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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1 Scopus citations


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 - Jul 15 2023

Bibliographical note

Publisher Copyright:
© 2023 American Physical Society.

ASJC Scopus subject areas

  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics


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