We demonstrate that currents induced in graphene by ultrashort laser pulses are sensitive to the exact shape of the electric-field waveform. By increasing the field strength, we found a transition of the light–matter interaction from the weak-field to the strong-field regime at around 2 V/nm, where intraband dynamics influence interband transitions. In this strong-field regime, the light-matter interaction can be described by the wavenumber trajectories of electrons in the reciprocal space. For linearly polarized light the electron dynamics are governed by repeated sub-optical-cycle Landau-Zener transitions between the valence- and conduction band, resulting in Landau-Zener-Stuckelberg interference, whereas for circular polarized light this interference is supressed.

When solids are exposed to intense optical fields, the intraband electron motion may influence interband transitions, potentially causing a transition of light-matter interaction from a quantum (photon-driven) regime to a semi-classical (field-driven) regime. We demonstrate this transition in monolayer graphene. We observe a carrier-envelope-phasedependent current in graphene irradiated with phase-stable two-cycle laser pulses, showing a striking reversal of the current direction as a function of the driving field amplitude at ~2 V/nm. This reversal indicates the transition into the field-driven (or strong-field) regime. We show furthermore that in this regime electron dynamics are governed by suboptical-cycle Landau-Zener-Stückelberg interference, comprised of coherent repeated Landau-Zener transitions. We expect these results to have direct ramifications for light-wave driven electronics 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, sub-optical-cycle interband population transfer and the non-perturbative change of the transient polarizability. 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. 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. 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 interference, 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). We expect these results to have direct ramifications for band-structure tomography and light-field-driven petahertz electronics.

Nonperturbative electron dynamics inside of solids under strong optical fields has recently found particular attention. Light-field driven effects such as high-harmonic generation and sub-optical-cycle interband population transfer have been reported for dielectrics and semiconductors. However, much less is known about strong-field phenomena in conducting materials. Graphene is an ideal playground for studying strong-field phenomena in a conductor because of its broadband optical response and its much weaker screening compared to conventional metals. Here we report a transition from a perturbative to a non-perturbative mechanism in generating optical-phase sensitive currents in graphene illuminated with few-cycle laser pulses [1]. The electric-field waveform of such an ultrashort laser pulse is characterized by the carrier-envelope-phase (CEP), which determines when the maximum peak of the field is found inside of the pulse envelope (Fig. 1a). We observed a CEP-dependent current in graphene stripes excited with linearly polarized laser pulses parallel to the graphene stripe with a peak field of up to 3 V/nm (Fig. 1a, b). The amplitude of the current scales nonlinearly as a function of the field strength (Fig. 1c). The CEP dependent current changes its sign at around 1.8 V/nm with increasing the field strength (Fig. 1d). The main experimental features, especially the tell-tale change in current direction as a function of field strength, are well reproduced by numerical simulations (Fig. 1e, f).

We investigate charge transport in C60-based single-molecule junctions with graphene electrodes employing a combination of density functional theory (DFT) electronic structure calculations and Landauer transport theory. In particular, the dependence of the transport properties on the conformation of the molecular bridge and the type of termination of the graphene electrodes is investigated. Furthermore, electron pathways through the junctions are analyzed using the theory of local currents. The results reveal, in agreement with previous experiments, a pronounced dependence of the transport properties on the bias polarity, which is rationalized in terms of the electronic structure of the molecule. It is also shown that the edge states of zigzag-terminated graphene induce additional transport channels, which dominate transport at low voltages. The importance of the edge states for transport depends profoundly on the interface geometry of the junctions.

On the way to ultraflat single-molecule junctions with transparent electrodes, we present a fabrication scheme based on epitaxial graphene nanoelectrodes. As a suitable molecule, we identified a molecular wire with fullerene anchor groups. With these two components, stable electrical characteristics could be recorded. Electrical measurements show that single-molecule junctions with graphene and with gold electrodes display a striking agreement. This motivated a hypothesis that the differential conductance spectra are rather insensitive to the electrode material. It is further corroborated by the assignment of asymmetries and spectral features to internal molecular degrees of freedom. The demonstrated open-access graphene electrodes and the electrode-insensitive molecules provide a model system that will allow for a thorough investigation of an individual single-molecule contact with additional probes.

We present a fabrication process for freely suspended membranes consisting of bi- and trilayer graphene grown on silicon carbide. The procedure, involving photoelectrochemical etching, enables the simultaneous fabrication of hundreds of arbitrarily shaped membranes with an area up to 500 μm2 and a yield of around 90%. Micro-Raman and atomic force microscopy measurements confirm that the graphene layer withstands the electrochemical etching and show that the membranes are virtually unstrained. The process delivers membranes with a cleanliness suited for high-resolution transmission electron microscopy (HRTEM) at atomic scale. The membrane, and its frame, is very robust with respect to thermal cycling above 1000 °C as well as harsh acidic or alkaline treatment.