I have a 1" carbon steerer and the inside dia. is 20 mm. I can't find a supplier for a Schmolke stem cap in this size.
I have tried a few places in EU but no response yet.

Got a cheap and better solution. SInce you have a 1 in tube just jam a bar end plug in there, and get a zipp set if you want carbon.

That's a good idea if it works. I just ordered a set of schmolke bar end plugs. I'll see if one of them will work. The Zipps are part carbon and part rubber. I don't think they would work.
I wonder if I could turn down the 22mm Schmolke to 20mm. My steerer is pretty thick as steerers go.
How thick are the walls of the Schmolke stem cap?