Shot Noise In The Superconductive Graphene And Quantum Pumping Properties In The Josephson Junction

We investigate the conductance and shot noise properties of quasi-particle transport through a superconducting barrier in graphene. Based on the Blonder, Tinkham, and Klapwijk(BTK) formulation, the theory to investigate the transport properties in the superconductive graphene is developed. In comparison, we consider the two cases which are the transport in the presence and absence of the specular Andreev reflection. It is shown that the conductance and shot noise exhibit essentially different features in the two cases. It is found that the shot noise is suppressed as a result of more tunneling channels contributing to the transport when the superconducting gate is applied. The dependences of the shot noise behavior on both the potential strength and the width of the superconducting barrier in the two cases are different.In the presence of the specular Andreev reflection, the shot noise spectrum is more sensitive to both the potential strength and the width of the superconducting barrier. In both cases, total transmission occurs at a certain parameter setting, which contributes greatly to the conductance and suppresses the shot noise at the same time.At the same time, we investigate the nonadiabatic transport properties of the one dimensional timedependent superconductor-normal metal-superconductor(SNS) Josephson junction biased by a current source and driven by a high frequency ac gate potential applied to the normal-metal layer. BCS superconductors are considered and treated with the time-dependent Bogoliubov-de Gennes equation. Using Floquet theory, we compute the transmission coefficients and the Wigner-Smith delay times as a function of the incident energy and find that they display resonances when one of the electron or hole Floquet wavevectors coincides with the bound quasiparticle state within the superconducting energy gap. The resonance varies with the phase difference between the two superconductors as a result of the bound quasiparticle level displacement. The supercurrent flowing through the SNS junction is dramatically enhanced by the resonances.