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Light-field control of real and virtual charge carriers


Light-driven electronic excitation is a cornerstone for energy and information transfer. In the interaction of intense and ultrafast light fields with solids, electrons may be excited irreversibly, or transiently during illumination only. As the transient electron population cannot be observed after the light pulse is gone, it is referred to as virtual, whereas the population that remains excited is called real1,2,3,4. Virtual charge carriers have recently been associated with high-harmonic generation and transient absorption5,6,7,8, but photocurrent generation may stem from real as well as virtual charge carriers9,10,11,12,13,14. However, a link between the generation of the carrier types and their importance for observables of technological relevance is missing. Here we show that real and virtual charge carriers can be excited and disentangled in the optical generation of currents in a gold–graphene–gold heterostructure using few-cycle laser pulses. Depending on the waveform used for photoexcitation, real carriers receive net momentum and propagate to the gold electrodes, whereas virtual carriers generate a polarization response read out at the gold–graphene interfaces. On the basis of these insights, we further demonstrate a proof of concept of a logic gate for future lightwave electronics. Our results offer a direct means to monitor and excite real and virtual charge carriers. Individual control over each type of carrier will markedly increase the integrated-circuit design space and bring petahertz signal processing closer to reality15,16.

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Fig. 1: Role of real and virtual charge carriers in current generation.
Fig. 2: Measured phase-resolved CEP-dependent current for graphene strip lengths L = 5 μm, L = 2 μm and L = 1 μm.
Fig. 3: Charge transfer simulations for gold–graphene–gold heterostructures (TD-NEGF).
Fig. 4: Petahertz logic gate.

Data availability

Source data are provided with this paper.


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We thank Y. Morimoto, J. Ristein and M. Hundhausen for discussions. This work has been supported in part by the Deutsche Forschungsgemeinschaft (SFB 953 ‘Synthetic Carbon Allotropes’, project number 182849149), the PETACom project financed by Future and Emerging Technologies Open H2020 program, ERC Grants NearFieldAtto and AccelOnChip, the Leonard Mandel Faculty Fellowship of the University of Rochester, and the US National Science Foundation under grant numbers CHE-1553939 and CHE-2102386.

Author information

Authors and Affiliations



T.B. and C.H. conveyed the current measurement experiments, analysed the data, performed TDSE simulations and provided the plots. A.G.R. and I.F. conducted the TD-NEGF simulations. H.B.W. provided the tools for sample fabrication. All authors discussed the obtained results and contributed to the writing of the manuscript. I.F. and P.H. co-supervised the study. T.B. and C.H. contributed equally.

Corresponding authors

Correspondence to Tobias Boolakee, Ignacio Franco or Peter Hommelhoff.

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Extended data figures and tables

Extended Data Fig. 1 Electric field and vector potential of Gaussian laser pulses used for simulations.

The maximum field strength is 2.3 V/nm, the pulse duration is 6 fs (intensity FWHM), the centre photon energy is 1.5 eV. a, For a CEP φCE = π/2 the electric field is antisymmetric with respect to time inversion while the vector potential is symmetric. b, For φCE = 0 the electric field is symmetric and the vector potential is antisymmetric.

Extended Data Fig. 2 Sample and measurement technique.

a, Scanning electron micrograph of the gold–graphene–gold heterostructures with various electrode distances. The yellow colouring indicates the gold electrodes. Insets, total photocurrent as a function of the focal position inside the dashed regions (E0 = 0.3 V/nm). For all measurements and unless otherwise stated, the laser spot was positioned in the centre of the graphene strips such that the total photocurrent is 0. b, Schematic diagram of the measurement scheme. The induced residual current is amplified by transimpedance amplifiers and detected by a dual-phase lock-in amplifier.

Extended Data Fig. 3 Total photocurrent and CEP-dependent current on an L=1 μm graphene strip as a function of E0.

a, Total photocurrent with the laser focus placed at the interface (compare with current maxima in Extended Data Fig. 2a, inset). b, CEP-dependent current for φCE=π (same data as in Fig. 2c). Insets show the data in a double-logarithmic scale with linear fits, while shaded points only are included in the fit in (b).

