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High-harmonic spectroscopy, an ultrafast all-optical technique initially conceptualized in atomic and molecular systems, has now emerged as a powerful platform for studying the structure and dynamics of condensed matter. Unlike that in the gas phase, solid-state high-harmonic generation relies on the fundamental response from high atomic density and periodicity, leading to interband transitions and coherent driving of electrons and holes in their respective bands. These mechanisms make high-harmonic spectroscopy particularly sensitive to the electronic band structure, topological properties and many-body correlations in condensed media. An advantage of high-harmonic spectroscopy over other spectroscopic methods is its ability to probe ultrafast phenomena, capturing femto- to attosecond dynamics of multi-band and strongly correlated electron interactions in solids. In this Review, we discuss the latest experimental and theoretical advances in ultrafast high-harmonic spectroscopy of solids and provide perspectives for future research in this field. High-harmonic spectroscopy on solids is an ultrafast all-optical technique to study the structure and dynamics of materials. This Review discusses areas of condensed-matter physics where this technique can provide particular insight.

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 real 1 – 4 . Virtual charge carriers have recently been associated with high-harmonic generation and transient absorption 5 – 8 , but photocurrent generation may stem from real as well as virtual charge carriers 9 – 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 reality 15 , 16 . Light-field control of real and virtual charge carriers in a gold–graphene–gold heterostructure is demonstrated, and used to create a logic gate for application in lightwave electronics.

The prediction and realization of topological insulators have sparked great interest in experimental approaches to the classification of materials1–3. The phase transition between non-trivial and trivial topological states is important, not only for basic materials science but also for next-generation technology, such as dissipation-free electronics4. It is therefore crucial to develop advanced probes that are suitable for a wide range of samples and environments. Here we demonstrate that circularly polarized laser-field-driven high-harmonic generation is distinctly sensitive to the non-trivial and trivial topological phases in the prototypical three-dimensional topological insulator bismuth selenide5. The phase transition is chemically initiated by reducing the spin–orbit interaction strength through the substitution of bismuth with indium atoms6,7. We find strikingly different high-harmonic responses of trivial and non-trivial topological surface states that manifest themselves as a conversion efficiency and elliptical dichroism that depend both on the driving laser ellipticity and the crystal orientation. The origins of the anomalous high-harmonic response are corroborated by calculations using the semiconductor optical Bloch equations with pairs of surface and bulk bands. As a purely optical approach, this method offers sensitivity to the electronic structure of the material, including its nonlinear response, and is compatible with a wide range of samples and sample environments.Researchers demonstrate a method based on circularly polarized laser-field-driven high-harmonic generation for probing non-trivial and trivial topological phases in a three-dimensional topological insulator.

Ultrafast control of electron dynamics in solid state systems has recently found particular attention. By increasing the electric field strength of laser pulses, the light-matter interaction in solids might turn from a perturbative into a novel non-perturbative regime, where interband transitions from the valence to the conduction band become strongly affected by intraband motion. We have demonstrated experimentally and numerically that this combined dynamics can be controlled in graphene with the electric field waveform of phase-stabilized few-cycle laser pulses (Higuchi et al 2017 Nature 550 224-8; Heide et al 2018 Phys. Rev. Lett. 121 207401). Here we show new experimental data and matching simulation results at comparably low optical fields, which allows us to focus on the highly interesting transition regime where the light-matter interaction turns from perturbative to non-perturbative. We find a 5th order power-law scaling of the laser induced waveform-dependent current at low optical fields, which breaks down for higher optical fields, indicating the transition.

