Abstract
Most theoretical discussions of transport in superconductors in which the gap parameter Δ( r, t) varies in space and time have made use of local models or of time-dependent versions of the Ginzburg-Landau theory. The general non-local theory is difficult to treat mathematically, but progress is being made with use of Green's function methods and with use of the WKB method for solution of the Bogoliubov quasiparticle equations. Applications of the latter method to vortex lines in type-II superconductors and to flow normal to the N-S in the intermediate state of type-I superconductors will be discussed. Although complete solutions have not been obtained, it is possible to see qualitatively how the transition from super to normal flow occurs in the boundaries and how electric fields are set up to drive current through the normal regions with consequent dissipation.
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