Theoretical Study On Josephson Phase Transition In Multi-Quantum Dots/Superconductor Composite System

With the development of nanotechnology,the manufacturing process of various devices is getting better and better,and various devices with micron or even nanometer scale can be well prepared.Among them,Quantum dot(QD),a quasi-zero-dimensional structure,which can restrict the electron in three-dimensional,has attracted the attention of many researchers.Moreover,when the quantum dot is coupled with the normal metal electrode,the Kondo temperature and conductance of the system will be changed due to the screen effect of two-stage Kondo effect on the electron spin in the quantum dot.However,when quantum dots are coupled with superconducting(SC)electrodes,the Fano effect,Josephson effect and the 0-π transition of Josephson current in the Josephson junction due to the competition and cooperation between various electronic correlation effects can be observed.Due to the π junction can construct superconducting quantum bits,it has a broad application prospect in quantum computing and quantum information transmission.Therefore,the research on the physical mechanism of 0-πtransition in Josephson junction is of great theoretical significance and application value.First,consider the case of coupling a normal metal electrode,the system is composed of three quantum dots coupled in series,and the electrode is only coupled with the first quantum dot,the whole system exhibits a T-shaped structure.By means of numerical renormalization group method,we find that the conductance spectrum of the system will show completely different characteristics under the condition of different coupling coefficients in QDs.By analyzing the ground state energy of different subspaces of quantum dot molecules and using the Schrieffer-Wolff transformation method,the expression of Kondo temperature of Kondo effect in the first stage of the system is derived,and the characteristics of transport properties in the system are explained in combination with the changing characteristics of state density and entropy of the system.Then,we study the properties of Josephson current when the QDs are coupled with superconducting electrodes.We found that due to the mutual competition mechanism of Kondo effect and spin correlation effect between QDs in the system,the 0-π transition phenomenon of Josephson current in the system can be observed by adjusting the coupling coefficient between the QDs.When the coupling coefficient between two QDs is relatively large,the two QDs will form a molecular state which is similar to a large QD and interact with another QD as the energy level of QDs changes.The magnitude of the coupling coefficient will lead to different positions of the molecular states.Therefore,by adjusting the coupling coefficient between the QDs,Josephson current will show a richer 0-π transition phenomenon.We believe that the competition and cooperation of various electronic correlation effects in the system is the intrinsic mechanism of 0-π transition.In addition,the two-stage Kondo effect will also cause the extreme value of Josephson current in the process of the conversion from three electrons to two electrons in the system,and the current will not change suddenly when the phase transition occurs.This work has reference value for the research of Josephson current in QD coupled superconducting electrode.