Spin-Valley Coherent Phases in Bilayer Graphene at Charge Neutrality*

Bernal-stacked Bilayer Graphene in the quantum Hall regime can be tuned by a Zeeman field and an electric field perpendicular to the layers. The manifold of Landau levels near charge neutrality is 8-fold near-degenerate. We theoretically analyse this system at $\nu=0$ by using the Hartree-Fock approximation on a Hamiltonian that contains, in addition to the long-range Coulomb interaction, short-range interactions with valley anisotropy. The Hamiltonian has U(1)$_{valley}\times$U(1)$_{spin}$ symmetry. A crucial ingredient in our analysis is the nonperturbative treatment of the trigonal warping parameter $t_3$. We find a new phase that breaks both the U(1) symmetries, and occurs for small values of $B_{\perp}$ and intermediate values of the perpendicular electric field. This phase, of realized in experimental samples, would support multiple flavors of merons and skyrmions.

1. Ganpathy Murthy, Efrat Shimshoni, and Herbert A. Fertig, arXiv:1707.02447, "Spin-Valley Coherent Phases of the $\nu=0$ Quantum Hall State in Bilayer Graphene".