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

TL;DR

This paper explores the behavior of Josephson junctions on topological insulators, revealing how geometry and magnetization influence supercurrent flow and uncovering novel effects like anomalous currents and non-monotonic critical current behavior.

Contribution

It provides new insights into how surface state geometry and ferromagnetic insulators affect Josephson effects in topological insulator-based junctions.

Findings

Elliptical Dirac cone causes a scaling factor in step junctions.

Andreev bound states do not contribute in edge junctions due to spin-momentum locking.

Ferromagnetic insulators induce anomalous Josephson currents and non-monotonic critical current behavior.

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.