Spin-Valley Coherent Phases of the $\nu =0$ Quantum Hall State in Bilayer Graphene

Abstract

Bilayer graphene (BLG) offers a rich platform for broken symmetry states stabilized by interactions. In this work we study the phase diagram of BLG in the quantum Hall regime at filling factor $\nu =0$ within the Hartree-Fock approximation. In the simplest non-interacting situation this system has eight (nearly) degenerate Landau levels near the Fermi energy, characterized by spin, valley, and orbital quantum numbers. We incorporate in our study two effects not previously considered: (i) the nonperturbative effect of trigonal warping in the single-particle Hamiltonian, and (ii) short-range SU(4) symmetry-breaking interactions that distinguish the energetics of the orbitals. We find within this model a rich set of phases, including ferromagnetic, layer-polarized, canted antiferromagnetic, Kekulé, a "spin-valley entangled" state, and a "broken U(1) $\times$ U(1)" phase. This last state involves independent spontaneous symmetry breaking in the layer and valley degrees of freedom, and has not been previously identified. We present phase diagrams as a function of interlayer bias $D$ and perpendicular magnetic field $B_{\perp }$ for various interaction and Zeeman couplings, and discuss which are likely to be relevant to BLG in recent measurements. Experimental properties of the various phases and transitions among them are also discussed.

More references and discussion added compared to v1

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• Helical Edge States and Quantum Phase Transitions in Tetralayer Graphene
• Landau Levels of Bilayer Graphene in a WSe${}_2$/Bilayer Graphene van der Waals Heterostructure
• Magnetic and Lattice Ordered Fractional Quantum Hall Phases in Graphene
• Temperature-induced phase transitions in the quantum Hall magnet of bilayer graphene
• Infrared spectroscopy of phase transitions in the lowest Landau levels of bilayer graphene
• Entanglement smectic and stripe order
• Uniquely identifying quantum Hall phases in charge neutral graphene