Spontaneous supercurrent and ${\phi}$0 phase shift parallel to magnetized topological insulator interfaces

TL;DR

This paper theoretically investigates how in-plane magnetization on topological insulator surfaces induces spontaneous supercurrents and a ${\

Contribution

It introduces a model showing how magnetization orientation influences spontaneous supercurrents and phase shifts in topological insulator-based Josephson junctions.

Findings

Spontaneous supercurrent flows parallel to the interface due to ${\

maximal supercurrent occurs near phase difference ${\\pi}

Spin-momentum locking affects the density of states at the interface

Abstract

Employing a Keldysh-Eilenberger technique, we theoretically study the generation of a sponta- neous supercurrent and the appearance of the ${\phi}$0 phase shift parallel to uniformly in-plane mag- netized superconducting interfaces made of the surface states of a three-dimensional topological insulator. We consider two weakly coupled uniformly magnetized superconducting surfaces where a macroscopic phase difference between the s-wave superconductors can be controlled externally. We find that, depending on the magnetization strength and orientation on each side, a spontaneous supercurrent due to the ${\phi}$0-states flows parallel to the interface at the junction location. Our calcula- tions demonstrate that nonsinusoidal phase relations of current components with opposite directions result in maximal spontaneous supercurrent at phase differences close to ${\pi}$. We also study the An- dreev subgap channels at the interface and show that the spin-momentum locking phenomenon in the surface states can be uncovered through density of states studies. We finally discuss realistic experimental implications of our findings.