Light-field-driven currents in graphene

Floquet engineering of interparticle correlations in electron-hole few-body system for strong radial confinement

We investigate the effects of off-resonant THz-frequency laser light coupling to bound few-body electron-hole system, i.e. the exciton and negatively charged trion confined in quantum wire. To solve this problem, we first conduct a unitary Hennerberger-Kramers transformation of the Hamiltonian and diagonalize its perturbative approximation to obtain the exciton and trion Floquet states. Within this framework, the light-matter coupling renormalizes an attractiveehinteraction, leaving the repulsiveeeunchanged, thus modifying corresponding two-particle correlation energies. Generally, the correlation energy ofehwould exceed theeeone for a semiconductor material with strongly localized heavy holes. However, as the former is weakened by increasing laser intensity, this relation can be reversed. Consequently, the trion may dissociate unconventionally, the hole gradually decouples from still strongly interacting electrons, and adequate energy and optical spectra changes accompany this process. The energy levels of the exciton and trion Floquet states are raised, while their optical brightness smoothly decreases for stronger laser intensities. We also show this process can be further modified by breaking the mirror symmetry of wire with a static electric field, and then the occurrence of the avoided crossings between the lowest energy levels of the trion depends on the laser intensity. These anticrossings shall be observed experimentally, confirming thus the usefulness of Floquet engineering for fast manipulations of the few-particle states in electron-hole systems on a subpicosecond time scale.

Direct coupling of light to valley current

The coupling of circularly polarized light to local band structure extrema ("valleys") in two dimensional semiconductors promises a new electronics based on the valley degree of freedom. Such pulses, however, couple only to valley charge and not to the valley current, precluding lightwave manipulation of this second vital element of valleytronic devices. Contradicting this established wisdom, we show that the few cycle limit of circularly polarized light is imbued with an emergent vectorial character that allows direct coupling to the valley current. The underlying physical mechanism involves the emergence of a momentum space valley dipole, the orientation and magnitude of which allows complete control over the direction and magnitude of the valley current. We demonstrate this effect via minimal tight-binding models both for the visible spectrum gaps of the transition metal dichalcogenides (generation time  ~ 1 fs) as well as the infrared gaps of biased bilayer graphene ( ~ 14 fs); we further verify our findings with state-of-the-art time-dependent density functional theory incorporating transient excitonic effects. Our findings both mark a striking example of emergent physics in the ultrafast limit of light-matter coupling, as well as allowing the creation of valley currents on time scales that challenge quantum decoherence in matter.

Attosecond electron microscopy and diffraction

Advances in attosecond spectroscopy have enabled tracing and controlling the electron motion dynamics in matter, although they have yielded insufficient information about the electron dynamic in the space domain. Hence, ultrafast electron and x-ray imaging tools have been developed to image the ultrafast dynamics of matter in real time and space. The cutting-edge temporal resolution of these imaging tools is on the order of a few tens to a hundred femtoseconds, limiting imaging to the atomic dynamics and leaving electron motion imaging out of reach. Here, we obtained the attosecond temporal resolution in the transmission electron microscope, which we coined "attomicroscopy." We demonstrated this resolution by the attosecond diffraction measurements of the field-driven electron dynamics in graphene. This attosecond imaging tool would provide more insights into electron motion and directly connect it to the structural dynamics of matter in real-time and space domains, opening the door for long-anticipated real-life attosecond science applications in quantum physics, chemistry, and biology.

Lightwave-electronic harmonic frequency mixing

Electronic frequency mixers are fundamental building blocks of electronic systems. Harmonic frequency mixing in particular enables broadband electromagnetic signal analysis across octaves of spectrum using a single local oscillator. However, conventional harmonic frequency mixers do not operate beyond hundreds of gigahertz to a few terahertz. If extended to the petahertz scale in a compact and scalable form, harmonic mixers would enable field-resolved optical signal analysis spanning octaves of spectra in a monolithic device without the need for frequency conversion using nonlinear crystals. Here, we demonstrate lightwave-electronic harmonic frequency mixing beyond 0.350 PHz using plasmonic nanoantennas. We demonstrate that the mixing process enables complete, field-resolved detection of spectral content far outside that of the local oscillator, greatly extending the range of detectable frequencies compared to conventional heterodyning techniques. Our work has important implications for applications where optical signals of interest exhibit coherent femtosecond-scale dynamics spanning multiple harmonics.

High-harmonic spin-orbit angular momentum generation in crystalline solids preserving multiscale dynamical symmetry

Symmetries essentially provide conservation rules in nonlinear light-matter interactions and facilitate control and understanding of photon conversion processes or electron dynamics. Since anisotropic solids have rich symmetries, they are strong candidates for controlling both optical micro- and macroscale structures, namely, spin angular momentum (circular polarization) and orbital angular momentum (spiral wavefront), respectively. Here, we show structured high-harmonic generation linked to the anisotropic symmetry of a solid. By strategically preserving a dynamical symmetry arising from the spin-orbit interaction of light, we generate multiple orbital angular momentum states in high-order harmonics. The experimental results exhibit the total angular momentum conservation rule of light even in the extreme nonlinear region, which is evidence that the mechanism originates from a dynamical symmetry. Our study provides a deeper understanding of multiscale nonlinear optical phenomena and a general guideline for using electronic structures to control structured light, such as through Floquet engineering.

