  The possibility of an inhomogeneous charge density wave phase is investigated
in a system of two coupled electron and hole monolayers separated by a
hexagonal boron nitride insulating layer. The charge density wave state is
induced through the assumption of negative compressibility of electron/hole
gases in a Coulomb drag configuration between the electron and hole sheets.
Under equilibrium conditions, we derive analytical expressions for the density
oscillation along the zigzag and armchair directions. We find that the density
modulation not only depends on the sign of the compressibility but also on the
anisotropy of the low energy bands. Our results are applicable to any two
dimensional system with anisotropic parabolic bands, characterized by different
effective masses. For equal effective masses, i.e., isotropic energy bands, our
results agree with Hrolak et al.[1]. Our numerical results are applied to
phosphorene.
