I've heard a lot about graphene and carbon nanotubes, but today was my first visit to the "molybdenum disulfide" Wikipedia entry. Researchers at Tu Wien in Austria have developed a microprocessor that uses 2D molybdenum disulfide as the semiconductor (via KurzweilAI).
"2D" materials are materials built out of a thin layer of atoms — sometimes they’re a single atom thick. There are a bunch of reasons this is a good idea for electronics: a chip that thin can be transparent, flexible, and use less power than a traditional silicon chip. Of course, first you have to figure out how to build one.
The 0.6mm² chip built by the Tu Wien team is a one-bit microprocessor with 115 transistors. It's not really Crysis-ready hardware, but it can run programs — either with its built-in memory, or external memory. Apparently the architecture can be expanded to support more than one bit of data at a time by connecting multiple devices in parallel. Either way, it's the most complex circuitry ever made out of a 2D material.
As with most in-the-lab accomplishments like this, we're a long ways from a real product based on this technology. This chip was basically built by hand, piece by piece, and in their paper the researchers mention a low yield of functional devices, due to the complexity.