The Born-Oppenheimer approximation in graphene: A time-dependent perspective

In graphene, electron-phonon interactions are known to play an important role in the loss of electronic wavefunction character and relaxation processes following photoexcitation. We model electronic interactions with nuclear vibrations from a microscopic, time-dependent perspective. Utilizing a time-dependent tight-binding Hamiltonian for the electronic degrees of freedom, we numerically determine the time-evolved electronic wavefunction in the presence of classical nuclei vibrating along normal modes. We examine the solutions by comparing them to those predicted within the adiabatic Born-Oppenheimer (ABO) approximation. We find that, for electronic states on energetically isolated potential energy surfaces, the adiabatic Born-Oppenheimer (ABO) approximation offers an accurate picture of time-evolution. But, in the presence of avoided crossings, the ABO approximation quickly breaks down as the electronic wavefunction becomes a superposition of ABO basis states. Moreover, electronic character is preserved over several vibrational periods for a finite lifetime, indicating highly diabatic time-evolution.