Lazy electrons in graphene

Significance The Born–Oppenheimer approximation has had an ambiguous role in condensed matter theory for many years. Without it, solids would seem to be a “pea soup” of electrons and nuclei. On the other hand, using the adiabatic Born–Oppenheimer, one inevitably encounters multiple narrow avoided crossings of electronic energy levels as a function of nuclear positions. “Adiabatic” is key here: there exist “diabatic” Born–Oppenheimer approximations that the time-dependent tight-binding work reported here shows are much more robust. We find that the electrons are “lazy” in that they respond weakly and slowly to nuclear geometry changes. Our results suggest an electron–nuclear diabatic wave function that may have significant impact on analytical and numerical approaches to spectroscopy and dynamics of extendedπ -electronic systems.