Anomalous Quantum Hall States in Bilayer Graphene*

Bernal stacked bilayer graphene has a collection of competing broken symmetry states characterized by flavor-dependent spontaneous valley polarization.[1] The possible states include polarized and unpolarized orbital magnets and various quantum anomalous Hall states. By carefully evaluating the orbital magnetizations of the competing states, we find that the phase diagram is profoundly altered by a B field by favoring states of which its natural filling factor ν_N ≡ σ_H /(e²/h) is close to the actual filling factor ν, increasingly so as the B field strengthens. We have explored how coupling of orbital magnetization to external B fields is manifested in the dependence of ground state properties on weak gate V_g and magnetic fields B that favor particular states. We construct the ground-state phase diagram of this system, vs. V_g and B at fixed ν, and vs. V_g and ν at fixed B, and obtain excellent agreement with two-point conductivity measurements. This work explains why the ν_N = ±4 quantum Hall Effect in bilayer graphene is stable to anomalously weak B fields, and suggests that ν_N = ±2 anomalous quantum Hall effects could occur in the absence of a B field in samples of sufficiently high quality.

[1] PRL 106 (15), 156801