  We study the phases of correlated charge-density waves that form at a high
magnetic field in two parallel graphene flakes separated by a thin insulator.
The predicted phases include the square and hexagonal charge-density-wave
bubbles, and a quasi-one-dimensional stripe phase. We find that the transition
temperature for such phases is within the experimentally accessible range and
that formation of interlayer-correlated states produces a negative
compressibility contribution to the differential capacitance of this system.