Strong-Field Bloch Electron Interferometry for Band-Structure Retrieval

When Bloch electrons in a solid are exposed to a strong optical field, they are coherently driven in their respective bands where they acquire a quantum phase as the imprint of the band shape. If an electron approaches an avoided crossing formed by two bands, it may be split by undergoing a Landau-Zener transition. We here employ subsequent Landau-Zener transitions to realize strong-field Bloch electron interferometry, allowing us to reveal band structure information. In particular, we measure the Fermi velocity (band slope) of graphene in the vicinity of the K points as (1.07±0.04)  nm fs^{-1}. We expect strong-field Bloch electron interferometry for band structure retrieval to apply to a wide range of material systems and experimental conditions, making it suitable for studying transient changes in band structure with femtosecond temporal resolution at ambient conditions.

Ultrafast Electron-Electron Scattering in Metallic Phase of 2H-NbSe_{2} Probed by High Harmonic Generation

Electron-electron scattering on the order of a few to tens of femtoseconds plays a crucial role in the ultrafast electron dynamics of conventional metals. When mid-infrared light is used for driving and the period of light field is comparable to the scattering time in metals, unique light-driven states and nonlinear optical responses associated with the scattering process are expected to occur. Here, we use high-harmonics spectroscopy to investigate the effect of electron-electron scattering on the electron dynamics in thin film 2H-NbSe_{2} driven by a mid-infrared field. We observed odd-order high harmonics up to 9th order as well as a broadband emission from hot electrons in the energy range from 1.5 to 4.0 eV. The electron-electron scattering time in 2H-NbSe_{2} was estimated from the broadband emission to be almost the same as the period of the mid-infrared light field. A comparison between experimental results and a numerical calculation reveals that competition and cooperation between the driving and scattering enhances the nonperturbative behavior of high harmonics in metals, causing a highly nonequilibrium electronic state corresponding to several thousand Kelvin.

Analytical Model of Optical-Field-Driven Subcycle Electron Tunneling Pulses from Two-Dimensional Materials

We develop analytical models of optical-field-driven electron tunneling from the edge and surface of free-standing two-dimensional (2D) materials. We discover a universal scaling between the tunneling current density (J) and the electric field near the barrier (F): In(J/|F|β) ∝ 1/|F| with β values of 3/2 and 1 for edge emission and vertical surface emission, respectively. At ultrahigh values of F, the current density exhibits an unexpected high-field saturation effect due to the reduced dimensionality of the 2D material, which is absent in the traditional bulk material. Our calculation reveals the dc bias as an efficient method for modulating the optical-field tunneling subcycle emission characteristics. Importantly, our model is in excellent agreement with a recent experiment on graphene. Our results offer a useful framework for understanding optical-field tunneling emission from 2D materials, which are helpful for the development of optoelectronics and emerging petahertz vacuum nanoelectronics.

Light-wave-controlled Haldane model in monolayer hexagonal boron nitride

In recent years, the stacking and twisting of atom-thin structures with matching crystal symmetry has provided a unique way to create new superlattice structures in which new properties emerge1,2. In parallel, control over the temporal characteristics of strong light fields has allowed researchers to manipulate coherent electron transport in such atom-thin structures on sublaser-cycle timescales3,4. Here we demonstrate a tailored light-wave-driven analogue to twisted layer stacking. Tailoring the spatial symmetry of the light waveform to that of the lattice of a hexagonal boron nitride monolayer and then twisting this waveform result in optical control of time-reversal symmetry breaking5 and the realization of the topological Haldane model6 in a laser-dressed two-dimensional insulating crystal. Further, the parameters of the effective Haldane-type Hamiltonian can be controlled by rotating the light waveform, thus enabling ultrafast switching between band structure configurations and allowing unprecedented control over the magnitude, location and curvature of the bandgap. This results in an asymmetric population between complementary quantum valleys that leads to a measurable valley Hall current7, which can be detected by optical harmonic polarimetry. The universality and robustness of our scheme paves the way to valley-selective bandgap engineering on the fly and unlocks the possibility of creating few-femtosecond switches with quantum degrees of freedom.

Tracking electron motion within and outside of Floquet bands from attosecond pulse trains in time-resolved ARPES

