In-gap states of a quantum dot coupled between a normal and a superconducting lead

We study the in-gap states of a quantum dot hybridized with one conducting and another superconducting electrode. The proximity effect suppresses the electronic states in the entire subgap regime |ω| < Δ, where Δ denotes the energy gap of the superconductor. The Andreev scattering mechanism can induce, however, some in-gap states whose line-broadening (inverse life-time) is controlled by the hybridization of the quantum dot with the normal electrode. We show that the number of such Andreev bound states is substantially dependent on the competition between the Coulomb repulsion and the induced on-dot pairing. We discuss the signatures of these in-gap states in the tunneling conductance, especially in a low-bias regime.