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

TL;DR

This paper explores the complex phase diagram of bilayer graphene at filling factor zero in the quantum Hall regime, revealing multiple novel phases influenced by interactions, trigonal warping, and symmetry breaking.

Contribution

It introduces a comprehensive Hartree-Fock analysis including trigonal warping and short-range interactions, identifying new phases like the broken U(1)×U(1) state in bilayer graphene.

Findings

Identified multiple phases including ferromagnetic, layer-polarized, and Kekulé states.

Discovered a novel 'broken U(1)×U(1)' phase with independent symmetry breaking.

Mapped phase diagrams as functions of bias and magnetic field.

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, Kekul\'e, 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.