Floquet engineering has recently emerged as a technique for controlling material properties with light. Floquet phases can be probed with time- and angle-resolved photoelectron spectroscopy (Tr-ARPES), providing direct access to the laser-dressed electronic bands. Applications of Tr-ARPES to date focused on observing the Floquet-Bloch bands themselves, and their build-up and dephasing on sub-laser-cycle timescales. However, momentum and energy resolved sub-laser-cycle dynamics between Floquet bands have not been analyzed. Given that Floquet theory strictly applies in time-periodic conditions, the notion of resolving sub-laser-cycle dynamics between Floquet states seems contradictory-it requires probe pulse durations below a laser cycle that inherently cannot discern the time-periodic nature of the light-matter system. Here we propose to employ attosecond pulse train probes with the same temporal periodicity as the Floquet-dressing pump pulse, allowing both attosecond sub-laser-cycle resolution and a proper projection of Tr-ARPES spectra on the Floquet-Bloch bands. We formulate and employ this approach inab-initiocalculations in light-driven graphene. Our calculations predict significant sub-laser-cycle dynamics occurring within the Floquet phase with the majority of electrons moving within and in-between Floquet bands, and a small portion residing and moving outside of them in what we denote as 'non-Floquet' bands. We establish that non-Floquet bands arise from the pump laser envelope that induces non-adiabatic electronic excitations during the pulse turn-on and turn-off. By performing calculations in systems with poly-chromatic pumps we also show that Floquet states are not formed on a sub-laser-cycle level. This work indicates that the Floquet-Bloch states are generally not a complete basis set for sub-laser-cycle dynamics in steady-state phases of matter.

High-Order Harmonic Generation in Solids: The Role of Intraband Transitions in Extreme Nonlinear Optics

High-order harmonic generation (HHG) in gases is frequently used nowadays to produce attosecond pulses and coherent radiation in the visible-to-soft X-ray spectral range. HHG in solids is a natural extension of the idea of HHG in gases, and its first observation about ten years ago opened the door to investigations on attosecond electron dynamics in solids and the development of solid-state attosecond light sources. The common process in both types of HHG is nonlinear photocarrier generation, and thus, transitions between different bands (interband transitions) are always important for HHG. As well, in the case of solids, the transitions within a band (intraband transitions) also need to be considered, because efficient carrier acceleration is possible due to them. This Perspective focuses on experimental findings that show how intraband transitions can be controlled because such an understanding will be essential in the development of unique optoelectronics that can operate at petahertz frequencies.

High harmonic generation in graphene quantum dots

We study theoretically the generation of high harmonics in disk graphene quantum dots placed in linearly polarized short pulse. The quantum dots (QD) are described within an effective model of the Dirac type and the length gauge was used to describe the interaction of quantum dots with an optical pulse. The generated radiation spectra of graphene quantum dots can be controlled by varying the quantum dot size, i.e. its radius. With increasing the quantum dot radius, the intensities of low harmonics mainly decrease, while the cutoff frequency increases. The sensitivity of the cutoff frequency to the QD size increases with the intensity of the pulse.

Light-driven nanoscale vectorial currents

Controlled charge flows are fundamental to many areas of science and technology, serving as carriers of energy and information, as probes of material properties and dynamics1 and as a means of revealing2,3 or even inducing4,5 broken symmetries. Emerging methods for light-based current control5-16 offer particularly promising routes beyond the speed and adaptability limitations of conventional voltage-driven systems. However, optical generation and manipulation of currents at nanometre spatial scales remains a basic challenge and a crucial step towards scalable optoelectronic systems for microelectronics and information science. Here we introduce vectorial optoelectronic metasurfaces in which ultrafast light pulses induce local directional charge flows around symmetry-broken plasmonic nanostructures, with tunable responses and arbitrary patterning down to subdiffractive nanometre scales. Local symmetries and vectorial currents are revealed by polarization-dependent and wavelength-sensitive electrical readout and terahertz (THz) emission, whereas spatially tailored global currents are demonstrated in the direct generation of elusive broadband THz vector beams17. We show that, in graphene, a detailed interplay between electrodynamic, thermodynamic and hydrodynamic degrees of freedom gives rise to rapidly evolving nanoscale driving forces and charge flows under the extremely spatially and temporally localized excitation. These results set the stage for versatile patterning and optical control over nanoscale currents in materials diagnostics, THz spectroscopies, nanomagnetism and ultrafast information processing.

Quantum control of flying doughnut terahertz pulses

The ability to manipulate the multiple properties of light diversifies light-matter interaction and light-driven applications. Here, using quantum control, we introduce an approach that enables the amplitude, sign, and even configuration of the generated light fields to be manipulated in an all-optical manner. Following this approach, we demonstrate the generation of "flying doughnut" terahertz (THz) pulses. We show that the single-cycle THz pulse radiated from the dynamic ring current has an electric field structure that is azimuthally polarized and that the space- and time-resolved magnetic field has a strong, isolated longitudinal component. We apply the flying doughnut pulse for a spectroscopic measurement of the water vapor in ambient air. Pulses such as these will serve as unique probes for spectroscopy, imaging, telecommunications, and magnetic materials.

Light-Shaping of Valley States

The established paradigm to create valley states, excitations at local band extrema ("valleys"), is through selective occupation of specific valleys via circularly polarized laser pulses. Here we show a second way exists to create valley states, not by valley population imbalance but by "light-shaping" in momentum space, i.e. controlling the shape of the distribution of excited charge at each valley. While noncontrasting in valley charge, such valley states are instead characterized by a valley current, identically zero at one valley and finite and large at the other. We demonstrate that these (i) are robust to quantum decoherence, (ii) allow lossless toggling of the valley state with successive femtosecond laser pulses, and (iii) permit valley contrasting excitation both with and without a gap. Our findings open a route to robust ultrafast and switchable valleytronics in a wide scope of 2d materials, bringing closer the promise of valley-based electronics.

