Microscopic self-consistent theory of Josephson junctions includingdynamical electron correlations

Abstract

We have developed a rapid computational algorithm that allows for a fullyself-consistent solution of the three-dimensional Bogoliubov-de Gennesequations for a Josephson junction. This microscopic model is appropriate forshort-coherence-length superconductors, Josephson junctions with stronglycorrelated proximity-coupled weak links and systems where the barrierthickness isthe same order of magnitude as the coherence length. This is a regime that isusually not described by the highly successful analytic theories of Josephsonjunctions developed over the past 35 years. The formalism is applied to thesimplest possible model as an example, but can easily incorporate correlationeffects (via the dynamical mean field theory) with relatively little extracost. We examine current-phase relations, effects of non-magnetic impurities,interfacial scattering and the local density of states within the barrier.This last `theoretical spectroscopy' shows the evolution of Andreev boundstates in the presence of a Josephson current, illustrating the expectedDoppler shift. We also calculate the figure of merit, IcRN, and findthat our self-consistent solutions produce a variation of this product, whichcan be dramatically increased for coherent SNSNS junctions which have anadditional thin superconducting layer within the normal-metal region.