# Why is it that all metals do not become superconductor by lowering the ambient temperature?

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?

• With the exception of lithium, monovalent metals do not become superconducting (alkalis, coinage metals). Something to do with a simple Fermi surface. – Pieter Oct 10 '18 at 15:42
• @mithusengupta123 Did you learned that every material, in general, have a bound state energy below fermi energy which corresponds to attractive effective potential, first given by cooper. According to this, superconducting state exist for all materials at temperature below certain critical temparature and the value of Tc is depends on the material properties. – Aman pawar Oct 10 '18 at 17:50
• @Amanpawar - well, there are requirements on the Fermi surface and the electron-ion coupling for there to, in fact, actually be an attractive effective potential. For many real metals, there is not actually a net attractive potential allowing for the formation of Cooper pairs. – Jon Custer Oct 10 '18 at 17:56
• There is no guarantee that pairing must happen at all in real materials. – Jon Custer Oct 10 '18 at 18:17
• It is possible that even good metals like gold and copper superconduct, but at temperatures too low to achieve. For other metals with magnetic order like iron, superconductivity will not happen at any temperature. Though who knows what happens when the temperature is so low that the nuclei de Broglie wavelength starts to matter! – KF Gauss Oct 12 '18 at 4:54

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,

1. Within a BCS framework, the phonon-electron coupling is too weak to lead to a discernible $$T_c$$.
2. 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.
3. (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.