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 δϕ-junction. We show in some range,π/2d≤my≤π/d, there is a π shift in the Josephson supercurrent. This research advances our understanding of quantum transport in 3DTIs and highlights their potential in emerging quantum technologies.
@article{arxiv.2409.04848,
title = {Planar Hall supercurrent and {\delta}{\phi}-shift in the topological Josephson junction},
author = {Morteza Salehi},
journal= {arXiv preprint arXiv:2409.04848},
year = {2025}
}