High Harmonic Generation In Graphene Research Articles

Shear-strain controlled high-harmonic generation in graphene

We propose a method for controlling the high-harmonic generation (HHG) with a high dynamic range in single-layer graphene. We find that, by utilizing shear strain, a significant enhancement or quenching of HHG is possible over a range of several orders of magnitude. This feature is made possible by the resonance mechanism at a van Hove singularity. Therein, the shear strain controls the configurations of the two Dirac cones, resulting in changes in the energy and dipole moment at the saddle point of the band dispersion. Our findings provide a way for modulating or switching light by using a nano-optomechanical device composed of single-layer graphene.

Gate-tunable quantum pathways of high harmonic generation in graphene

Under strong laser fields, electrons in solids radiate high-harmonic fields by travelling through quantum pathways in Bloch bands in the sub-laser-cycle timescales. Understanding these pathways in the momentum space through the high-harmonic radiation can enable an all-optical ultrafast probe to observe coherent lightwave-driven processes and measure electronic structures as recently demonstrated for semiconductors. However, such demonstration has been largely limited for semimetals because the absence of the bandgap hinders an experimental characterization of the exact pathways. In this study, by combining electrostatic control of chemical potentials with HHG measurement, we resolve quantum pathways of massless Dirac fermions in graphene under strong laser fields. Electrical modulation of HHG reveals quantum interference between the multi-photon interband excitation channels. As the light-matter interaction deviates beyond the perturbative regime, elliptically polarized laser fields efficiently drive massless Dirac fermions via an intricate coupling between the interband and intraband transitions, which is corroborated by our theoretical calculations. Our findings pave the way for strong-laser-field tomography of Dirac electrons in various quantum semimetals and their ultrafast electronics with a gate control.

Doping and gap size dependence of high-harmonic generation in graphene: Importance of consistent formulation of light-matter coupling

High-harmonic generation (HHG) in solids is a fundamental nonlinear phenomenon, which can be efficiently controlled by modifying system parameters such as doping-level and temperature. In order to correctly predict the dependence of HHG on these parameters, consistent theoretical formulation of the light-matter coupling is crucial. Recently, contributions to the current that are often missing in the HHG analysis based on the semiconductor Bloch equations have been pointed out [J. Wilhelm, et.al. PRB 103 125419 (2021)]. In this paper, by systematically analyzing the doping and gap-size dependence of HHG in gapped graphene, we discuss the practical impact of such terms. In particular, we focus on the role of the current $J_{\rm ra}^{(2)}$, which originates from the change of the intraband dipole via interband transition. When the gap is small and the system is close to half filling, intraband and interband currents mostly cancel, thus suppressing the HHG signal - an important property that is broken when neglecting $J_{\rm ra}^{(2)}$. Furthermore, without $J_{\rm ra}^{(2)}$, the doping and gap-size dependence of HHG becomes qualitatively different from the full evaluation. Our results demonstrate the importance of the consistent expression of the current to study the parameter dependence of HHG for the small gap systems.

Efficient high-harmonic generation in graphene with two-color laser field at orthogonal polarization

High-order frequency mixing in graphene using a two-color radiation field consisting of the fundamental and the second harmonic fields of an ultrashort linearly polarized laser pulse is studied. It is shown that the harmonics originated from the interband transitions are efficiently generated in the case of the orthogonally polarized two-color field. In this case, the generated high-harmonics are stronger than those obtained in the parallel polarization case by more than two orders of magnitude. This is in sharp contrast with the atomic and semiconductor systems, where parallel polarization case is more preferable. The physical origin of this enhancement is also deduced from the three-step semi-classical electron-hole collision model, extended to graphene with pseudo-relativistic energy dispersion. In particular, we discuss the influence of the many particle Coulomb interaction on the HHG process within dynamical Hartree-Fock approximation. Our analysis shows that in all cases we have an overall enhancement of the HHG signal compared with the free-charged carrier model due to the electron-hole attractive interaction.

Non-classical high harmonic generation in graphene driven by linearly-polarized laser pulses.

Recent studies in high-order harmonic generation (HHG) in solid targets reveal new scenarios of extraordinary rich electronic dynamics, in comparison to the atomic and molecular cases. For the later, the main aspects of the process can be described semiclassically in terms of electrons that recombine when the trajectories revisit the parent ion. HHG in solids has been described by an analogous mechanism, in this case involving electron-hole pair recombinations. However, it has been recently reported that a substantial part of the HHG emission corresponds to situations where the electron and hole trajectories do not overlap in space. According to the present knowledge, HHG from this imperfect recollisions reflects the quantum nature of the process, arising in systems with large Berry curvatures or for elliptically polarized driving fields. In this work, we demonstrate that imperfect recollisions are also relevant in the more general case. We show the signature of such recollisions in the HHG spectrum from monolayer graphene -a system with null Berry curvature- irradiated by linearly polarized driving fields. Our calculations also reveal that imperfect multiple-order recollisions contribute to the harmonic emission when electron-hole excursion times exceed one cycle of the driving field. We believe that our work adds a substantial contribution to the full understanding of the sub-femtosecond dynamics of HHG in solid systems.

High harmonic generation in graphene–boron nitride heterostructures

High harmonic generation and enhancement by tuning the interlayer separation in two-dimensional van der Waals heterostructures are investigated.

Circularly polarized extreme ultraviolet high harmonic generation in graphene.