Mapping Light-Dressed Floquet Bands by Highly Nonlinear Optical Excitations and Valley Polarization

Ultrafast nonlinear optical phenomena in solids have been attracting a great deal of interest as novel methodologies for the femtosecond spectroscopy of electron dynamics and control of the properties of materials. Here, we theoretically investigate strong-field nonlinear optical transitions in a prototypical two-dimensional material, hBN, and show that the k-resolved conduction band charge occupation patterns induced by an elliptically polarized laser can be understood in a multiphoton resonant picture, but, remarkably, only if using the Floquet light-dressed states instead of the undressed matter states. Our work demonstrates that Floquet dressing affects ultrafast charge dynamics and photoexcitation even from a single pump pulse and establishes a direct measurable signature for band dressing in nonlinear optical processes in solids, opening new paths for ultrafast spectroscopy and valley manipulation.

Gauge Invariant Formulation of the Semiconductor Bloch Equations

We derive gauge invariant semiconductor Bloch equations (GI-SBEs) that contain only gauge invariant band structure; shift vectors, and triple phase products. The validity and utility of the GI-SBEs is demonstrated in intense laser driven solids with broken inversion symmetry and nontrivial topology. The GI-SBEs present a useful platform for modeling and interpreting light-matter interactions in solids, in which the gauge freedom of the Bloch basis functions obscures physics and creates numerical obstacles.

Giant and Controllable Valley Currents in Graphene by Double Pumped THz Light

The field of valleytronics considers the creation and manipulation of "valley states", charge excitations characterized by a particular value of the crystal momentum in the Brillouin zone. Here we show, using the example of minimally gapped (≤40 meV) graphene, that there exist lightforms that create almost perfect valley contrasting current states (up to ∼80% valley purity) in the absence of a valley contrasting charge excitation. These "momentum streaked" THz waveforms act by deforming the excited state population in momentum space such that current flows at one valley yet is blocked at the conjugate valley. This approach both unlocks the potential of graphene as a materials platform for valleytronics, as gaps of 10-40 meV are robustly found in useful experimental contexts such as graphene/hBN systems, while simultaneously providing a tool toward ultrafast light control of valley currents in diverse minimally gapped matter, including many topological insulator systems.

Enhanced optical conductivity and many-body effects in strongly-driven photo-excited semi-metallic graphite

The excitation of quasi-particles near the extrema of the electronic band structure is a gateway to electronic phase transitions in condensed matter. In a many-body system, quasi-particle dynamics are strongly influenced by the electronic single-particle structure and have been extensively studied in the weak optical excitation regime. Yet, under strong optical excitation, where light fields coherently drive carriers, the dynamics of many-body interactions that can lead to new quantum phases remain largely unresolved. Here, we induce such a highly non-equilibrium many-body state through strong optical excitation of charge carriers near the van Hove singularity in graphite. We investigate the system's evolution into a strongly-driven photo-excited state with attosecond soft X-ray core-level spectroscopy. We find an enhancement of the optical conductivity of nearly ten times the quantum conductivity and pinpoint it to carrier excitations in flat bands. This interaction regime is robust against carrier-carrier interaction with coherent optical phonons acting as an attractive force reminiscent of superconductivity. The strongly-driven non-equilibrium state is markedly different from the single-particle structure and macroscopic conductivity and is a consequence of the non-adiabatic many-body state.

Band Nonlinearity-Enabled Manipulation of Dirac Nodes, Weyl Cones, and Valleytronics with Intense Linearly Polarized Light

We study low-frequency linearly polarized laser-dressing in materials with valley (graphene and hexagonal-Boron-Nitride) and topological (Dirac- and Weyl-semimetals) properties. In Dirac-like linearly dispersing bands, the laser substantially moves the Dirac nodes away from their original position, and the movement direction can be fully controlled by rotating the laser polarization. We prove that this effect originates from band nonlinearities away from the Dirac nodes. We further demonstrate that this physical mechanism is widely applicable and can move the positions of the valley minima in hexagonal materials to tune valley selectivity, split and move Weyl cones in higher-order Weyl semimetals, and merge Dirac nodes in three-dimensional Dirac semimetals. The model results are validated with ab initio calculations. Our results directly affect efforts for exploring light-dressed electronic structure, suggesting that one can benefit from band nonlinearity for tailoring material properties, and highlight the importance of the full band structure in nonlinear optical phenomena in solids.

Giant room-temperature nonlinearities in a monolayer Janus topological semiconductor

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 2H MoS2 for 18th order harmonic generation; > 20 times higher than 2H MoS2 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.

Residual current under the combined effect of carrier envelope phase and chirp: phase shift and peak enhancement

We theoretically investigate the residual current of linearly polarized light incident on graphene under the combined effect of carrier envelope phase and chirp. Phase shift and peak residual current enhancement are significantly obtained. Phase shift is the natural result of introducing a linear chirp in the presence of carrier envelope phase. By comparing the residual current integrated along the kx direction for different chirp rates and carrier envelope phases, the enhancement can be observed from two regions, where multiphoton interference is involved. By increasing the chirp rate, the light-graphene interaction turns from a non-perturbative to a perturbative regime. Thus the results of the combined effect can help to find suitable parameters to study regime transition and control of electronic dynamics. We expect that this study contributes to the signal processing at optical frequencies and to the development of optoelectronic integrated device applications.

