In particular, some UC Riverside researchers found that so-called bilayer graphene (BLG), which also has high mobility, can become an insulator once the number of electrons drops far enough. They did this by making a BLG sheet one plate of a capacitor, pulling away electrons. This isn't a gradual process of conductivity changing linearly as electrons are depleted; at a certain point, there's a fundamental shift in how the electrons organize themselves.
They go so far as to describe this shift as a form of "symmetry breaking," which gives mass to particles – and they fancy this as the embodiment of a new quantum particle.
You can find more on what's either a new particle or just another bit of useful knowledge about how to work with graphene in their unusually explanatory release.