Delocalized electrons: conductivity and superconductivity

Abstract

When wavefunction of crystal was projected out in atomic basis, we found that electrons of s orbital had localization-delocalization duality, and the ones of p and d orbital were only localized in three dimensional crystal lattice. The existence of s type delocalized electrons is based on three dimensional ordering of electron density in metals. Then charge carriers of metals for conductivity are just such delocalized electrons so that the ones for superconductivity are electron pairs of s wave. This way could also be generalized to two dimensional case for CuO2 plane of cuprate superconductor to explain its phase diagram qualitatively. We also gave some ab initio explain for Hubbard model.