Why is BCS theory unable to predict superconducting materials?
The figure below shows a plot of the superconducting critical temperatures of the elements versus the inverse Hall coefficient. Note that superconductors are predominantly found among materials with positive Hall coefficient. Materials with positive Hall coefficient have hole carriers. Materials with negative Hall coefficient have electron carriers. BCS theory doesn’t know the difference between electrons and holes, it treats them as equivalent quasiparticles. However as pointed out by Chapnik many years ago, superconductors seem to care a lot about whether the carriers are electrons or holes: if carriers are electrons (negative Hall coefficient) the material, whether element or compound, is not superconducting. BCS theory cannot explain this very general empirical observation. The theory of hole superconductivity proposes an explanation for why superconductors have to have hole carriers. A simple garage analogy illustrates the basic point qualitatively: single holes have difficulty pr
