Topological structure of the London equation

A topological current is shown to exist in superconductivity. Using the phi-mapping topological current theory, we have obtained a rigorous London equation with topological current, which reveals the inner relation between the condensate wave function psi and the induction (B) over right arrow. It is also shown that the equation is characterized by the Hopf index and Brouwer degree of phi mapping. As a result, the so-called modified London equation, which describes the distribution of the magnetic field for isolated vortices, is only a special case of the equation. Our theory, obtained without using any particular models or hypotheses, can also be applied to the illustration of a vortex-antivortex pair, vortex ring, and multicharged vortex. [S0163-1829(98)04025-9].