We investigate the electron tunneling through a normal-metal–quantum-dot–superconductor (N-QD-S) system where multiple discrete levels of the QD are considered. By using the nonequilibrium-Green’s-function method, the current I and the probability of the Andreev reflection $T^A\left(\omega \right)$ are derived and studied in detail. In addition to the resonant behavior of the Andreev tunneling as obtained in previous works, we find that the current I versus the gate voltage $v_g$ exhibits different kinds of peaks, depending on the bias voltage, the level spacing of the QD, and the energy gap of the superconducting electrode. Besides, in $I-V$ characteristics extra peaks superimposed on the conventional current plateaus emerge, which stem from the resonant Andreev reflections. In the case with strongly asymmetric barriers, the BCS spectral density can be obtained directly from the $I-V$ characteristics.

• Received 27 May 1998

DOI:https://doi.org/10.1103/PhysRevB.59.3831