Josephson effect in normal and ferromagnetic topological insulator planar, step and edge junctions

Abstract

We investigate Josephson junctions on the surface of a three-dimensional topological insulator in planar, step, and edge geometries. The elliptical nature of the Dirac cone representing the side surface states of the topological insulator results in a scaling factor in the Josephson current in a step junction as compared to the planar junction. In edge junctions, the contribution of the Andreev bound states to the Josephson current vanishes due to spin-momentum locking of the surface states. Furthermore, we consider a junction with a ferromagnetic insulator between the superconducting regions. In these ferromagnetic junctions, we find an anomalous finite Josephson current at zero phase difference if the magnetization is pointing along the junction (and perpendicular to the Josephson current). An out-of-plane magnetization with respect to the central region of the junction opens up an exchange gap and leads to a non-monotonic behavior of the critical Josephson current for sufficiently large magnetization as the chemical potential increases.

arXiv comment8 pages, 5 figures

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• Anomalous Josephson effect in semiconducting nanowires as a signature of the topologically nontrivial phase
• Geometric Josephson effects in chiral topological nanowires
• Anomalous Josephson effect in planar noncentrosymmetric superconducting devices
• Novel Majorana mode and magnetoresistance in ferromagnetic superconducting topological insulator
• Transport in a thin topological insulator with potential and magnetic barriers
• Dominant Majorana bound energy and critical current enhancement in ferromagnetic-superconducting topological insulator
• Nonlinear standing waves on planar branched systems: Shrinking into metric graph