Stark control of electrons across the molecule-semiconductor interface

Controlling matter at the level of electrons using ultrafast laser sources represents an important challenge for science and technology. Recently, we introduced a general laser control scheme (the Stark control of electrons at interfaces or SCELI) based on the Stark effect that uses the subcycle structure of light to manipulate electron dynamics at semiconductor interfaces [A. Garzón-Ramírez and I. Franco, Phys. Rev. B 98, 121305 (2018)]. Here, we demonstrate that SCELI is also of general applicability in molecule-semiconductor interfaces. We do so by following the quantum dynamics induced by non-resonant few-cycle laser pulses of intermediate intensity (non-perturbative but non-ionizing) across model molecule-semiconductor interfaces of varying level alignments. We show that SCELI induces interfacial charge transfer regardless of the energy level alignment of the interface and even in situations where charge exchange is forbidden via resonant photoexcitation. We further show that the SCELI rate of charge transfer is faster than those offered by resonant photoexcitation routes as it is controlled by the subcycle structure of light. The results underscore the general applicability of SCELI to manipulate electron dynamics at interfaces on ultrafast timescales.

Build-up and dephasing of Floquet-Bloch bands on subcycle timescales

Strong light fields have created opportunities to tailor novel functionalities of solids1-5. Floquet-Bloch states can form under periodic driving of electrons and enable exotic quantum phases6-15. On subcycle timescales, lightwaves can simultaneously drive intraband currents16-29 and interband transitions18,19,30,31, which enable high-harmonic generation16,18,19,21,22,25,28-30 and pave the way towards ultrafast electronics. Yet, the interplay of intraband and interband excitations and their relation to Floquet physics have been key open questions as dynamical aspects of Floquet states have remained elusive. Here we provide this link by visualizing the ultrafast build-up of Floquet-Bloch bands with time-resolved and angle-resolved photoemission spectroscopy. We drive surface states on a topological insulator32,33 with mid-infrared fields-strong enough for high-harmonic generation-and directly monitor the transient band structure with subcycle time resolution. Starting with strong intraband currents, we observe how Floquet sidebands emerge within a single optical cycle; intraband acceleration simultaneously proceeds in multiple sidebands until high-energy electrons scatter into bulk states and dissipation destroys the Floquet bands. Quantum non-equilibrium calculations explain the simultaneous occurrence of Floquet states with intraband and interband dynamics. Our joint experiment and theory study provides a direct time-domain view of Floquet physics and explores the fundamental frontiers of ultrafast band-structure engineering.

THz induced giant spin and valley currents

Spin and valley indices represent the key quantum labels of quasi-particles in a wide class of two-dimensional materials and form the foundational elements of the fields of spintronics and valleytronics. Control over these degrees of freedom, therefore, remains the central challenge in these fields. Here, we show that femtosecond laser light combining optical frequency circularly polarized pulse and a terahertz (THz) frequency linearly polarized pulse, a so-called "hencomb" pulse, can generate precisely tailored and 90% pure spin currents for the dichalcogenide WSe₂ and >75% pure valley currents for bilayer graphene with gaps greater than 120 millielectron volts (dephasing time, 20 femtoseconds). The frequency of the circular light component and the polarization vector of the THz light component are shown to represent the key control parameters of these pulses. Our results thus open a route toward light control over spin/valley current states at ultrafast times.

Theoretical Approach for Electron Dynamics and Ultrafast Spectroscopy (EDUS)

In this manuscript, we present a theoretical framework and its numerical implementation to simulate the out-of-equilibrium electron dynamics induced by the interaction of ultrashort laser pulses in condensed-matter systems. Our approach is based on evolving in real time the density matrix of the system in reciprocal space. It considers excitonic and nonperturbative light-matter interactions. We show some relevant examples that illustrate the efficiency and flexibility of the approach to describe realistic ultrafast spectroscopy experiments. Our approach is suitable for modeling the promising and emerging ultrafast studies at the attosecond time scale that aim at capturing the electron dynamics and the dynamical electron-electron correlations via X-ray absorption spectroscopy.

Optical Control of High-Harmonic Generation at the Atomic Thickness

High-harmonic generation (HHG), an extreme nonlinear optical phenomenon beyond the perturbation regime, is of great significance for various potential applications, such as high-energy ultrashort pulse generation with outstanding spatiotemporal coherence. However, efficient active control of HHG is still challenging due to the weak light-matter interaction displayed by currently known materials. Here, we demonstrate optically controlled HHG in monolayer semiconductors via the engineering of interband polarization. We find that HHG can be efficiently controlled in the excitonic spectral region with modulation depths up to 95% and ultrafast response speeds of several picoseconds. Quantitative time-domain theory of the nonlinear optical susceptibilities in monolayer semiconductors further corroborates these experimental observations. Our demonstration not only offers an in-depth understanding of HHG but also provides an effective approach toward active optical devices for strong-field physics and extreme nonlinear optics.

