  In their original formulation of superconductivity, the London brothers
predicted the exponential suppression of an $electrostatic$ field inside a
superconductor over the so-called London penetration depth, $\lambda_L$.
Despite a few experiments indicating hints of perturbation induced by
electrostatic fields, no clue has been provided so far on the possibility to
manipulate metallic superconductors via field-effect. Here we report
field-effect control of the supercurrent in $all$-metallic transistors made of
different Bardeen-Cooper-Schrieffer (BCS) superconducting thin films. At low
temperature, our field-effect transistors (FETs) show a monotonic decay of the
critical current under increasing electrostatic field up to total quenching for
gate voltage values as large as $\pm 40$V in titanium-based devices. This
$bipolar$ field effect persists up to $\sim 85\%$ of the critical temperature
($\sim 0.41$K), and in the presence of sizable magnetic fields. A similar
behavior was observed in aluminum thin film FETs. A phenomenological theory
accounts for our observations, and points towards the interpretation in terms
of an electric-field-induced perturbation propagating inside the
superconducting film. In our understanding, this affects the pairing potential
and quenches the supercurrent. These results could represent a groundbreaking
asset for the realization of an $all$-metallic superconducting field-effect
electronics and leading-edge quantum information architectures.
