Microscopic self-consistent theory of Josephson junctions including dynamical electron correlations

We have developed a rapid computational algorithm that allows for a fully s elf-consistent solution of the three-dimensional Bogoliubov-de Gennes equat ions for a Josephson junction. This microscopic model is appropriate for sh ort-coherence-length superconductors, Josephson junctions with strongly cor related proximity-coupled weak links and systems where the barrier thicknes s is the same order of magnitude as the coherence length. This is a regime that is usually not described by the highly successful analytic theories of Josephson junctions developed over the past 35 years. The formalism is app lied to the simplest possible model as an example, but can easily incorpora te correlation effects (via the dynamical mean field theory) with relativel y little extra cost. We examine current-phase relations, effects of non-mag netic impurities, interfacial scattering and the local density of states wi thin the barrier. This last 'theoretical spectroscopy' shows the evolution of Andreev bound states in the presence of a Josephson current, illustratin g the expected Doppler shift. We also calculate the figure of merit, IcRN, and find that our self-consistent solutions produce a variation of this pro duct, which can be dramatically increased for coherent SNSNS junctions whic h have an additional thin superconducting layer within the normal-metal reg ion.