Bidirectional residual current in monolayer graphene under few-cycle laser irradiation

By numerically solving the time-dependent Schrödinger equation and semiconductor Bloch equations, the light-induced residual current in monolayer graphene driven by a circularly polarized few-cycle laser is investigated. An evident current direction reversal is disclosed when the amplitude of the driving electric field exceeds a certain threshold value, which is absent in recent investigation [Nature550, 224 (2017)10.1038/nature23900]. Here the internal physical mechanism for the current reversal is inter-optical-cycle interference under a suitable long laser wavelength. Moreover, the reversal-related laser field amplitude depends sensitively on the ratio of ponderomotive energy to photon energy.

Recent Development of Ultrafast Optical Characterizations for Quantum Materials

The advent of intense ultrashort optical pulses spanning a frequency range from terahertz to the visible has opened a new era in the experimental investigation and manipulation of quantum materials. The generation of strong optical field in an ultrashort time scale enables the steering of quantum materials nonadiabatically, inducing novel phenomenon or creating new phases which may not have an equilibrium counterpart. Ultrafast time-resolved optical techniques have provided rich information and played an important role in characterization of the nonequilibrium and nonlinear properties of solid systems. Here, some of the recent progress of ultrafast optical techniques and their applications to the detection and manipulation of physical properties in selected quantum materials are reviewed. Specifically, the new development in the detection of the Higgs mode and photoinduced nonequilibrium response in the study of superconductors by time-resolved terahertz spectroscopy are discussed.

Analysis of low-frequency THz emission from monolayer graphene irradiated by a long two-color laser pulse

Terahertz (THz) radiations from graphene are expected to provide a powerful light source for their wide applications. However, their conversion efficiencies are limited with either long-duration or few-cycle single-color laser pulses. Here, we theoretically demonstrate that THz waves can be efficiently generated from monolayer graphene by using a long-duration two-color laser pulse at normal incidence. Our simulated results show that low-frequency THz emissions are sensitive to the phase difference between two colors, the laser intensity, and the fundamental wavelength. Their dependence on these parameters can be very well reproduced by asymmetry parameters accounting for electron populations of conduction and valence bands. On the contrary, a newly defined σ parameter including the Landau-Zener tunneling probability cannot precisely predict such dependence. Furthermore, the waveform of THz electric field driven by two-color laser pulses exhibits the typical feature of a half-cycle pulse.

Topological resonance in graphene-like materials

In topological materials, interacting with short and strong optical pulses, electrons can accumulate a topological phase during the pulse. Such phase can compensate the dynamic phase resulting in topological resonance, which is visible as a large inter-band transfer of electron population. We study theoretically the topological resonance in materials of the gapped multilayer graphene type. We show that the resonance can be observed only in the systems with finite bandgap. For graphene monolayer the topological resonance can occur only in the field of an elliptically polarized pulse, while for graphene systems with many layers the topological resonance can be also realized in a linearly polarized pulse.

Light-field-driven electronics in the mid-infrared regime: Schottky rectification

The speed of an active electronic semiconductor device is limited by RC timescale, i.e., the time required for its charging and discharging. To circumvent this ubiquitous limitation of conventional electronics, we investigate diodes under intense mid-infrared light-field pulses. We choose epitaxial graphene on silicon carbide as a metal/semiconductor pair, acting as an ultrarobust and almost-transparent Schottky diode. The usually dominant forward direction is suppressed, but a characteristic signal occurs in reverse bias. For its theoretical description, we consider tunneling through the light-field-modulated Schottky barrier, complemented by a dynamical accumulation correction. On the basis only of the DC parametrization of the diode, the model provides a consistent and accurate description of the experimentally observed infrared phenomena. This allows the conclusion that cycle-by-cycle dynamics determines rectification. As the chosen materials have proven capabilities for transistors, circuits, and even a full logic, we see a way to establish light-field-driven electronics with rapidly increasing functionality.

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 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.

Intense Laser Pulse Interaction With Graphene and Graphene Ribbons

In this work we investigate quantum mechanically the interaction of an intense ultrashort laser pulse with the graphene monolayer as well as with the armchair graphene ribbons of different widths. We consider a tight binding (TB) Hamiltonian of the monolayer graphene and give two rules for deriving the dispersion relations of the armchair graphene ribbons of any width, N, from the TB eigenvalues of the monolayer. The band structure of the monolayer and the armchair ribbons of different widths are discussed with illustrations. The time-dependent wavefunctions of the systems and the expectation values of interest are determined by solving the coupled equations of the band amplitudes "exactly" (numerically). First, simulations are made for the population excitation in the conduction band (CB) from the valence band (BV), the VB-CB interband correlation (or "coherence"), the intraband, the interband and the total currents in the monolayer graphene. The graphene currents are compared with the corresponding currents induced in an armchair ribbon (width, N = 3). The change from the 2D monolayer to the 1D ribbon shows a remarkable transition of the dominance of the intraband current that leads to a near steady total current in the monolayer, to a dominance of the interband current in the ribbon that induces an oscillatory current in the ribbon beyond the pulse duration. The difference observed might be a combined effect of the "confinement" in one dimention and a finite band-gap minimum in the case of the ribbon. However, this transition should be further investigated for better clarity. A brief comparison of the radiation spectra emitted from the monolayer and from the ribbon is also made. They show a grossly similar structure and a relative insensitivity with respect to the detailed structure of the targets chosen. This might be due to the dominance of virtual continuum-continuum transitions, to and from the bands states, that lie behind the fundamental quantum process of high harmonic emissions. Lastly, the dependence of the charge currents, induced in a ribbon of unit width (N = 1), on the carrier-envelope-phase (CEP) of the incident laser pulse is investigated. It is seen that the shape of the main part of the current produced in the ribbon can be fully reversed by changing the CEP of the ultrashort laser pulse from 0 to π. More generally, it is suggested that the pulse shape of the charge carriers in the ribbon could be designed by similarly tailoring the form of the vector potential of the incident laser pulse.

