Planar Hall supercurrent and {\delta}{\phi}-shift in the topological Josephson junction

TL;DR

This paper theoretically explores how in-plane magnetization in topological insulator-based Josephson junctions induces a planar Hall supercurrent, causes a -shift, and enables -junction behavior, revealing new quantum transport phenomena.

Contribution

It develops a theory linking planar Hall supercurrent, spin transfer torque, and -shift in topological insulator Josephson junctions, highlighting novel quantum effects.

Findings

In-plane magnetization induces a planar Hall supercurrent.

A -shift occurs in the Josephson supercurrent under certain conditions.

The system can behave as a -junction with supercurrent flow at zero phase difference.

Abstract

We theoretically investigate Josephson junctions comprising superconductors and ferromagnets on the surface of three-dimensional topological insulators. We use Bogoliubov-deGennes formalism and show the in-plane magnetization creates a difference between the upward and downward population of Andreev modes and produces a planar Hall supercurrent. Due to the strong spin-orbit interaction of Dirac fermions, bending on the supercurrent imposes a spin transfer torque on the junction. We develop a theory and demonstrate the relation between planar Hall supercurrent and spin transfer torque. The parallel component of in-plane magnetization creates an anomalous supercurrent that can flow even in zero superconducting phase difference and make $\delta\phi$-junction. We show in some range,$\pi/2d \leq m_y \leq \pi/d$, there is a $\pi$ shift in the Josephson supercurrent. This research advances our understanding of quantum transport in 3DTIs and highlights their potential in emerging quantum technologies.