Hybrid van der Waals heterostructures of organic semiconductors and transition metal dichalcogenides (TMDs) are promising candidates for various optoelectronic devices, such as solar cells and biosensors. Energy-transfer processes in these materials are crucial for the efficiency of such devices, yet they are poorly understood. In this work, we develop a fully microscopic theory describing the effect of the Förster interaction on exciton dynamics and optics in a WSe2/tetracene heterostack. We demonstrate that the differential absorption and time-resolved photoluminescence can be used to track the real-time evolution of excitons. We predict a strongly unidirectional energy transfer from the organic to the TMD layer. Furthermore, we explore the role temperature has in activating the Förster transfer and find a good agreement to previous experiments. Our results provide a blueprint to tune the light-harvesting efficiency through temperature, molecular orientation and interlayer separation in TMD/organic heterostructures.
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