Once you make the gate of a transistor small/thin enough, quantum effects take over. Electrons will randomly teleport into and through the gate causing the transistor to conduct when it shouldn't. I don't have numbers to hand, but it's on the order of a few atoms wide. There's really nothing that can be done about it either, as far as we know. Electrons just aren't physical objects at this scale, you can't simply exclude them from any given volume of space. The electron wave function will simply just appear wherever it wants (within the electron probability cloud). The only way to stop it is to make your insulating junction thicker than the probability cloud.
I don't know which is more ridiculous, the fact that reality works like this, or, that a species of apes was able to figure this out.
Yes, single-atom manipulation has already been demonstrated:
* https://en.wikipedia.org/wiki/IBM_(atoms)
Can you make transistors using that technique? Can you smaller?
Beyond that, engineering a quark-gluon plasma as a processor? I'd watch that Star Trek episode. (we might fantasize about stuff like that but we're roughly monkeys smashing rocks together in a cave vs. building an iPhone sort of gap away from that kind of thing unless somebody has a really good idea)
You also have quantum computing, which I think can/does use subatomic particles? Not sure about that one