Hund's Rules for the N=0 Landau Levels of Trilayer Graphene

Abstract

The N=0 Landau levels of ABC and ABA trilayer graphene both have approximate 12-fold degeneracies that are lifted by interactions to produce strong quantum Hall effects (QHE) at all integer filling factors between nu=-6 and nu=6. We discuss similarities and differences between the strong-magnetic-field weak-disorder physics of the two trilayer cases, and between trilayer and bilayer cases. These differences can be used to identify the stacking order of high-quality trilayer samples by studying their quantum Hall effects.

arXiv comment6 pages, 3 figures and 1 table

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• Transport studies of dual-gated ABC and ABA trilayer graphene: band gap opening and band structure tuning in very large perpendicular electric field
• Emergent Dirac gullies and gully-symmetry breaking quantum Hall states in ABA trilayer graphene
• Interacting electrons on trilayer honeycomb lattices
• Gapped broken symmetry states in ABC trilayer graphene
• New Dirac points and multiple Landau level crossings in biased trilayer graphene
• Competing Ordered States in Bilayer Graphene
• Broken Symmetry Quantum Hall States in Dual Gated ABA Trilayer Graphene
• Ferromagnetism in ABC-trilayer graphene
• Landau level splittings, phase transitions, and non-uniform charge distribution in trilayer graphene
• Ferroelectric and anomalous quantum Hall states in bare rhombohedral trilayer graphene
• Strong electronic interaction and multiple quantum Hall ferromagnetic phases in trilayer graphene
• SU(3) Quantum Hall Ferromagnetism in SnTe
• Stacking order, interaction and weak surface magnetism in layered graphene sheets
• High-magnetic-field Tunneling Spectra of ABC-Stacked Trilayer Graphene
• Distinct Competing Ordered ν=2 States in Bilayer Graphene
• Tunable symmetries of integer and fractional quantum Hall phases in heterostructures with multiple Dirac bands
• Observation of Chirality Transition of Quasiparticles at Stacking Solitons in Trilayer Graphene
• Flat band electrons and interactions in rhombohedral trilayer graphene
• Intrinsic and substrate induced spin-orbit interaction in chirally stacked trilayer graphene
• Tunable Infrared Phonon Anomalies in Trilayer Graphene
• Fine structure of the lowest Landau level in suspended trilayer graphene
• Spontaneous Chiral Symmetry Breaking in Bilayer Graphene
• Phase diagram of insulating crystal and quantum Hall states in ABC-stacked trilayer graphene
• Landau level diagram and the continuous rotational symmetry breaking in trilayer graphene
• Inter-subband Landau level couplings induced by in-plane magnetic fields in trilayer graphene
• Validity of the two-band model of bilayer and trilayer graphene in a magnetic field
• Buckled honeycomb lattice and unconventional magnetic response
• Gully quantum Hall ferromagnetism in biased trilayer graphene
• High-resolution Tunneling Spectroscopy of ABA-stacked Trilayer Graphene
• Orbital Lamb shift and mixing of the pseudo-zero-mode Landau levels in ABC-stacked trilayer graphene
• Spontaneous symmetry breaking and quantum Hall valley ordering on the surface of topological hexaborides
• Particle-hole symmetry and bifurcating ground state manifold in the quantum Hall ferromagnetic states of multilayer graphene
• Interaction-enhanced electron-hole and valley asymmetries in the lowest Landau level of ABA-stacked trilayer graphene
• Orbital mixing in few-layer graphene and non-Abelian Berry phase
• Quantum Parity Hall effect in ABA Graphene