Particle-hole symmetry and bifurcating ground state manifold in the quantum Hall ferromagnetic states of multilayer graphene

Abstract

The orbital structure of the quantum Hall ferromagnetic states in the zero-energy Landau level in chiral multilayer graphene (AB, ABC, ABCA, etc.\ stackings) is determined by the exchange interaction with all levels, including deep-lying states in the Dirac sea. This exchange field favors orbitally coherent states with a U(1) orbital symmetry if the filling factor $\nu$ is not a multiple of the number of layers. If electrons fill the orbital sector of a fixed spin/valley component to one-half, e.g., at $\nu =\pm 3,\pm 1$ in the bilayer and at $\nu =\pm 2,\pm 6$ in the ABCA four-layer, there is a transition to an $Z_2\times$U(1) manifold. For weak interaction, the structure in the zero-energy Landau band compensates for the different exchange interaction on the sublattices in the Landau orbitals; on the other side, the ground state comes in two copies that distribute charge on the sublattices differently. We expect a sequence of similar bifurcations in multilayers of Bernal stacking.

5+25 pages, 3+3 figures, typos corrected

References in corpus (16)

• Unconventional quantum Hall effect and Berry's phase of 2pi in bilayer graphene
• Landau Level Splitting in Graphene in High Magnetic Fields
• Electronic states and Landau levels in graphene stacks
• Multicomponent fractional quantum Hall effect in graphene
• Chiral Decomposition in the Electronic Structure of Graphene Multilayers
• Orbital diamagnetism in multilayer graphenes: Systematic study with the effective mass approximation
• Magneto-optical properties of multilayer graphenes
• Local Compressibility Measurements of Correlated States in Suspended Bilayer Graphene
• Transport studies of dual-gated ABC and ABA trilayer graphene: band gap opening and band structure tuning in very large perpendicular electric field
• Intra-Landau level Cyclotron Resonance in Bilayer Graphene
• Competing Ordered States in Bilayer Graphene
• Structure and the Lamb-shift-like quantum splitting of the pseudo-zero-mode Landau levels in bilayer graphene
• Phase diagram of insulating crystal and quantum Hall states in ABC-stacked trilayer graphene
• Theory of inter-Landau level magnetoexcitons in bilayer graphene
• Renormalized Landau Levels and Particle-Hole Symmetry in Graphene
• Orbital Lamb shift and mixing of the pseudo-zero-mode Landau levels in ABC-stacked trilayer graphene

Cited by in corpus (3)

• Electron-Hole Asymmetric Integer and Fractional Quantum Hall Effect in Bilayer Graphene
• Phase diagram of a graphene bilayer in the zero-energy Landau level
• Symmetry characterization of the collective modes of the phase diagram of the $\nu =0$ quantum Hall state in graphene: Mean-field and spontaneously broken symmetries