  We investigate the physical mechanisms for achieving an electrical control of
conventional spin-singlet superconductivity in thin films by focusing on the
role of surface orbital polarization. Assuming a multi-orbital description of
the metallic state, due to screening effects the electric field acts by
modifying the strength of the surface potential and, in turn, yields
non-trivial orbital-Rashba couplings. The resulting orbital polarization at the
surface and in its close proximity is shown to have a dramatic impact on
superconductivity. We demonstrate that, by varying the strength of the electric
field, the superconducting phase can be either suppressed, i.e. turned into
normal metal, or undergo a $0-\pi$ transition with the $\pi$ phase being marked
by non-trivial sign change of the superconducting order parameter between
different bands. These findings unveil a rich scenario to design
heterostructures with superconducting orbitronics effects.
