We develop the theory of the crystallization phenomena for charged interlayer excitons (CIE) discovered recently in highly excited transition-metal-dichalcogenide (TMD) heterobilayers. We derive the ratio of the average potential interaction energy to the average kinetic energy and discuss the ’cold’ long-range crystallization phase transition for the many-particle CIE system in the absence and in the presence of a perpendicular magnetostatic field. In the zero-magnetic-field case, the strongly correlated phases are predicted — crystal and Wigner crystal for the unlike-charge and like-charge CIEs, respectively, — that can be selectively realized with TMD bilayers of properly chosen electron-hole effective masses by just varying their interlayer separation distance. In the non-zero-magnetic-field case, we generalize the effective g-factor concept previously formulated for interlayer excitons to include the formation of CIEs. We show that magnetic-field-induced Wigner crystallization and melting of CIEs can be observed in strong-field magneto-photoluminescence experiments with TMD heterobilayes of systematically varied electron-hole doping concentrations. Our results extend the potential capabilities of the TMD bilayer heterostructures, and can be used for coherent photon emission control, charge transport and spinoptronics application development with this new family of transdimensional quantum materials.
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