Layer Correlated Phase in Double Layer Graphene at Δν=0

The question of the bulk phase of a quantum Hall system at the half filling is a very old and interesting one. In the recent advancement in Graphene material it is possible to create a double layer system of Graphene without inter-layer tunneling. In these systems the filling fraction of each layer (ν₁ and ν₂) can be controlled independently [1]. In this work we restrict the Hamiltonian using simple symmetry arguments. We study the ground state of this system in the Hartree-Fock approximation at Δν(=ν₁-ν₂)=0=ν₁=ν₂ (similar to what has been done for monolayer Graphene [2]). In addition to the phases found in [2] we found the existence of layer correlated phases.
We also propose on the possible direct experimental evidence to detect layer correlated phase.

[1] J. I. A. Li, T. Taniguchi, K. Watanabe, J. Hone,A. Levchenko, and C. R. Dean, PRL 117, 046802 (2016)

[2] M. Kharitonov, Phys. Rev. B85, 155439 (2012)