Polarization-sensitive optoionic membranes from chiral plasmonic nanoparticles

Optoelectronic effects differentiating absorption of right and left circularly polarized photons in thin films of chiral materials are typically prohibitively small for their direct photocurrent observation. Chiral metasurfaces increase the electronic sensitivity to circular polarization, but their out-of-plane architecture entails manufacturing and performance trade-offs. Here, we show that nanoporous thin films of chiral nanoparticles enable high sensitivity to circular polarization due to light-induced polarization-dependent ion accumulation at nanoparticle interfaces. Self-assembled multilayers of gold nanoparticles modified with L-phenylalanine generate a photocurrent under right-handed circularly polarized light as high as 2.41 times higher than under left-handed circularly polarized light. The strong plasmonic coupling between the multiple nanoparticles producing planar chiroplasmonic modes facilitates the ejection of electrons, whose entrapment at the membrane-electrolyte interface is promoted by a thick layer of enantiopure phenylalanine. Demonstrated detection of light ellipticity with equal sensitivity at all incident angles mimics phenomenological aspects of polarization vision in marine animals. The simplicity of self-assembly and sensitivity of polarization detection found in optoionic membranes opens the door to a family of miniaturized fluidic devices for chiral photonics.

Electro-optic characterization of synthesized infrared-visible light fields

The measurement and control of light field oscillations enable the study of ultrafast phenomena on sub-cycle time scales. Electro-optic sampling (EOS) is a powerful field characterization approach, in terms of both sensitivity and dynamic range, but it has not reached beyond infrared frequencies. Here, we show the synthesis of a sub-cycle infrared-visible pulse and subsequent complete electric field characterization using EOS. The sampled bandwidth spans from 700 nm to 2700 nm (428 to 110 THz). Tailored electric-field waveforms are generated with a two-channel field synthesizer in the infrared-visible range, with a full-width at half-maximum duration as short as 3.8 fs at a central wavelength of 1.7 µm (176 THz). EOS detection of the complete bandwidth of these waveforms extends it into the visible spectral range. To demonstrate the power of our approach, we use the sub-cycle transients to inject carriers in a thin quartz sample for nonlinear photoconductive field sampling with sub-femtosecond resolution.

Optoelectronic Current through Unbiased Monolayer Amorphous Carbon Nanojunctions

Monolayer amorphous carbon (MAC) is a recently synthesized disordered 2D carbon material. An ensemble of MAC nanofragments contains diverse manifestations of lattice disorder, and because of disorder the key unifying characteristic of this ensemble is poor electronic conductance. Curiously, our computational analysis of the electronic properties of MAC nanofragments revealed an additional commonality: a robust presence of charge-transfer character for electronic transitions from the occupied to virtual orbitals. This charge-transfer property suggests possible applications in optoelectronics. In this Letter, we demonstrate computationally that a laser pulse induces directional electronic currents in unbiased MAC nanojunctions and discuss the effects of pulse intensity on the magnitude of electron transfer.

Fingerprint of the Interbond Electron Hopping in Second-Order Harmonic Generation

We experimentally explore the fingerprint of the microscopic electron dynamics in second-order harmonic generation (SHG). It is shown that the interbond electron hopping induces a novel source of nonlinear polarization and plays an important role even when the driving laser intensity is 2 orders of magnitude lower than the characteristic atomic field. Our model predicts anomalous anisotropic structures of the SHG yield contributed by the interbond electron hopping, which is identified in our experiments with ZnO crystals. Moreover, a generalized second-order susceptibility with an explicit form is proposed, which provides a unified description in both the weak and strong field regimes. Our work reveals the nonlinear responses of materials at the electron scale and extends the nonlinear optics to a previously unexplored regime, where the nonlinearity related to the interbond electron hopping becomes dominant. It paves the way for realizing controllable nonlinearity on an ultrafast time scale.

