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

TL;DR

This paper investigates the dynamic response of a quantum dot hybrid system with normal and superconducting leads under step-like pulse bias, revealing symmetric responses at low bias and asymmetric, oscillatory behaviors at high bias, with implications for quantum transport.

Contribution

It provides a detailed analysis of the response times and oscillatory behaviors of a normal-superconductor hybrid system under different pulse bias regimes using non-equilibrium Green function methods.

Findings

Turn-on and turn-off times are slower in the linear bias regime due to Andreev reflection.

At large bias, the current oscillates with frequency proportional to the bias voltage.

Response times are faster for larger biases and depend on coupling strength.

Abstract

The response of a quantum dot coupled with one normal lead and a superconductor lead driven by a step-like pulse bias $V_L$ is studied using the non-equilibrium Green function method. In the linear pulse bias regime, the responses of the upwards and downwards bias are symmetric. In this regime the turn-on time and turn-off time are much slower than that of the normal system due to the Andreev reflection. On the other hand, for the large pulse bias $V_L$, the instantaneous current exhibits oscillatory behaviors with the frequency $\hbar\Omega =qV_L$. The turn on/off times are in (or shorter than) the scale of $1/V_L$, so they are faster for the larger bias $V_L$. In addition, the responses for the upwards and downwards bias are asymmetric at large $V_L$. The turn-on time is larger than the turn-off time but the relaxation time \cite{note1} depends only on the coupling strength $\Gamma$ and it is much smaller than the turn-on/off times for the large bias $V_L$.