Josephson effect in superconductive SNS heterostructures with barriers

The dc Josephson effect in a planar superconductor-normal-metal-superconductor (SNS) junction is studied in the existence of a δ barrier in the normal region. The Green function of the structure is obtained by solving the Gorkov equations for the structure and then the current is calculated from the Green functions. The effect of the strength and position of the barrier is investigated. The current shows a weak dependence on the position of the barrier and it is seen to be maximum when the barrier is at the middle of the normal region. Also it is found that the current shows a stronger dependence on the strength of the barrier at low temperatures. A comparative discussion of three possible types of Josephson junctions, the SIS, SCS, and SNS contacts, is presented