Canted Antiferromagnetic Phase of the $\nu \mathbf{=}0$ Quantum Hall State in Bilayer Graphene

Motivated to understand the nature of the strongly insulating $\nu =0$ quantum Hall state in bilayer graphene, we develop the theory of the state in the framework of quantum Hall ferromagnetism. The generic phase diagram, obtained in the presence of the isospin anisotropy, perpendicular electric field, and Zeeman effect, consists of the spin-polarized ferromagnetic (F), canted antiferromagnetic (CAF), and partially (PLP) and fully (FLP) layer-polarized phases. We address the edge transport properties of the phases. Comparing our findings with the recent data on suspended dual-gated devices, we conclude that the insulating $\nu =0$ state realized in bilayer graphene at lower electric field is the CAF phase. We also predict a continuous and a sharp insulator-metal phase transition upon tilting the magnetic field from the insulating CAF and FLP phases, respectively, to the F phase with metallic edge conductance $2e^2/h$, which could be within the reach of available fields and could allow one to identify and distinguish the phases experimentally.

Figure 1

(left) Lattice structure of BLG. (right) Occupation of the $01\otimes K{K}^{\prime }\otimes s$ space of each orbital by four electrons in the $\nu =0$ QHFM state in BLG. The energy of the $K{K}^{\prime }\otimes s$-symmetric interactions is minimized by forming 01-pseudospin-singlet pairs [14, 15]. Correspondence between the $\nu =0$ QHFM states in BLG and MLG is shown.

Figure 2

Phase diagram of the $\nu =0$ QHFM in BLG in the space of isospin anisotropy energies ($u_{\perp }$, $u_z$) at fixed electric ${ϵ}_V$ and Zeeman ${ϵ}_Z$ energies.

Figure 3

(left) Phase diagram in the space (${ϵ}_V$, ${ϵ}_Z$) of electric and Zeeman energies at fixed anisotropy energies $u_{\perp ,z}$, for the case (5) of AF phase favored by the isospin anisotropy. The horizontal, solid (violet) line denotes the evolution of the system with applied electric field, realized in Refs. 4, 6, with the CAF-PLP insulator-insulator transition at ${ϵ}_V={ϵ}_V^{*}$ characterized by a conductance spike. (right) Qualitative behavior of the edge transport gap ${\Delta }_{\mathrm{edge}}$ as a function of ${ϵ}_V$ and ${ϵ}_Z$. In the CAF phase, ${\Delta }_{\mathrm{edge}}$ gradually decreases upon tilting the magnetic field and closes completely once the F phase is reached.