Lazy electrons in graphene.

Within a tight-binding approximation, we numerically determine the time evolution of graphene electronic states in the presence of classically vibrating nuclei. There is no reliance on the Born-Oppenheimer approximation within the p-orbital tight-binding basis, although our approximation is "atomically adiabatic": the basis p-orbitals are taken to follow nuclear positions. Our calculations show that the strict adiabatic Born-Oppenheimer approximation fails badly. We find that a diabatic (lazy electrons responding weakly to nuclear distortions) Born-Oppenheimer model provides a much more accurate picture and suggests a generalized many-body Bloch orbital-nuclear basis set for describing electron-phonon interactions in graphene.