  Iron-based superconductors have great potential for high-power applications
due to their prominent high-field properties. One of the central issues in
enhancing the critical current density of iron-based superconducting wires is
to reveal the roles and limitations of grain boundaries in supercurrent
transport. Here, we finely tuned the electronic properties of grain boundaries
by doping Ba1-xKxFe2As2 superconductors in a wide range (0.25<x<0.598). It is
found that the intra-grain Jcintra peaks near x~0.287, while the inter-grain
Jcinter has a maximum at about x~0.458. Remarkably, the grain boundary
transparency parameter defined as Jcinter/Jcintra rises monotonically with
doping. Through detailed microscopic analysis, we suggest that the FeAs
segregation phase commonly existing at grain boundaries and the adjacent grains
constitute superconductor-normal metal-superconductor (SNS) Josephson junctions
which play a key role in transporting supercurrent. A sandwich model based on
the proximity effect and the SNS junction is proposed to well interpret our
data. It is found that overdoping in superconducting grains largely strengthens
the proximity effect and consequently enhances the intergrain supercurrent. Our
results will shed new insights and inspirations for improving the application
parameters of iron-based superconductors by grain boundary engineering.
