  In a small subset of type II superconductor films, the critical current is
determined by a weakened Bean-Livingston barrier posed by the film surfaces to
vortex penetration into the sample. A film property thus depends sensitively on
the surface or interface to an adjacent material. We theoretically investigate
the dependence of vortex barrier and critical current in such films on the
Rashba spin-orbit coupling at their interfaces with adjacent materials.
Considering an interface with a magnetic insulator, we find the spontaneous
supercurrent resulting from the exchange field and interfacial spin-orbit
coupling to substantially modify the vortex surface barrier, consistent with a
previous prediction. Thus, we show that the critical currents in
superconductor-magnet heterostructures can be controlled, and even enhanced,
via the interfacial spin-orbit coupling. Since the latter can be controlled via
a gate voltage, our analysis predicts a class of heterostructures amenable to
gate-voltage modulation of superconducting critical currents. It also sheds
light on the recently observed gate-voltage enhancement of critical current in
NbN superconducting films.