Nonlinear optical materials possess wide applications, ranging from terahertz and mid-infrared detection to energy harvesting. Recently, the correlations between nonlinear optical responses and certain topological properties, such as the Berry curvature and the quantum metric tensor, have attracted considerable interest. Here, we report giant room-temperature nonlinearities in non-centrosymmetric two-dimensional topological materials—the Janus transition metal dichalcogenides in the 1  T’ phase, synthesized by an advanced atomic-layer substitution method. High harmonic generation, terahertz emission spectroscopy, and second harmonic generation measurements consistently show orders-of-the-magnitude enhancement in terahertz-frequency nonlinearities in 1  T’ MoSSe (e.g., > 50 times higher than 2 H MoS 2 for 18 th order harmonic generation; > 20 times higher than 2 H MoS 2 for terahertz emission). We link this giant nonlinear optical response to topological band mixing and strong inversion symmetry breaking due to the Janus structure. Our work defines general protocols for designing materials with large nonlinearities and heralds the applications of topological materials in optoelectronics down to the monolayer limit. Electronic band topology may be leveraged to enhance nonlinear optical properties in monolayer semiconductors. Here, the authors report giant room-temperature nonlinearity enhancements in Janus transition metal dichalcogenides.

The injection of directional currents in solids with strong optical fields has attracted tremendous attention as a route to realize ultrafast electronics based on the quantum-mechanical nature of electrons at femto- to attosecond timescales. Such currents are usually the result of an asymmetric population distribution imprinted by the temporal symmetry of the driving field. Here we compare two experimental schemes that allow control over the amplitude and direction of light-field-driven currents excited in graphene. Both schemes rely on shaping the incident laser field with one parameter only: either the carrier-envelope phase (CEP) of a single laser pulse or the relative phase between pulses oscillating at angular frequencies and 2 , both for comparable laser parameters. We observe that the efficiency in generating a current via two-color-control exceeds that of CEP control by more than two orders of magnitude (7 nA vs. 18 pA), as the + 2 field exhibits significantly more asymmetry in its temporal shape. We support this finding with numerical simulations that clearly show that two-color current control in graphene is superior, even down to single-cycle pulse durations. We expect our results to be relevant to experimentally access fundamental properties of any solid at ultrafast timescales, as well as for the emerging field of petahertz electronics.

We report a coherent layer-by-layer build-up of high-order harmonic generation (HHG) in artificially stacked transition metal dichalcogenides (TMDC) crystals in their various stacking configurations. In the experiments, millimeter-sized single crystalline monolayers are synthesized using the gold foil-exfoliation method, followed by artificially stacking on a transparent substrate. High-order harmonics up to the 19th order are generated by the interaction with a mid-infrared (MIR) driving laser. We find that the generation is sensitive to both the number of layers and their relative orientation. For AAAA stacking configuration, both odd- and even-orders exhibit a quadratic increase in intensity as a function of the number of layers, which is a signature of constructive interference of high-harmonic emission from successive layers. Particularly, we observe some deviations from this scaling at photon energies above the bandgap, which is explained by self-absorption effects. For AB and ABAB stacking, even-order harmonics remain below the detection level, consistent with the presence of inversion symmetry. Our study confirms our capability of producing nonperturbative high-order harmonics from stacked layered materials subjected to intense MIR fields without damaging samples. Our results have implications for optimizing solid-state HHG sources at the nanoscale and developing high-harmonics as an ultrafast probe of artificially stacked layered materials. Because the HHG process is a strong-field driven process, it has the potential to probe high-momentum and energy states in the bandstructure combined with atomic-scale sensitivity in real space, making it an attractive probe of novel material structures such as the Moiré pattern.

NRC publication: Yes

Light-field-driven control of electrons in a conductor is demonstrated by inducing a current by laser pulses in graphene that is sensitive to the carrier-envelope phase. A light on current advances in graphene A new field of ultrafast electronics has emerged in recent years that uses strong electromagnetic (light) fields to steer electrons. It is difficult to explore such effects in metals because of screening by the charge carriers, so mainly insulators and semiconductors have been studied in this area. However, different physics applies to graphene, a two-dimensional material in which only weak screening is present. Takuya Higuchi et al . have now generated electric currents in graphene with ultrafast light fields. The current is sensitive 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 timescale. The results open up new opportunities for creating light-field-driven petahertz electronics. 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 , 2 , 3 , 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–Stückelberg 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 , 13 , 14 . We expect these results to have direct ramifications for band-structure tomography 2 and light-field-driven petahertz electronics 8 .

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.