  Recent experiments suggest the possibility to tune superconductivity in
metallic nanowires by application of modest gate voltages. It is largely
debated whether the effect is due to an electric field at the superconductor
surface or small currents of high-energy electrons. We shed light on this
matter by studying the suppression of superconductivity in sample geometries
where the roles of electric field and electron-current flow can be clearly
separated. Our results show that suppression of superconductivity does not
depend on the presence or absence of an electric field at the surface of the
nanowire, but requires a current of high-energy electrons. The suppression is
most efficient when electrons are injected into the nanowire, but similar
results are obtained also when electrons are passed between two remote
electrodes at a distance $d$ to the nanowire (with $d$ in excess of
$1~\mathrm{\mu m}$). In the latter case, high-energy electrons decay into
phonons which propagate through the substrate and affect superconductivity in
the nanowire by generating quasiparticles. We show that this process involves a
non-thermal phonon distribution, with marked differences from the loss of
superconductivity due to Joule heating near the nanowire or an increase in the
bath temperature.
