Josephson Current In Carbon Nanotube Quantum Dot Coupled With Superconducting Electrodes

With the development of nanoseale fabrication techniques, it is now possible to study electrical transport at the level of individual electronic states. To be artificial structures quantum dots own obvious advantage and convenience. We can adjust easily related parameters through regulating electrode voltages of quantum dot and then achieve control’s aim. When attaching superconducting electrodes to a quantum dot, the hybrid structure of superconductor-quantum dot-superconductor has formed. The hybrid structure combines the macroscopie quantum phenomenon involving many electrons and the ability in controlling single electron and produces a lot of particular phenomena.There are three main parts in this article. The first chapter gives background introduction of research contents. Firstly we introduce briefly the basic proper-ties of carbon nanotube quantum dot and electronic transport in it. And then we discribe what is kondo effect and the differences between in metal containing magnetic impurities and in quantum dot.Thirdly we introduce the BCS theory of superconductivity and Andreev reflection occurring in the interface between superconductor and normal metal. At last we give some introductions about Josephson current. The second chapter introduces the Green Function theory in dealing with quantum dot’s transport problems. Trough using the equation of motion of Green Function and taking approximation, we can get the retard Green Function of system which makes us obtain whatever we want, just like the den-sity of states and Josephson current. The third chapter gives my work content. We use the Anderson impurity model to describe superconductor-quantum dot-superconductor system, and then gives derivation process of the Green Function of quantum dot electron.The final results and related discussion will present in the third section of this chapter.The results contain two parts:When not considring the spin-orbit coupling,we can observe the O-πtransition of Joseph-son current in adjusting both level positon of qnantum dot and coupling length between quantum dot and electrodes.But when considering the spin-orbit cou-pling,the situation changes complicated and appears new phenomena.