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 generation1,2,3,4, sub-optical-cycle interband population transfer5 and the non-perturbative change of the transient polarizability6,7. 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 fields6,8. 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 threshold9,10. 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–Stückelberg interference11, 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)12,13,14. We expect these results to have direct ramifications for band-structure tomography2 and light-field-driven petahertz electronics8.
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This work has been supported in part by the European Research Council (Consolidator Grant NearFieldAtto) and the Deutsche Forschungsgemeinschaft (grant SFB 953). We thank M. I. Stockman for discussions.
Extended data figures
This file contains methods 1-11 and references.
About this article
Nature Communications (2018)