Anisotropic charge density wave in electron-hole double monolayers: Applied to phosphorene

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.