Theoretical Study On Supercurrent Properties In Complex Josephson Junctions

In recent years,with the development of the semiconductor industry,people’s demand for electronic devices has become higher and higher.The size of semiconductor devices is gradually reaching sub-micron or even nano-scale.Among them,the quantum dot as a quasi-zero-dimensional structure has attracted more and more attention.There are a variety of electron-related effects in the superconducting tunnel junctions that couple quantum dot molecules,resulting in a variety of interesting changes in the Josephson current flowing through the superconducting junction.The Josephson junction has a very broad application prospect for designing electronic devices with microelectromechanical functions as well as quantum computing and quantum information processing.Therefore,it is of great theoretical significance and application value to continue to study the superfluid nature of Josephson’s knot.In this context,in this context,using the idea of zero-bandwidth approximation of superconducting electrodes,the method of strictly diagonalizing the matrix and the numerical renormalization group(NRG)method,the contralateral coupled magnetic impurity superconducting junction and the three terminals are adopted respectively.The Josephson current in the superconducting electrode double quantum dot coupled superconducting junction was investigated.First,we investigated the effect of magnetic impurities on the Josephson current in a superconducting junction.By studying the two cases where a magnetic impurity is coupled to a quantum dot and a superconducting electrode,we give the results of a supercurrent analysis of a Josephson junction.It has been found that magnetic impurities can effectively induce Josephson phase transitions in superconducting junctions,which is closely related to the spin correlation between magnetic impurities and junctions.Compared with the results of antiferromagnetic spin correlation between quantum dots and magnetic impurities,ferromagnetic spin correlation has a more effective effect on Josephson phase transition.At the same time,we also found that the Coulomb interaction in quantum dots has little effect on the phase transition.Next,when the magnetic impurity is coupled to a superconducting electrode,it exhibits a substitution effect of the Josephson phase transition,which is substantially opposite to the case where the magnetic impurity and the quantum dot are coupled.This work helps to describe the effect of magnetic impurities on the superfluid characteristics of the Josephson junction.Then,we studied the superfluid condition in the Josephson junction of three quantum dots coupled with three terminal superconducting electrodes.Our study found that the current in the Josephson junction exhibits a 4π cycle phenomenon due to the influence of the intermediate superconducting electrode.Moreover,due to the coupling between the two quantum dots,a new transition phase is observed when electrons are transferred from the left electrode to the right electrode in the superconducting junction.When the Coulomb strength in the point is strong enough,the intermediate bistable(BS)phase discovered not long ago will occur,which is related to the topology and coupling of the superconducting junction.Compared with the two-channel Josephson junction,in the same topology and coupling mode,only the three-terminal Josephson junction has a significant transition phase.When the Josephson current is in the transition phase region,the amplitude of the superfluid in the Josephson junction increases significantly and exhibits a more complex superfluid morphology.As the Coulomb intensity in quantum dots continues to increase,the traditional transition phase transforms into a new transition phase and eventually remains in the BS phase,while the current direction is reversed.This study helped to achieve current steering in the Josephson junction.