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Monolayers of transition metal dichalcogenides (TMDC) became one of the moststudied nanostructures in the last decade. Combining two different TMDCmonolayers results in a heterostructure whose properties can be individuallytuned by the twist angle between the lattices of the two van-der-Waals layersand the relative placement of the layers, leading to Moir\'e cells. For smalltwist angles, lattice reconstruction leads to strong strain fields in theMoir\'e cells. In this paper, we combine an existing theory for latticereconstruction with a quantum dynamic theory for interlayer excitons and theirdynamics due to exciton phonon scattering using a polaron transformation. Theexciton theory is formulated in real space instead of the commonly usedquasi-momentum space to account for imperfections in the heterolayer breakinglattice translational symmetry. We can analyze the structure of the localizedand delocalized exciton states and their exciton-phonon scattering rates forsingle phonon processes using Born-Markov approximation and multi-phononprocesses using a polaron transformation. Furthermore, linear optical spectraand exciton relaxation Green functions are calculated and discussed.

Theory of interlayer exciton dynamics in 2D TMDCs Heterolayers under the influence of strain reconstruction and disorder