Landau level transitions indoped graphene in a time dependent magnetic field

The aim of this work is to describe the Landau levels transitions of Bloch electrons in doped graphene with an arbitrary time dependent magnetic field in the long wavelength approximation. In particular, transitions from the m Landau level to the m + 1 and m + 2 Landau levels are studied using time-dependent perturbation theory. Time intervals are computed in which transition probabilities tend to zero at low order in the coupling constant. In particular, Landau level transitions are studied in the case of Bloch electrons travelling in the direction of the applied magnetic force and the results are compared with classical and revival periods of electrical current in graphene. Finally, current probabilities are computed for the n = 0 and n = 1 Landau levels showing expected oscillating behavior with modified cyclotron frequency.