Strong-coupling phases of trions and excitons in electron-hole bilayers at commensurate densities

We introduce density imbalanced electron-hole bilayers at a commensurate 2 : 1 density ratio as a platform for realizing novel phases of electrons, excitons, and trions. Through the independently tunable carrier densities and interlayer spacing, competition between kinetic energy, intralayer repulsion, and interlayer attraction yields a rich phase diagram. By a combination of theoretical analysis and numerical calculation, we find a variety of strong-coupling phases in different parameter regions, including quantum crystals of electrons, excitons, and trions. We also propose an "excitonic supersolid" phase that features electron crystallization and exciton superfluidity simultaneously. The material realization and experimental signature of these phases are discussed in the context of semiconductor transition metal dichalcogenide bilayers.