI (Grants No. 19H05790, No. 20H00354, and No. 21H05233).

FundersFunder number
National Science FoundationNSF-DMR-1904986, NSF-DMR-1644779
Aspen Center for Physics1066293
State of Florida
Japan Society for the Promotion of Science21H05233, 20H00354, 19H05790
United States-Israel Binational Science Foundation2016130, 2018726
Israel Science FoundationDMR-1914451, ECCS-1936406, 993/19


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