  It is common knowledge that noble metals are excellent conductors but do not
exhibit superconductivity. On the other hand, quantum confinement in thin films
has been consistently shown to induce a significant enhancement of the
superconducting critical temperature in several superconductors. It is
therefore an important fundamental question whether ultra-thin film confinement
may induce observable superconductivity in non-superconducting metals. We
present a generalization, in the Eliashberg framework, of a BCS theory of
superconductivity in good metals under thin-film confinement. By numerically
solving these new Eliashberg-type equations, we find the dependence of the
superconducting critical temperature on the film thickness $L$. This
parameter-free theory predicts a maximum increase in the critical temperature
for a specific value of the film thickness, which is a function of the number
of free carriers in the material. Exploiting this fact, we predict that
ultra-thin films of gold, silver and copper of suitable thickness could be
superconductors at low but experimentally accessible temperatures. We
demonstrate that this is a fine-tuning problem where the thickness must assume
a very precise value, close to half a nanometer.
