How do you make a hole in graphene without creating a mobius strip?
Answer: By using the absorption of a phonon by an electron in the lower cone of momentum space to raise it to the upper cone leaving a hole. Using brute force to knock a carbon atom out of a benzene ring, i.e., hexagon, leaves a pentagon which looks like a mobius strip in momentum space.
Raman spectroscopy confirms that graphene violates the adiabatic Born–Oppenheimer approximation which is based on separating the motions of electrons and phonons, and considering these as frozen. This is invalid because of the role of hole creation in phonon propagation. It is interesting how you have three types of dark excitons and one light in nanotubes. It is even more interesting to use excitons, i.e., bound electron hole pairs, in bilayer graphene to form a Bose Einstein condensate. I read about plasmons in graphene, but do not know if they really exist.