Phase diagram of insulating crystal and quantum Hall states in ABC-stacked trilayer graphene

Abstract

In the presence of a perpendicular magnetic field, ABC-stacked trilayer graphene's chiral band structure supports a 12-fold degenerate N=0 Landau level (LL). Along with the valley and spin degrees of freedom, the zeroth LL contains additional quantum numbers associated with the LL orbital index . Remote inter-layer hopping terms and external potential difference ${\Delta }_B$ between the layers lead to LL splitting by introducing a gap between the degenerate zero-energy triplet LL orbitals. Assuming that the spin and valley degrees of freedom are frozen, we study the phase diagram of this system resulting from competition of the single particle LL splitting and Coulomb interactions within the Hartree-Fock approximation at integer filling factors. Above a critical value ${\Delta }_{LL}^c$ of the external potential difference i,e, for $|{\Delta }_{LL}|>{\Delta }_{LL}^c$, the ground state is a uniform quantum Hall state where the electrons occupy the lowest unoccupied LL orbital index. For $|{\Delta }_{LL}|<{\Delta }_{LL}^c$ (which corresponds to large positive or negative values of ${\Delta }_B$) the uniform QH state is unstable to the formation of a crystal state at integer filling factors. This phase transition should be characterized by a Hall plateau transition as a function of ${\Delta }_{LL}$ at a fixed filling factor. We also study the properties of this crystal state and discuss its experimental detection.

arXiv comment16 pages with 13 figures

References in corpus (27)

• Two-Dimensional Gas of Massless Dirac Fermions in Graphene
• Experimental Observation of Quantum Hall Effect and Berry's Phase in Graphene
• Landau level degeneracy and quantum Hall effect in a graphite bilayer
• Unconventional quantum Hall effect and Berry's phase of 2pi in bilayer graphene
• Quantum Hall Ferromagnetism in Graphene
• Electronic states and Landau levels in graphene stacks
• Stacking-Dependent Band Gap and Quantum Transport in Trilayer Graphene
• Band Structure of ABC-Stacked Graphene Trilayers
• Broken symmetry states and divergent resistance in suspended bilayer graphene
• Trigonal warping and Berry's phase N pi in ABC-stacked multilayer graphene
• Quantum Hall effect and Landau level crossing of Dirac fermions in trilayer graphene
• Chiral Decomposition in the Electronic Structure of Graphene Multilayers
• The experimental observation of quantum Hall effect of l = 3 chiral charge carriers in trilayer graphene
• Skyrmion Lattice in Two-Dimensional Chiral Magnet
• Symmetry breaking of the zero energy Landau level in bilayer graphene
• Intra-Landau level Cyclotron Resonance in Bilayer Graphene
• Landau Level Spectrum of ABA- and ABC-stacked Trilayer Graphene
• Integer Quantum Hall Effect in Trilayer Graphene
• Quantum Hall Effects in Graphene-Based Two-Dimensional Electron Systems
• Zero-temperature phases for chiral magnets in three dimensions
• Quantum Hall Effect and Semimetallic Behavior of Dual-Gated ABA-Stacked Trilayer Graphene
• Anomalous Exciton-Condensation in Graphene Bilayers
• Pseudo-zero-mode Landau levels and collective excitations in bilayer graphene
• Hund's Rules for the N=0 Landau Levels of Trilayer Graphene
• Orbital order in bilayer graphene at filling factor $\nu =-1$
• Bilayer graphene as an helical quantum Hall ferromagnet
• Quantum Hall Solitons with Intertwined Spin and Pseudospin at $\nu =1$

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• Validity of the two-band model of bilayer and trilayer graphene in a magnetic field
• Orbital Lamb shift and mixing of the pseudo-zero-mode Landau levels in ABC-stacked trilayer graphene
• Particle-hole symmetry and bifurcating ground state manifold in the quantum Hall ferromagnetic states of multilayer graphene
• Orbital magnetization of interacting Dirac fermions in graphene
• Tunneling in ABC trilayer graphene superlattice
• Bound states of quasiparticles with quartic dispersion in an external potential: WKB approach
• Dynamical polarization in ABC-stacked multilayer graphene in a magnetic field