I've been looking for densely weaved bed sheets and pillow cases and such, and well, the search term you generally want for that is "satin". Tons of products use a satin weave out of cotton.
Problem is, satin fabric was traditionally made with silk, back in medieval China, so there's the possibility that when a company writes down "satin", they implicitly mean "silk".
I have yet to actually see it in any shops, as presumably the price would be much higher, but it still means I have to double-check every time, which is really annoying...