Phase diagram of a graphene bilayer in the zero-energy Landau level

Abstract

Bilayer graphene under a magnetic field has an octet of quasidegenerate levels due to spin, valley, and orbital degeneracies. This zero-energy Landau level is resolved into several incompressible states whose nature is still elusive. We use a Hartree-Fock treatment of a realistic tight-binding four-band model to understand the quantum ferromagnetism phenomena expected for integer fillings of the octet levels. We include the exchange interaction with filled Landau levels below the octet states. This Lamb-shift-like effect contributes to the orbital splitting of the octet. We give phase diagrams as a function of applied bias and magnetic field. Some of our findings are in agreement with experiments. We discuss the possible appearance of phases with orbital coherence.

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• Thermal Transport Signatures of Broken-Symmetry Phases in Graphene
• 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
• Quantum Hall ferroelectric helix in bilayer graphene
• Landau Level Phases in Bilayer Graphene under Pressure at Charge Neutrality
• Infrared spectroscopy of phase transitions in the lowest Landau levels of bilayer graphene
• Orbital mixing in few-layer graphene and non-Abelian Berry phase