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

TL;DR

This paper investigates the phase diagram of bilayer graphene's zero-energy Landau level under magnetic fields, revealing complex quantum ferromagnetic states and orbital coherence phenomena through a Hartree-Fock analysis.

Contribution

It provides a detailed phase diagram considering realistic interactions and includes the effect of filled Landau levels, advancing understanding of quantum phases in bilayer graphene.

Findings

Agreement with experimental observations

Identification of orbital coherence phases

Orbital splitting influenced by exchange interactions

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.