Response time of a normal-metal/superconductor hybrid system under a step-like pulse bias

The response of a quantum dot coupled with one normal lead and a superconductor lead driven by a step-like pulse bias VL is studied using the nonequilibrium Green's function method. In the linear pulse bias regime, the responses of the upward and downward biases are symmetric. In this regime, the turn-on time and turn-off time are much slower than those of the normal system due to the Andreev reflection. On the other hand, for the large pulse bias VL, the instantaneous current exhibits oscillatory behaviors with the frequency Ω=q VL. The turn-on/off times are in (or shorter than) the scale of 1 VL, so they are faster for the larger bias VL. In addition, the responses for the upward and downward biases are asymmetric at large VL. The turn-on time is larger than the turn-off time, but the relaxation time depends only on the coupling strength Γ and it is much smaller than the turn-on/off times for the large bias VL. [The turn-on/off time describes how fast a device can turn on/off a current, which is also named rise/fall time in M. Plihal, Phys. Rev. B 61, R13341 (2000), while the relaxation time was referred to how fast the device can go to a new steady state after a bias is abruptly switched on. It is also named saturation time in A. Schiller and S. Hershfield, Phys. Rev. B 62, R16271 (2000).]