Material that lets air and sunlight in & keeps rain out?
Sunlight, no. "Breathable", yes. That's what "Gore-tex" fabric is famous for. They were the first / biggest, but now many other suppliers have released similar breathable waterproof fabrics made from PTFE (a.k.a. "teflon") fibers. I don't think however that Gore-tex makes anything clear or even opaque.

And go get a second mortgage on your house if you want a large tarp made of it; the cost is very very high.