Circularly polarized extreme ultraviolet (XUV) radiation is highly interesting for investigation of chirality-sensitive light-matter interactions. Recent breakthroughs have enabled the generation of such light sources via high harmonic generation (HHG) from rare gases. There is a growing interest in extending HHG medium from gases to solids, especially to 2D materials, as they hold great promise to develop ultra-compact solid-state photonic devices and provide insights into electronic properties of the materials themselves. However, so far reported, HHG in graphene driven by terahertz to mid-infrared fields generates only low harmonic orders, and no harmonics driven by circularly polarized lasers have been reported. Here, using first-principles simulations within a time-dependent density-functional theory framework, we show that it is possible to generate HHG extending to the XUV spectral region in monolayer extended graphene excited by near-infrared lasers. Moreover, we demonstrate that a single circularly polarized driver is enough to ensure HHG in graphene with circular polarization. The corresponding spectra reflect the six-fold rotational symmetry of the graphene crystal. Extending HHG in graphene to the XUV spectral regime and realizing circular polarization represent an important step toward the development of novel nanoscale attosecond photonic devices and numerous applications, such as spectroscopic investigation and nanoscale imaging of ultrafast chiral and spin dynamics in graphene and other 2D materials.

Extremely efficient terahertz high-harmonic generation in graphene by hot Dirac fermions

Multiple optical harmonic generation-the multiplication of photon energy as a result of nonlinear interaction between light and matter-is a key technology in modern electronics and optoelectronics, because it allows the conversion of optical or electronic signals into signals with much higher frequency,andthe generation of frequency combs.Owing to the unique electronic band structure of graphene, which features massless Dirac fermions1-3, it has been repeatedly predicted that optical harmonic generation in graphene should be particularly efficient at the technologically important terahertz frequencies4-6. However, these predictionshave yet to be confirmed experimentally under technologically relevant operation conditions. Here we report the generation of terahertz harmonics up to the seventh order in single-layer graphene at room temperature and under ambient conditions, driven by terahertz fields of only tens of kilovolts per centimetre, and with field conversion efficiencies in excess of 10-3, 10-4 and 10-5 for the third, fifth and seventh terahertz harmonics, respectively. These conversion efficienciesare remarkably high, given that the electromagnetic interaction occurs in a single atomic layer. The key to such extremely efficient generation of terahertz highharmonics in graphene is the collective thermal response of its background Dirac electrons to the driving terahertz fields. The terahertz harmonics, generated via hot Dirac fermion dynamics, were observed directly in the time domain as electromagnetic field oscillations at these newlysynthesized higher frequencies. The effective nonlinear optical coefficients of graphene for the third, fifth and seventh harmonics exceed the respective nonlinear coefficients of typical solids by 7-18 orders of magnitude7-9. Our results provide a direct pathway to highly efficient terahertz frequencysynthesis using the present generation of graphene electronics, which operate at much lower fundamental frequencies of only a few hundreds of gigahertz.

High-harmonic generation in graphene enhanced by elliptically polarized light excitation.

The electronic properties of graphene can give rise to a range of nonlinear optical responses. One of the most desirable nonlinear optical processes is high-harmonic generation (HHG) originating from coherent electron motion induced by an intense light field. Here, we report on the observation of up to ninth-order harmonics in graphene excited by mid-infrared laser pulses at room temperature. The HHG in graphene is enhanced by an elliptically polarized laser excitation, and the resultant harmonic radiation has a particular polarization. The observed ellipticity dependence is reproduced by a fully quantum mechanical treatment of HHG in solids. The zero-gap nature causes the unique properties of HHG in graphene, and our findings open up the possibility of investigating strong-field and ultrafast dynamics and nonlinear behavior of massless Dirac fermions.

High-harmonic generation in graphene: Interband response and the harmonic cutoff

We numerically examine the high-harmonic generation in graphene caused by an intense few-cycle terahertz laser field by solving the time-dependent Dirac equation. The observed spectra feature a complex interplay of interband and intraband electron dynamics. At high harmonic frequencies, we observe a plateau region with a cut-off frequency linearly proportional to the laser field. The linear dependence of the cutoff on the field resembles the behavior for electrons driven in bulk crystals but differs from the case of atoms or molecules. The unique features of the graphene band structure allow for a transparent decomposition of interband and intraband contributions and for an analytic estimate of the harmonic cut-off frequency in excellent agreement with the simulations.

Plasmon-assisted high-harmonic generation in graphene

High-harmonic generation in condensed-matter systems is both a source of fundamental insight into quantum electron motion and a promising candidate to realize compact ultraviolet and ultrafast light sources. While graphene is anticipated to efficiently generate high-order harmonics due to its anharmonic charge-carrier dispersion, experiments performed on extended samples using THz illumination have revealed only a weak effect. The situation is further complicated by the enormous electromagnetic field intensities required by this highly nonperturbative nonlinear optical phenomenon. Here we argue that the large light intensity required for high-harmonic generation to occur can be reached by exploiting localized plasmons in doped graphene nanostructures. We demonstrate through rigorous time-domain simulations that the synergistic combination of strong plasmonic near-field enhancement and a pronounced intrinsic nonlinearity result in efficient broadband high-harmonic generation within a single material. Our results support the strong potential of nanostructured graphene as a robust, electrically tunable platform for high-harmonic generation.