The Spin Transport Properties Of Josephson Junction With Majorana Bound States

The Majorana bound state has attracted much attention due to its unique properties.Scientists continuously study the bound state of Majorana,in order to applied in real life one day.The practical schemes of detecting Majorana bound states are not enough.However,using the current Josephson to study Majorana bound state is one of the feasible methods,we investigated the spin Josephson current that coupling the Majorana bound states with Josephson junction,to explore the effect of Majorana bound states.In this paper,we study the spin transport properties of Josephson junctions with Majorana bound states using the Green's function method.This model is a quantum dot applied weak Zeeman energy coupling a topological superconducting nanowire as the center,the two superconducting electrodes have different superconducting phases by the applied magnetic flux which are sandwiching the quantum dot,which caused the Josephson current.When the weak coupling can not directly penetrate into the superconductor through the quasiparticle,and the energy of the quasiparticle is much smaller than that of the energy of the superconducting gap,the Josephson effect can be understood as the Andreev reflection.The spin current Josephson current that coupling the Majorana bound states with Josephson junction is studied in the model.Firstly,without considering the spin case of single quantum dot;considering the quantum dot coupled a trivial topological superconducting nanowire;considering the quantum dot coupled a non-trivial topological superconducting nanowire have proposed numerical calculation and theoretical analysis.When the quantum dot coupled a trivial topological superconducting nanowire,the total current is Josephson when the depression;while the quantum dot coupled a non-trivial topological superconducting nanowire,Josephson current permeability will appear obvious caused by Majorana bound state to coupled the quantum dot.Secondly,considering the spin case,respectively calculation and analysis of the spin Josephson current of the quantum dot coupled a non-trivial topological and coupled nothing were studied;we found that spin currents are different due to the penetration of Majorana quantum dots bound to Josephson junction.Finally,the process of that the quantum dot coupling a trivial topological superconducting nanowire turn to coupling a non-trivial,thecalculation and analysis of its transformation were studied,we found that there were Josephson current platform structure in this process.The reason is that a Majorana bound at the terminal of the topological superconducting nanowire state was formed which as a leakage to the quantum dot.