  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.
