Of primary interest for the design of novel optoelectronic devices are densely packed ordered arrays of quantum dots (QDs), which can be produced via self-assembly or other nanofabrication techniques. In such arrays, also known as supercrystals, the interaction between the QDs results in a collective optical response. Despite the active research on arrays made of perovskite QDs, a rigorous theory of their collective excitations is still lacking. In this Paper, we develop a quantum-mechanical theory of Frenkel excitons in planar perovskite QD arrays with square lattice. -18

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