TOPOLOGICAL-STRUCTURE OF THE LONDON EQUATION

A topological current is shown to exist in superconductivity. Using th e phi-mapping topological current theory, we have obtained a rigorous London equation with topological current, which reveals the inner rela tion between the condensate wave function psi and the induction (B) ov er 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 th e equation. Our theory, obtained without using any particular models o r hypotheses, can also be applied to the illustration of a vortex-anti vortex pair, vortex ring, and multicharged vortex. [S0163-1829(98)0402 5-9].