A Study Of The Transport Properties Of Josephson Junctions Based On Three-dimensional Topological Insulators

Since the discovery of topological insulators(TIs),they have been triggering much interest,and exhibited some novel physical properties.In addition,the TIs have very important and wide applications in superconducting spintronics and quantum computing.The bulk of the TIs is insulated,while their two-dimensional edge states or three-dimensional surface states with no energy gap are metallic.These states are protected by time reversal symmetry and robust again disorder and the interference of impurities.In particular,the TIs themselves do not have superconductivity and ferromagnetism,but they can be achieved through proximity effects.Because the TIs have a unique energy band structure,superconducting tunnel junctions based on TIs could exhibit novel quantum transport properties.And thus,in this paper,we extend the Blonder-Tinkham-Klapwijk(BTK)theory to study the quantum transport prope-rties in the three-dimensional(3D)TI-based Josephson junction.Firstly,we study the supercurrent properties in the s-wave superconductor(SC)/F1/F2/F3/SC based on 3D TI with F1,F2 and F3 being three ferromagnetic insulators(FI),where,the magnetic exchange fields in F1,F2 and F3 are along the directions of x,y,and z axes,respectively.It was found that the magnetic exchange field strength and width of the F1 region can not only induce“0-?”and“similar 0-?”transitions but also lead to the so-called“?₀”junction which is used to design the phase battery.However,the magnetic exchange field strength and width in F2 and F3 regions only suppress the Josephson current,and they have a stronger inhibiting effect on the superconducting current in F2 region.Correspondingly,we also analyzed the relationship between the bound energy and phase difference,then obtained the different behaviors in Majorana Fermi zero modes.Secondly,the magnetic anisotropic heat transport properties of SC/FI/SC Josephson junction based on 3D TIs are studied,and three novel heat transport properties have been revered:(1)The thermal conductivity and heat flow are very sensitive to the size and direction of the magnetic exchange field;(2)The appearance of negative differential thermal conductance(NDTC)is due to the change in the size and direction of the magnetic exchange field;(3)The interplay between Majorana fermion and heat transport is obtained.These novel phenomena are caused by the competitive relationship between energy gap function and temperature combined with chiral surface states.Therefore,the magnetic exchange field can not only regulate heat transport,but also probe and confirm the presence of Majorana fermions.We expect that the unusual heat transport of the heterojunction will help design the cryogenic device with heat dissipation and quantum thermal interferometer.