Light-field-driven currents in graphene

The ability to steer electrons using the strong electromagnetic field of light has opened up the possibility of controlling electron dynamics on the sub-femtosecond (less than 10(-15) seconds) timescale. In dielectrics and semiconductors, various light-field-driven effects have been explored, including high-harmonic generation(1-4), sub-optical-cycle interband population transfer(5) and the non-perturbative change of the transient polarizability(6,7). In contrast, much less is known about light-field-driven electron dynamics in narrow-bandgap systems or in conductors, in which screening due to free carriers or light absorption hinders the application of strong optical fields(6,8). Graphene is a promising platform with which to achieve light-field-driven control of electrons in a conducting material, because of its broadband and ultrafast optical response, weak screening and high damage threshold(9,10). Here we show that a current induced in monolayer graphene by two-cycle laser pulses is sensitive to the electric-field waveform, that is, to the exact shape of the optical carrier field of the pulse, which is controlled by the carrier envelope phase, with a precision on the attosecond (10(-18) seconds) timescale. Such a current, dependent on the carrier-envelope phase, shows a striking reversal of the direction of the current as a function of the driving field amplitude at about two volts per nanometre. This reversal indicates a transition of light-matter interaction from the weak-field (photon-driven) regime to the strong-field (light-field driven) regime, where the intraband dynamics influence interband transitions. We show that in this strong-field regime the electron dynamics are governed by sub-optical-cycle Landau-Zener-Stuckelberg interference(11), composed of coherent repeated Landau-Zener transitions on the femtosecond timescale. Furthermore, the influence of this sub-optical-cycle interference can be controlled with the laser polarization state. These coherent electron dynamics in graphene take place on a hitherto unexplored timescale, faster than electron-electron scattering (tens of femtoseconds) and electron-phonon scattering (hundreds of femtoseconds)(12-14). We expect these results to have direct ramifications for band-structure to mography2 and light-field-driven petahertz electronics(8).