A normal metal-quantum dot-superconductor hybrid system is investigated. This setup has been extensively studied since it shows a quantum phase transition between doublet and singlet ground states when the Coulomb charging energy is comparable to the superconducting gap strength. Recently, the setup has also received renowned interests due to its intimate connection with the Majorana physics. Using the Hubbard-I solution which is appropriate to describe the Coulomb blockade phenomenon, we calculate the differential conductances and examine the subgap excitations which is called Andreev bound states. The existing theoretical studies using the Hartree-Fock decoupling are criticised. We then compare our results with an experiment and find good agreements with that.
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