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We study theoretically the neutral and charged excitons in two-dimensional semiconductors with anisotropic dispersion of charge carriers. Such a situation is realized in CrSBr-based van der Waals heterostructures. We calculate the binding energies of excitons and trions and explore their dependence on the mass ratio, dielectric screening, and interlayer distance in bilayer structures. We also address the effects of exciton-light coupling, including the radiative decay and long-range electron-hole exchange interaction, and briefly analyze correlations between the excitons and the Fermi sea of resident electrons. The estimates for CrSBr bilayers are in reasonable agreement with recent experiments.

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