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ABC-stacked trilayer graphenes chiral band structure results in three ($n=0,1,2$) Landau level orbitals with zero kinetic energy. This unique feature has important consequences on the interaction driven states of the 12-fold degenerate (including spi n and valley) N=0 Landau level. In particular, at many filling factors $ u_{T} =pm5,pm4,pm2,pm1$ a quantum phase transition from a quantum Hall liquid state to a triangular charge density wave occurs as a function of the single-particle induced LL orbital splitting $Delta_{LL}$. This phase transition should be characterized by a re-entrant integer quantum Hall effect with the Hall conductivity corresponding to the {it adjacent} interaction driven integer quantum Hall plateau.
109 - Yafis Barlas , R. Cote , K. Nomura 2008
Interaction driven integer quantum Hall effects are anticipated in graphene bilayers because of the near-degeneracy of the eight Landau levels which appear near the neutral system Fermi level. We predict that an intra-Landau-level cyclotron resonance signal will appear at some odd-integer filling factors, accompanied by collective modes which are nearly gapless and have approximate $k^{3/2}$ dispersion. We speculate on the possibility of unususal localization physics associated with these modes.
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