A unified theory of superconductivity

In this paper, we study the reliability of BCS theory as a scientific explanation of the mystery of superconductivity. It is shown clearly that the phonon-mediated BCS theory is fundamentally incorrect. Two kinds of glues, pairing (pseudogap) glue and superconducting glue, are suggested based on a real space Coulomb confinement effect. The scenarios provide a unified explanation of the pairing symmetry, pseudogap and superconducting states, charge stripe order, spin density wave (SDW), checkerboard-type charge-ordered phase, magic doping fractions and vortex structures in conventional and unconventional (the high-Tc cuprates and MgB2) superconductors. The theory agrees with the existence of a pseudogap in high-temperature superconductors, while no pseudogap feature could be observed in MgB2 and most of the conventional superconductors. Our results indicate that the superconducting phase can coexist with a inclined hexagonal vortex lattice in pure MgB2 single crystal with a charge carrier density ps=1.49*10^{22}/cm^{3}. Finally, the physical reasons why the good conductors (for example, Ag, Au, and Cu) and the overdoped high-Tc superconductors are non-superconducting are also explored.