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.
Categories: cond-mat.supr-con cond-mat.mes-hall cond-mat.mtrl-sci cond-mat.str-el quant-ph