The Supercurrent Properties Of Topological Josephson Junctions Based On Topological Insulators

In recent years,topological insulators(TIs)have drawn great attentions,due to their novel features and potential applications in superconducting spintronics and quantum computation.The TIs are thoroughly new quantum states,which have a bulk band gap and gapless edge states or metallic surface states owing to the time-reversal symmetry.These edge and surface states are robust against disorder and nonmagnetic impurity.In particular,for a narrow two-dimensional(2D)TI with two edges getting close to each other,the overlap between edge states from opposite edges produces an energy gap,leading to the so-called interedge coupling,although the intraedge backscattering is still forbidden.Resultantly,the properties of 2D TI can be greatly modified and one remarkable property is the elastic interedge backscattering between the edge states at the two sides.In this article,applying the Blonder-Tinkham-Klapwijk(BTK)theory based on the Bogoliubov-de Gennes(BdG)equation,we study the supercurrent properties in the topological Josephson junctions based upon a TI.Firstly,we study the supercurrent properties in the superconductor(SC)/NM/SC Josephson junctions on a narrow 2D TI,taking into account the interedge coupling.It is shown that the interedge coupling could give rise to a 0-? transition modulated by the gate voltage,originating from an additional ? phase difference caused by the interedge backscattering.The 0-? transition in turn can manifest the helical spin texture of the edge states.Moreover,it is also shown that the interedge coupling could also give rise to the anomalous Josephson effect(the so-called ?0junctions),where the ground state phase shift ?0 that can be tuned continuously by the gate voltage,and thus can act as a phase battery.More interestingly,the ?0 junction owns the direction dependence of critical current,which can be adjusted by gate voltage,implying a very efficient performance of the device as a supercurrent rectifier.Secondly,we study the supercurrent properties in the SC/ferromagnetic insulator(FI)/NM/FI/SC Josephson junctions on a three-dimensional TI with the magnetizations of the two FIs having the same value.It is shown that when the direction of magnetization is fixed along the x axis in the left FI but is changed in the x-z plane in the right FI,a 0-? transition and the ground state phase shift ?0 can be manipulated by tuning the misorientation angle ? of the two FI layers,and thus the junction can be used as a magnetically controlled phase battery.In addition,when the magnetizations of the two FIs are both along the y axis,two properties are shown.One is that in the parallel(P)magnetization configuration,Josephson critical current Ic is strongly suppressed by increasing the strength of magnetic exchange energy m,exhibiting a supercurrent on/off switch effect.And the other is that,when the magnetization configuration is switched from the P to antiparallel(AP)configuration,the critical current Ic.in the AP is less than that in the P,exhibiting a very large supercurrent spin valve effect with supercurrent magnetoresistance(SMR)ratio as large as about 100%.