Aluminium becomes a superconductor at a temperature below $1.91$K. But I am quite certain that all metals do not exhibit superconductivity even when the temperature is lowered to nanokelvin or below. Why is it that all metals do not become superconductor?
This is actually an unsolved and very interesting problem. Consider for example the case of the three best known conventional conductors: gold, silver, and copper. None of them have been shown to superconduct. This is one of the reasons for the controversy surrounding this paper.
A few potential reasons are,
- Within a BCS framework, the phonon-electron coupling is too weak to lead to a discernible $T_c$.
- The Fermi surface is too complex/asymmetric and leads to strong mixing of the Landau parameters. So a strong onsite Coulomb repulsion (which leads to strong repulsion in the s-wave channel) would affect all angular momentum channels, and suppress non-BCS mechanisms like Kohn-Luttinger.
- (not applicable to the aforementioned elemental metals) The metal is too dilute which leads to a small density of state at the Fermi level thereby suppressing superconductivity.