  We report on the first realization of Nb-based \textit{all-metallic} gated
Dayem nano-bridge field-effect transistors (Nb-FETs). These Josephson devices
operate up to a temperature of $\sim 3$ K, and exhibit full suppression of the
supercurrent thanks to the application of a control gate voltage. The
dependence of the kinetic inductance and of the transconductance on gate
voltage promises a performance already on par with so far realized metallic
Josephson transistors, and let to foresee the implementation of a
superconducting digital logic based on Nb-FETs. We conclude by showing the
practical realization of a scheme implementing an all-metallic gate-tunable
\emph{half-wave} rectifier to be used either for superconducting electronics or
for photon detection applications.
