Subgap spectrum for an interacting hybrid superconducting quantum dot

We examine the formation of Andreev bound states in a metal-quantum-dot-BCS superconductor system in the Coulomb blockade regime and the Kondo regime. We propose to use the so-called Hubbard-I decoupling scheme in the context of the equation-of-motion technique to provide a proper physical description for the Coulomb blockade regime. Here, we find the appearance of anticrossings in the subgap spectrum due to the prevalence of even parity states independently on the dot gate position. On the contrary, for the Kondo regime the subgap structure exhibits parity crossings between the alternance of singlet and doublet states. Besides, we show how the nature of the ground state in this regime can be distinguished from evolution of the Andreev states in the presence of a magnetic