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Bound States at Semiconductor -- Mott Insulator Interfaces

Utilizing the hierarchy of correlations in the context of a Fermi-Hubbard model, we deduce the presence of quasi-particle bound states at the interface between a Mott insulator and a semiconductor, as well as within a semiconductor-Mott-semiconductor heterostructure forming a quantum well. In the case of the solitary interface, the existence of bound states necessitates the presence of an additional perturbation with a minimal strength depending on the spin background of the Mott insulator. Conversely, within the quantum well, this additional perturbation is still required to have bound states while standing-wave solutions even exist in its absence.