A Manifold Approach to Superconductivity

Although, it’s been only a 113 years since the discovery of superconductors and superconductivity the development in condensed matter physics is impeccable. Today we know a lot about them, their types and the phenomenon associated with them but the cause of superconductivity in type-II superconductors is still debatable. Although there have been profound theories like Ginzburg-Landau theory, London penetration effect describing flux pinning, spin fluctuations, quantum vortices in super fluids and so on, they aren’t completely able to describe the phenomenon in cuprates, non-phononic mechanisms in superconductors etc. In this paper we approach electrons as superfluid in a complex manifold and topological variations in the manifold due to application of magnetic field to justify the two critical field strengths in type two superconductors and the cause of superconductivity in type-II superconductors. We find that in type-II superconductors, they can superconduct with the presence of non-zero resistance i.e. superconductivity is more fundamental than zero resistance in type-II superconductors, the actual case being the energy gap function created by overlapping of electron wave functions in complex n- dimensional manifolds.