On the Theory of Superconductivity

The existing phenomenological theory of superconductivity is unsatisfactory, since it does not allow us to determine the surface tension at the boundary between the normal and the superconducting phases, and does not allow for the possibility to describe correctly the destruction of superconductivity by a magnetic field or current. In the present paper, a theory is constructed which is free from these faults. We find equations for the ψ-function of the ‘superconducting electrons’ which we introduced and for the vector potential. We have solved these equations for the one-dimensional case (a superconducting half-space and flat plates).

The theory makes it possible to express the surface tension in terms of the critical magnetic field and the penetration depth of the magnetic field in superconductors. The penetration depth depends in a strong field on the field strength and this effect will be especially evident in the case of small size superconductors. The destruction of superconductivity in thin plates by a magnetic field is through a second-order phase transition, and it only becomes a first-order transition starting with plates of a thickness more than a certain critical thickness. While the critical external magnetic field increases with the decreasing thickness of the plates, the critical current for destroying the superconductivity of plates decreases with decreasing thickness.