Spatially indirect exciton condensate phases in double bilayer graphene

We present a theory of spatially indirect exciton condensate states in systems composed of a pair of electrically isolated Bernal graphene bilayers. The ground-state phase diagram in a two-dimensional displacement-field/interbilayer-bias space includes layer-polarized semiconductors, spin-density-wave states, exciton condensates, and states with mixed excitonic and spin order. We find that two different condensate states, distinguished by a chirality index, are stable under different electrical control conditions.