  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.
