Multiphoton intersubband transitions in an armchair graphene ribbon subject to dc electric field

We study analytically the influence of the time-independent electric field on the multi-photon absorption and Rabi oscillations (Franz–Keldysh (F–K) effect) in an armchair graphene nanoribbon (AGNR), caused by the time-oscillating electric field of an intense light wave. Constant (dc) electric field is taken to be much weaker than the ac light wave field. Both fields are polarized parallel to the ribbon axis. Following the Wallace model, the Dirac equation for the massless electron subject to the ribbon confinement and electric fields is employed. In the resonant approximation, the electron–hole pair production rate for the electron transitions between the valence and conduction size-quantized subbands, corresponding multiphoton absorption coefficient, as well as the characteristics of the Rabi oscillations are derived in an explicit form. We explicitly trace the dependencies of the absorption coefficient and Rabi oscillations parameters on the electric fields magnitudes and ribbon width. An interplay between the two mechanisms of the intersubband transitions is found to occur. It is shown that the Rabi frequency and intensities of the absorption peaks are determined mostly by the strong electric field of the light wave (multiphoton assisted mechanism), whereas the weak dc electric field drastically modifies the frequency spectra of the Rabi oscillations and multiphoton absorption (tunneling mechanism). Estimates of the expected experimental values for the typical AGNR, electric field strengths and driving frequencies show the experimental feasibility of the F–K effect. Our results demonstrate that the AGNRs are a suitable 1D condensed matter media, in which the quantum electrodynamic vacuum decay can be detected using the current laboratory technologies.