Exciton Condensate Stability in Double Bilayer Graphene in the Quantum Hall Regime

Semiconductor double-layers in the quantum Hall regime favor exciton condensate ground state when the two layers are brought into close proximity and the total Landau level filling factor is close to an integer. The exciton condensate state has spontaneous interlayer phase coherence, and is easily detected by drastic change in the drag resistance. Colossal drag has been observed in conventional semiconductor quantum wells at total filling factor 1, and in bilayer graphene with partially occupied N=0 Landau levels. Here we consider the dependence of stability of the exciton condensate state on the orbital degree of freedom that exists within bilayer graphene’s N=0 Landau level, which contains separate Landau levels with wavefunctions like those of parabolic bands with n=0 and 1. The phase diagram in this case is enriched by the competition between orbital order within each layer and interlayer phase coherence. By studying the stability of the exciton condensate relative to fluctuations that break translational invariance in different ways, we explain the absence of exciton condensate except when both bilayers have n=0 and address behavior near n=0/1 boundaries of individual layers.