| In recent years,topological insulator materials have attracted great attention and become one of the important research hotspots and frontiers in condensed matter physics.It is a kind of material different from the traditional metal and insulator.It is a metal state system with internal insulation but no gap on the surface.In addition,when a topological insulator comes into contact with a superconductor or ferromagnetic insulator,the time inversion symmetry is destroyed.Due to the proximity effect,the boundary or surface state presents a unique quantum transport characteristic,which has great potential application value in the fields of spintronics and quantum information.In this paper,applying the Blonder-Tinkham-Klapwijk(BTK)theory based on the Bogoliubov-de Gennes(BdG)equation,we study the supercurrent properties of the topological Josephson junction composed of ferromagnetic insulator and non-traditional superconductor based on a three-dimensional topological insulator(TI)through theoretical analysis and numerical calculation.Firstly,we study properties of superconducting current in s-wave superconductor/ferromagnetic insulator/normal TI/ferromagnetic insulator/d-wave superconductors(s-SC/FI1/N/FI2/d-SC)Josephson junction without considering the topological insulators coupling on the surface of the two cases,,among them d-wave superconductor is dxv-wave or dx2-v2-wave superconductors.Fixed ferromagnetic region F1 along the x axial direction,the exchange of F2 magnetic field direction in x-z plane or x-y plane,and both are equal in size,it was found that anomalous Josephson effect can occur,and the Superfluid exchange with changing the angle of directions between the magnetic fields,so as to realize the functions of the phase battery and so on.In particular,"Superfluid Rectification Effect" and"Quantization Platform Phenomenon" can also occur in the s-SC/FI1/N/FI2/dx2-v2-SC Josephson junctions on a three-dimensional TI.Not only that,when the direction of the magnetic exchange field in the two ferromagnetic regions is fixed in the x axial direction,the phase stored by the phase accumulator in a certain range of magnetic exchange field is almost unchanged,realizing the magnetic control quantization platform phenomenon.In addition,changing the length of the ferromagnetic region not only has an important effect on the size of the strange Josephson effect,but also can achieve 0-? junction transformation.Secondly,without considering the topological insulators coupling on the surface of the two cases,we study superconducting current properties of d-wave superconductor/ferromagnetic insulator/normal TI/ferromagnetic insulator/d-wave superconductors(d-SC/FI1/N/FI2/d-SC)Josephson junction under different magnetic configurations,among them d-wave superconductor is dxv-wave or dx2-v2-wave superconductors.Fixed the direction of the ferromagnetic region along the x axis or the y axis and the direction of the ferromagnetic region in three equal planes,and the magnitude of the two is equal.The results show that,in addition to changing magnetic exchange direction angle in the y-z plane in dxv-wave symmetry superconducting junction,it follows the regular Josephson effect.The anomalous Josephson effect will also occur in the other kinds of structures.With changing the angel between the directions of two exchange magnetic fields in planes,the superfluid is correspondingly affected and it is used to implement the anomalous Josephson current.In addition,under the condition that fixed the components along the x axis or along the y axis are equal,if the size of the components along the other axis are changed,the anomalous Josephson effect will also occur in the junction. |
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