Spontaneous supercurrent and φ0 phase shift parallel to magnetized topological insulator interfaces

Employing a Keldysh-Eilenberger technique, we theoretically study the generation of a spontaneous supercurrent and the appearance of the phi(0) phase shift parallel to uniformly in-plane magnetized 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 nanojunction location. Our calculations 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 Andreev 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.