Possible superconductivity in very thin magnesium films

It is known that noble metals such as gold, silver and copper are not supercon- 1 ductors, so as magnesium. This is due to the weakness of the electron-phonon interaction 2 which makes them excellent conductors but not superconductors. As it has recently been 3 shown for gold, silver and copper, even for magnesium it is possible that in very particular 4 situations superconductivity may occur. Quantum confinement in thin films has been 5 consistently shown to induce a significant enhancement of the superconducting critical 6 temperature in several superconductors. It is therefore an important fundamental question 7 whether ultra-thin film confinement may induce observable superconductivity in non- 8 superconducting metals such as magnesium. We study this problem using a generalization, 9 in the Eliashberg framework, of a BCS theory of superconductivity in good metals under 10 thin-film confinement. By numerically solving these new Eliashberg-type equations, we 11 find the dependence of the superconducting critical temperature on the film thickness, L. 12 This parameter-free theory predicts superconductivity in very thin magnesium films. We 13 demonstrate that this is a fine-tuning problem where the thickness must assume a very 14 precise value, close to half a nanometer.