The vortex structure of Dirac's equation for superconducting pairs in a magnetic field

It has been suggested recently that one can attach an electrodynamic meaning to quantum states of particles in a magnetic field described by Dirac's equation, the electric and magnetic fields and currents being linearly related to the components of the four-vector wavefunctions. As such one can calculate the internal fields from knowledge of quantum states and conversely knowledge of the fields allows to reconstruct the wavefunctions. In this paper we present the internal fields and currents in superconductors in a magnetic field by using this method, corresponding to Landau's states of lowest energy. We find that such states exhibit vortex structure with a London's behaviour at distances sufficiently far from their center; the structure of an isolated vortex is studied through the form of the field and current corresponding isomorphically to the state. The lower and upper critical fields arise from the condition of overlap of orbits within a length of the order of the London's and coherence length respectively. The lattice of vortices around the upper field is found. Some properties of excited states are also discussed. This method could reveal useful in visualization techniques of quantum states in type II superconductors