2D layered materials (2DLMs) are a subject of intense research for a wide variety of applications (e.g., electronics, photonics, and optoelectronics) due to their unique physical properties. Most recently, increasing research efforts on 2DLMs are projected toward the nonlinear optical properties of 2DLMs, which are not only fascinating from the fundamental science point of view but also intriguing for various potential applications. Here, the current state of the art in the field of nonlinear optics based on 2DLMs and their hybrid structures (e.g., mixed-dimensional heterostructures, plasmonic structures, and silicon/fiber integrated structures) is reviewed. Several potential perspectives and possible future research directions of these promising nanomaterials for nonlinear optics are also presented.

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Nonlinear Optics with 2D Layered Materials.

This article reviews the theoretical and experimental work related to the electronic properties of bilayer graphene systems. Three types of bilayer stackings are discussed: the AA, AB, and twisted bilayer graphene. This review covers single-electron properties, effects of static electric and magnetic fields, bilayer-based mesoscopic systems, spin-orbit coupling, dc transport and optical response, as well as spontaneous symmetry violation and other interaction effects. The selection of the material aims to introduce the reader to the most commonly studied topics of theoretical and experimental research in bilayer graphene.

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Electronic properties of graphene-based bilayer systems

As conventional electronics approaches its limits
 1
 , nanoscience has urgently sought methods of fast control of electrons at the fundamental quantum level
 2
 . Lightwave electronics
 3
 —the foundation of attosecond science
 4
 —uses the oscillating carrier wave of intense light pulses to control the translational motion of the electron’s charge faster than a single cycle of light5–15. Despite being particularly promising information carriers, the internal quantum attributes of spin
 16
 and valley pseudospin17–21 have not been switchable on the subcycle scale. Here we demonstrate lightwave-driven changes of the valley pseudospin and introduce distinct signatures in the optical readout. Photogenerated electron–hole pairs in a monolayer of tungsten diselenide are accelerated and collided by a strong lightwave. The emergence of high-odd-order sidebands and anomalous changes in their polarization direction directly attest to the ultrafast pseudospin dynamics. Quantitative computations combining density functional theory with a non-perturbative quantum many-body approach assign the polarization of the sidebands to a lightwave-induced change of the valley pseudospin and confirm that the process is coherent and adiabatic. Our work opens the door to systematic valleytronic logic at optical clock rates.

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Lightwave valleytronics in a monolayer of tungsten diselenide

The ground-breaking demonstration of the electric field effect in graphene reported more than a decade ago prompted the strong push towards the commercialization of graphene as evidenced by a wealth of graphene research, patents and applications. Graphene flake production capability has reached thousands of tonnes per year, while continuous graphene sheets of tens of metres in length have become available. Various graphene technologies developed in laboratories have now transformed into commercial products, with the very first demonstrations in sports goods, automotive coatings, conductive inks and touch screens, to name a few. Although challenges related to quality control in graphene materials remain to be addressed, the advancement in the understandings of graphene will propel the commercial success of graphene as a compelling technology. This Review discusses the progress towards commercialization of graphene for the past decade and future perspectives. This Review reflects on the 15 years of advances in the field of 2D materials towards commercialization of graphene and its future perspectives.

Path towards graphene commercialization from lab to market.

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-Stuckelberg 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.

Light-field-driven currents in graphene

Contrary to common belief, bilayer graphene is not defect-free: the abundance of partial dislocations leads to a mosaic-like network structure. As a result, as now shown, the magnetoresistance of bilayer graphene depends linearly, rather than quadratically, on the external magnetic field. The magnetoresistance of conductors usually has a quadratic dependence on magnetic field1, however, examples exist of non-saturating linear behaviour in diverse materials2,3,4,5,6. Assigning a specific microscopic mechanism to this unusual phenomenon is obscured by the co-occurrence and interplay of doping, mobility fluctuations and a polycrystalline structure7,8. Bilayer graphene has virtually no doping fluctuations, yet provides a built-in mosaic tiling due to the dense network of partial dislocations9,10. We present magnetotransport measurements of epitaxial bilayer graphene that exhibits a strong and reproducible linear magnetoresistance that persists to B = 62 T at and above room temperature, decorated by quantum interference effects at low temperatures. Partial dislocations thus have a profound impact on the transport properties in bilayer graphene, a system that is frequently assumed to be dislocation-free. It further provides a clear and tractable model system for studying the unusual properties of mosaic conductors.

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Linear magnetoresistance in mosaic-like bilayer graphene

We investigate coherent electron dynamics in graphene, interacting with the electric field waveform of two orthogonally polarized, few-cycle laser pulses. Recently, we demonstrated that linearly polarized driving pulses lead to sub-optical-cycle Landau-Zener quantum path interference by virtue of the combination of intraband motion and interband transition [Higuchi et al., Nature 550, 224 (2017)NATUAS0028-083610.1038/nature23900]. Here we introduce a pulsed control laser beam, orthogonally polarized to the driving pulses, and observe the ensuing electron dynamics. The relative delay between the two pulses is a tuning parameter to control the electron trajectory, now in a complex fashion exploring the full two-dimensional reciprocal space in graphene. Depending on the relative phase, the electron trajectory in the reciprocal space can, e.g., be deformed to suppress the quantum path interference resulting from the driving laser pulse. Intriguingly, this strong-field-based complex matter wave manipulation in a two-dimensional conductor is driven by a high repetition rate laser oscillator, rendering unnecessary complex and expensive amplified laser systems.

Coherent Electron Trajectory Control in Graphene.

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 real1-4. Virtual charge carriers have recently been associated with high-harmonic generation and transient absorption5-8, but photocurrent generation may stem from real as well as virtual charge carriers9-14. 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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Light-field control of real and virtual charge carriers

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. 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.

https://iopscience.iop.org/article/10.1088/1367-2630/ab13ce/pdf

Christian Heide

Papers

Light-field-driven currents in graphene

Linear magnetoresistance in mosaic-like bilayer graphene

Coherent Electron Trajectory Control in Graphene.

Light-field control of real and virtual charge carriers

Interaction of carrier envelope phase-stable laser pulses with graphene: the transition from the weak-field to the strong-field regime