A new basis set for the description of electrons in superconductors

In the usual description of electrons in metals and superconductors, the single electron states are assumed to satisfy Bloch's theorem. This is because the electron–ion interaction is privileged over the electron–electron interaction. However the theory of hole superconductivity proposes that in the transition to superconductivity carriers ‘undress’ from the electron–ion interaction. I propose here a new basis set to describe electrons in the superconducting state that does not satisfy Bloch's theorem but instead is designed to optimize the electron–electron interaction. The new basis set favors a superconducting state where a spin current exists and where states near the bottom of the band become partially occupied, as predicted by the theory of hole superconductivity.