Due to a strong Coulomb interaction, excitons dominate the excitation kinetics in 2D materials. While Coulomb-scattering between electrons has been well studied, the interaction of excitons is more challenging and remains to be explored. As neutral composite bosons consisting of electrons and holes, excitons show a non-trivial scattering dynamics. Here, we study on microscopic footing exciton-exciton interaction in transition-metal dichalcogenides and related van der Waals heterostructures. We demonstrate that the crucial criterion for efficient scattering is a large electron/hole mass asymmetry giving rise to internal charge inhomogeneities of excitons and emphasizing their cobosonic substructure. Furthermore, both exchange and direct exciton-exciton interactions are boosted by enhanced exciton Bohr radii. We also predict an unexpected temperature dependence that is usually associated to phonon-driven scattering and we reveal an orders of magnitude stronger interaction of interlayer excitons due to their permanent dipole moment. The developed approach can be generalized to arbitrary material systems and will help to study strongly correlated exciton systems, such as moire super lattices.
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