  We develop the theory of the magnetic-field-induced Wigner crystallization
effect for charged interlayer excitons (CIE) discovered recently in
transition-metal-dichalcogenide (TMD) heterobilayers. We derive the ratio of
the average potential interaction energy to the average kinetic energy for the
many-particle CIE system subjected to the perpendicular magnetic field of an
arbitrary strength, analyze the weak and strong field regimes, and discuss the
'cold' crystallization phase transition for the CIE system in the strong field
regime. We also generalize the effective g-factor concept previously formulated
for interlayer excitons, to include the formation of CIEs in electrostatically
doped TMD heterobilayers. 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 advance the
capabilities of this new family of transdimensional quantum materials.