Extended Data Fig. 4 CEP dependence of currents for logic switching.

a, Measured and simulated CEP-dependent current (blue, data and simulation as in Fig. 4b) and lock-in phase (purple). The shaded range ΔφCE=[–2π, 0] is further analysed in (c), where it is mapped to ΔφCE=[0, 2π]. b, Using Eq. (8) of Methods, the Δφg dependence of the current is exemplified for two data points (light and dark green) of (a). Dashed lines indicate the root mean square values, i.e., the currents shown in (a). c, Measured current as a function of ΔφCE and demodulated along Δφg. The light and dark green lines correspond to the data points marked in (a) and analysed in (b). d, Simulated current as a function of ΔφCE and Δφg. The model curve of θ (purple line) is indicated with an arbitrary offset with respect to (a). e, Measured current (c) in the basis of individual CEPs φA and φB. f, Simulated current in the same basis as (e).

Extended Data Fig. 5 Realization of various logic gates.

a, Simulated CEP-dependent current as a function of φA and φB with equal current amplitudes JA, JB induced by laser pulses A (bulk graphene) and B (interface). The purple crosses mark phases φA, φB considered in (b). b, CEP-dependent current for 16 combinations of φA and φB as needed for the operation of logic gates. Positive current is assigned to an output logic level Y of 1 while zero or negative current is assigned to 0 (see colour bar). The green dots mark the combinations required for the formation of the logic gates shown below. cf, Truth tables of AND (c), OR (d), NAND (e) and NOR (f) are obtained by appropriate choice of CEPs φA and φB as marked in (b). The green arrows (rings) on the insets depicting the heterostructure mark the current direction (zero current) driven on the graphene and at the interface.

Extended Data Fig. 6 Raman spectrum of monolayer epitaxial graphene on SiC.

The coupling to the SiC induces a strain-induced blue-shift of 64 cm–1 to the 2D-peak compared to freestanding graphene, while it consists of one peak only (~48 cm–1 FWHM) as expected for monolayer graphene36. The occurrence of a D-peak indicates defects emerging primarily from domain boundaries37.

Extended Data Fig. 7 Optical near-field simulation of the heterojunction.

a, Schematic of the structure used in finite-difference time-domain simulations. Two electrodes consisting of 5 nm titanium and 30 nm gold separated by a 1 μm graphene strip are supported by a SiC substrate. Similar to experimental conditions, the structure is illuminated with a Gaussian focus placed in the centre. b, Field enhancement ξ within the graphene layer (red line). In the centre, ξ reaches the analytic factor given by the polarization response of bare SiC (grey dashed line) while it rises to 2 in the optical near-field of the electrodes. c, Variation of the CEP ΔφCE across the graphene strip. ΔφCE is independent of the exact value of the CEP.

Extended Data Fig. 8 Line-scan of CEP-dependent current.

Measured CEP-dependent currents are plotted as a function of the focus position that is moved from one to the other gold electrode (shaded areas) across a 5 × 1.8 μm2 graphene strip on an axis centred to the graphene strip width. The current projections j±π/2 (purple data points) and j0,π (blue data points) are shown. A peak field strength of E0 = 2.7 V/nm is applied. Error bars indicate the standard deviation.

Extended Data Fig. 9 Transient evolution of charge motion and electron population obtained from a TDSE model.

a, b, Charge motion for a CEP of φCE = π/2 (a) and φCE = 0 (b). The grey lines show the electric field of the pulses with E0 = 2.3 V/nm, centred at t = 0. c, d, Normalized electron population ρQ contributing to the charge transfer. The population is normalized to the number of available states in the first Brillouin zone of graphene. For φCE = 0, ρQ returns to zero after the pulse is gone, while for φCE = π/2, a residual population remains and leads to an increasing charge transfer, see also insets.

Extended Data Fig. 10 Two-pulse experiment.

CEP-stable laser pulses from a Ti:Sa oscillator are split into pulse copies (A, B) in a Michelson interferometer. The SiO2 wedge pairs are used to balance the dispersion (path A and B), and to vary ΔφCE (path A). The temporal delay is changed by variation of path length A. Introducing an angle in path B results in spatially separated foci on the sample, see microscope image. BS, beam splitter; OAP, off-axis parabolic mirror.

Supplementary information


Supplementary Video 1 Extraction of lock-in observables in the two-pulse scheme. a, Simulated net currents induced by laser pulses A (jA, orange) and B (jB, red) are modulated as a function of Δφg, and additionally, the phase of jA is shifted continuously by ΔφCE. Their superposition (jtotal, blue) is the signal fed into the dual-phase lock-in amplifier, where the root-mean-square value of jtotal (J, horizontal blue line) and its phase θ are measured as a function of ΔφCE. b, Simulated current amplitude J (blue) and its phase θ (purple), as extracted experimentally by the lock-in amplifier.

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Boolakee, T., Heide, C., Garzón-Ramírez, A. et al. Light-field control of real and virtual charge carriers. Nature 605, 251–255 (2022).

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