Electron Transitions For Dirac Hamiltonians With Flat Bands Under Electromagnetic Radiation: Application To The Alpha - T-3 Graphene Model

In a system with a Dirac-like linear dispersion there are always states that fulfill the resonance condition for electromagnetic radiation of arbitrary frequency Omega. When a flat band is present, two coexistent kinds of resonant transitions are found. Considering the alpha - T-3 graphene model as a minimal model with a flat band and Dirac cones and describing the dynamics using the interaction picture, we study the band transitions induced by an external electromagnetic field. We find that transitions depend upon the relative angle between the electron momentum and the electromagnetic field wave vector. For parllel incidence, the transitions are found using Floquet theory, while for other angles perturbation theory is used. In all cases, the transition probabilities and the frequencies are found. For the parallel momentum, no symmetry is broken by the field, and light does not change the spectrum, while for some limit special cases of the parameter alpha or by charge doping, the system behaves as a three-level or two-level Rabi system. All these previous results were compared with numerical simulations. Good agreement was found between both. The obtained results show a rich system in which different kinds of transitions coexist.