It looks like clear plastic corrugated roof panels to me.

They sell it at Menards or your local big box hardware store. We have it over our pergola. You have to slope the pergola slightly to get the water to run down. We love it. ours are "smoke" colored which look like they are lightly tinted car windows. This way you don't see the dirt as bad on top and they won't yellow.

I believe these are fiberglass, although the clear may be something else -- another poster said they were "polycarbonate." Lowes and Home Depot carry these as well and they also come in opaque colors.

How is the beam attached to the post. I am building something very similar and want to go with a thick front beam on a 6x6 cedar post. Have you used some sort of simpson ties? Or just bolted them down from the top? Thanks.

We offer polycarbonate sheets (very similar to, but better than fiberglass) in several tints on our website: http://www.postframeaccessories.com/polycarbonate.html. It is highly impact resistant and won't yellow overtime unlike fiberglass sheets which are similar but less expensive.

can you also grow vines over it or does the polycarbonate heat up and burn the plants?