Anomalous Josephson current through a topological noncoplanar ferromagnetic trilayer

We present an anomalous Josephson effect in a TI-based Josephson junction with a ferromagnetic insulator (FI) trilayer which has noncoplanar magnetizations. It is shown that there exist equal spin-singlet and -triplet correlations due to the magnetism-tuning chiral Dirac energy band structure combined with the spin precession and selective equal spin Andreev reflection by chiral Majorana modes (CMMs). The consequent anomalous Josephson supercurrent is exhibited, in which a 0-π or similar 0 - π state transition through phase shift is induced only by exchange field strengths of the first FI region, while the ϕ0 supercurrent and the maximum one gradually drop with the increase of exchange field strengths of the second and third FI regions without relative state transitions. The much different features are found by varying the lengths of trilayer. The Andreev bound states without hybridization for the CMM administrate these features, which could be used to probe and confirm the zero energy CMM. In addition, the corresponding free energies are presented and discussed.

Suppressed Andreev reflection and helical Andreev bound states in triplet superconductor three-dimensional topological insulator

Effect of proximity-induced unconventional p-wave superconductivity in a three-dimensional topological insulator-based S/F/S structure on the Andreev bound states (ABSs) and Josephson supercurrent is studied. We investigate, in detail, the suppression of Andreev reflection and helical ABSs in the presence of three types of triplet superconducting gap. The magnetization of ferromagnetic section is perpendicular to the surface of junction. The influence of such features on the supercurrent flow on the surface of the topological insulator is studied. We carry out our goal by introducing a relevant form of Dirac spinors for gapless renormalized by chemical potential μ excitation states. Therefore, it enables us to consider the virtual Andreev process, simultaneously, and we propose to investigate it in a tunneling conductance junction. It is shown that the results obtained in this case are completely different from those in conventional superconductivity, as s- or d-waves, for example, the magnetization is found to decrease the gap for px and px+ipy case, whereas increase it for py order. Strongly suppressed Andreev reflection is demonstrated.