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Twisted transition metal dichalcogenides (TMDs) present an intriguingplatform for exploring excitons and their transport properties. By introducinga twist angle, a moir\'e superlattice forms, providing a spatially dependentexciton energy landscape. Based on a microscopic many-particle theory, weinvestigate in this work polaron-induced changes in exciton transportproperties in the MoSe$_2$/WSe$_2$ heterostructure. We demonstrate that polaronformation and the associated enhancement of moir\'e excitonic mass lead to asignificant band flattening. As a result, the hopping rate and the propagationvelocity undergo noticeable temperature and twist-angle dependent changes. Wepredict a reduction of the hopping strength ranging from 80% at a twist angleof 1$^\circ$ to 30% at 3$^\circ$ at room temperature. The provided microscopicinsights into the spatio-temporal exciton dynamics in presence of a moir\'epotential further deepens our understanding of the intriguing moir\'e excitonphysics.

Polaron-induced changes in moir\'e exciton propagation in twisted van der Waals heterostructures