Intense Laser Pulse Interaction With Graphene and Graphene Ribbons

In this work we investigate quantum mechanically the interaction of an intense ultrashort laser pulse with the graphene monolayer as well as with the armchair graphene ribbons of different widths. We consider a tight binding (TB) Hamiltonian of the monolayer graphene and give two rules for deriving the dispersion relations of the armchair graphene ribbons of any width, N, from the TB eigenvalues of the monolayer. The band structure of the monolayer and the armchair ribbons of different widths are discussed with illustrations. The time-dependent wavefunctions of the systems and the expectation values of interest are determined by solving the coupled equations of the band amplitudes “exactly” (numerically). First, simulations are made for the population excitation in the conduction band (CB) from the valence band (BV), the VB-CB interband correlation (or “coherence”), the intraband, the interband and the total currents in the monolayer graphene. The graphene currents are compared with the corresponding currents induced in an armchair ribbon (width, N = 3). The change from the 2D monolayer to the 1D ribbon shows a remarkable transition of the dominance of the intraband current that leads to a near steady total current in the monolayer, to a dominance of the interband current in the ribbon that induces an oscillatory current in the ribbon beyond the pulse duration. The difference observed might be a combined effect of the “confinement” in one dimention and a finite band-gap minimum in the case of the ribbon. However, this transition should be further investigated for better clarity. A brief comparison of the radiation spectra emitted from the monolayer and from the ribbon is also made. They show a grossly similar structure and a relative insensitivity with respect to the detailed structure of the targets chosen. This might be due to the dominance of virtual continuum-continuum transitions, to and from the bands states, that lie behind the fundamental quantum process of high harmonic emissions. Lastly, the dependence of the charge currents, induced in a ribbon of unit width (N = 1), on the carrier-envelope-phase (CEP) of the incident laser pulse is investigated. It is seen that the shape of the main part of the current produced in the ribbon can be fully reversed by changing the CEP of the ultrashort laser pulse from 0 to π. More generally, it is suggested that the pulse shape of the charge carriers in the ribbon could be designed by similarly tailoring the form of the vector potential of the incident laser pulse.