IBM has made an integrated circuit from carbon nanotubes:

With an 18-micron long carbon nanotube, the scientists built a 10-transistor ring oscillator, a device typically constructed to test new manufacturing technologies or materials. Using one instead of many carbon nanotubes to build an IC reduces the manufacturing steps and therefore cost...

...Electrical current moves more freely and faster through carbon nanotube than silicon, making carbon nanotube a more energy-efficient material for a speedier chip. It also is super small. A nanometer is a billionth of a meter, and a carbon nanotube is 50,000 times thinner than a human hair.

All these properties make carbon nanotube an appealing candidate for improving performance by piling on more and smaller transistors on a chip without causing overheating.

Moore's Law marches on.

"...Electrical current moves more freely and faster through carbon nanotube than silicon"

I thought silicon was an insulator. Am I mistaken - or did the reporter have a slip-of-the-mind?

Silicon is a semi-conductor

Silicon is a semi-conductor

I'm not an expert on things at this level (any level?), but isn't the fact silicon is a semiconductor what makes it valuable for its purpose? The whole point of using silicon is because electricity doesn't pass through it swiftly and easily -- helping to make the logic gates effective.

Or has the state of the art reached a point where that bit of resistance is no longer required?

No, the state of the art has reached a point at which there are better ways to build logic gates than using flow of holes and electrons in fluctuating fields. But I'm not sufficiently familiar with the actual mechanism in this case to explain it, unfortunately.

Semiconductors do not use pure silicon but dope it with metals like Arsenic and Gallium to give it their special electrical properties that make them usable.
Please read:

http://hyperphysics.phy-astr.gsu.edu/Hbase/solids/dope.html