We present here calculations on electronic spectra of a system consisting of a quantum dot connected to superconducting leads on its either side. In these calculations the generated spectra has contributions from both, the single particle tunneling, and from the tunneling Cooper pair of electrons. In this, the Anderson model is used for the theoretical construct, and hence, the single particle tunneling, the Josephson tunneling, the energy states of the quantum dot and the super conducting order parameter for BCS superconductors are principally considered. The Green's function equation of motion technique is used to obtain the single particle spectral function. Our results from the numerical computations in the present work indicate, under certain conditions, the occurrence of breaking of Cooper pairs at the junctions between the superconducting leads and the quantum dot. These are seen to be, understandably, depending on the interaction terms included in our model. Our present work suggests a way to understand the interplay of single particle and the ‘Cooper pairs tunneling’ in the resultant electronic spectra in the light of extended Anderson model applicable to the system. It thus presents a theoretical understanding on the transmission of supercurrents through nanoscopic junctions, such as that considered here.

我们在这里介绍系统的电子光谱计算，该系统由在其任一侧连接到超导引线的量子点组成。在这些计算中，所产生的光谱具有单粒子隧穿和隧穿库珀电子对的贡献。在此，将安德森模型用于理论构建，因此，主要考虑了BCS超导体的单粒子隧穿，约瑟夫森隧穿，量子点的能态和超导阶数参数。运动的格林函数方程用于获得单粒子光谱函数。我们从当前工作中的数值计算得出的结果表明，在某些条件下，在超导引线和量子点之间的结处发生库珀对断裂。可以理解，这些取决于我们模型中包括的交互术语。我们目前的工作提出了一种方法，该方法根据适用于系统的扩展安德森模型，可以理解所得电子光谱中单个粒子与“库珀对隧穿”之间的相互作用。因此，它提供了关于通过纳米结的超电流传输的理论理解，例如这里所考虑的。我们目前的工作提出了一种方法，该方法根据适用于系统的扩展安德森模型，可以理解所得电子光谱中单个粒子与“库珀对隧穿”之间的相互作用。因此，它提供了关于通过纳米结的超电流传输的理论理解，例如这里所考虑的。我们目前的工作提出了一种方法，该方法根据适用于系统的扩展安德森模型，可以理解所得电子光谱中单个粒子与“库珀对隧穿”之间的相互作用。因此，它提供了关于通过纳米结的超电流传输的理论理解，例如这里所考虑的。