Equilibrium properties of double-screened dipole-barrierSINISJosephson junctions

We report on a self-consistent microscopic study of the dc Josephson effect in SINIS junctions, where screened dipole layers at the $\mathrm{SN}$ interfaces generate a double-barrier multilayered SIN structure. Our approach starts from a microscopic Hamiltonian defined on a simple cubic lattice, with an attractive Hubbard term accounting for the short coherence length superconducting order in the semi-infinite leads, and a spatially extended charge distribution (screened dipole layer) induced by the difference in Fermi energies of the superconductor S and the clean normal metal interlayer N. We analyze the influence of such spatially inhomogeneous barriers on the proximity effect, the current-phase relations, the critical supercurrent and the normal-state junction resistance, for different normal interlayer thicknesses and barrier heights. These results are of relevance for high-$T_c$ grain boundary junctions, and also reveal one of the mechanisms that can lead to low critical currents of apparently ballistic $\mathrm{SNS}$ junctions while increasing its normal-state resistance in a much weaker fashion. When the N region is a doped semiconductor, we find a substantial change in the dipole layer (generated by a small Fermi-level mismatch) upon crossing the superconducting critical temperature, which is a signature of the proximity effect and which might be related to recent Raman studies in Nb/InAs bilayers.