Electronic Coherence and Coherent Dephasing in the Optical Control of Electrons in Graphene

Electronic coherence is of utmost importance for the access and control of quantum-mechanical solid-state properties. Using a purely electronic observable, the photocurrent, we measure a lower bound of the electronic coherence time of 22 ± 4 fs in graphene. The photocurrent is ideally suited to measure electronic coherence, as it is a direct result of coherent quantum-path interference, controlled by the delay between two ultrashort two-color laser pulses. The maximum delay for which interference between the population amplitude injected by the first pulse interferes with that generated by the second pulse determines the electronic coherence time. In particular, numerical simulations reveal that the experimental data yields a lower bound on the electronic coherence time, masked by coherent dephasing due to the broadband absorption in graphene. We expect that our results will significantly advance the understanding of coherent quantum control in solid-state systems ranging from excitation with weak fields to strongly driven systems.

Light-Driven Extremely Nonlinear Bulk Photogalvanic Currents

We predict the generation of bulk photocurrents in materials driven by bichromatic fields that are circularly polarized and corotating. The nonlinear photocurrents have a fully controllable directionality and amplitude without requiring carrier-envelope-phase stabilization or few-cycle pulses, and can be generated with photon energies much smaller than the band gap (reducing heating in the photoconversion process). We demonstrate with ab initio calculations that the photocurrent generation mechanism is universal and arises in gaped materials (Si, diamond, MgO, hBN), in semimetals (graphene), and in two- and three-dimensional systems. Photocurrents are shown to rely on sub-laser-cycle asymmetries in the nonlinear response that build-up coherently from cycle to cycle as the conduction band is populated. Importantly, the photocurrents are always transverse to the major axis of the co-circular lasers regardless of the material's structure and orientation (analogously to a Hall current), which we find originates from a generalized time-reversal symmetry in the driven system. At high laser powers (∼10^{13}  W/cm^{2}) this symmetry can be spontaneously broken by vast electronic excitations, which is accompanied by an onset of carrier-envelope-phase sensitivity and ultrafast many-body effects. Our results are directly applicable for efficient light-driven control of electronics, and for enhancing sub-band-gap bulk photogalvanic effects.

Carrier-Envelope-Phase Modulated Currents in Scanning Tunneling Microscopy

Carrier-envelope-phase (CEP) stable optical pulses combined with state-of-the-art scanning tunneling microscopy (STM) can track and control ultrafast electronic tunneling currents. On the basis of nonequilibrium Green's function formalism, we present a time and frequency domain theoretical study of CEP-stable pulse-induced tunneling currents between an STM tip and a metal substrate. It is revealed that the experimentally observed phase shift between the maximum tunneling current and maximum electric field is caused by the third-order response to the electric field. The shift is also found to be sensitive to the duration of pulses. The tunneling process can thus be precisely manipulated by varying the phase and duration of these pulses.

Bilayer graphene in strong ultrafast laser fields

We theoretically investigate the interaction of an ultrastrong femtosecond-long linearly polarized optical pulse with AB-stacked bilayer graphene (BLG). The pulse excite electrons from the valence into the conduction band (CB), resulting in finite CB population. Such a redistribution of electrons results in the generation of current which can be manipulated by the angle of incidence of the pulse. For the normal incidence, the current along a direction transverse to the polarization of the optical pulse is zero. However, the interlayer symmetry is broken up by a finite angle of incidence due to which BLG possesses a single axis of symmetry. Thus, for an oblique incidence, if the pulse is polarized normal to the symmetry axis then there is an induction of electric current in the direction perpendicular to the polarization of the pulse. We show that the magnitude and the direction of such a current as well as charge transfer along this direction can be manipulated by tuning the angle of incidence of the laser pulse. Further, the symmetry of the system prohibits the generation of transverse current if the pulse is polarized along the axis of symmetry of BLG.

Coherent Excitation and Control of Plasmons on Gold Using Two-Dimensional Transition Metal Dichalcogenides

The hybrid combination of two-dimensional (2D) transition metal dichalcogenides (TMDs) and plasmonic materials open up novel means of (ultrafast) optoelectronic applications and manipulation of nanoscale light-matter interaction. However, control of the plasmonic excitations by TMDs themselves has not been investigated. Here, we show that the ultrathin 2D WSe₂ crystallites permit nanoscale spatially controlled coherent excitation of surface plasmon polaritons (SPPs) on smooth Au films. The resulting complex plasmonic interference patterns are recorded with nanoscale resolution in a photoemission electron microscope. Modeling shows good agreement with experiments and further indicates how SPPs can be tailored with high spatiotemporal precision using the shape of the 2D TMDs with thicknesses down to single molecular layers. We demonstrate the use of WSe₂ nanocrystals as 2D optical elements for exploring the ultrafast dynamics of SPPs. Using few-femtosecond laser pulse pairs we excite an SPP at the boundary of a WSe₂ crystal and then have a WSe₂ monolayer wedge act as a delay line inducing a spatially varying phase difference down to the attosecond time range. The observed effects are a natural yet unexplored consequence of high dielectric functional values of TMDs in the visible range that should be considered when designing metal-TMD hybrid devices. As the 2D TMD crystals are stable in air, can be defect free, can be synthesized in many shapes, and are reliably positioned on metal surfaces, using them to excite and steer SPPs adds an interesting alternative in designing hybrid structures for plasmonic control.

Enhancement of the photocurrents injected in gapped graphene by the orthogonally polarized two-color laser field

We theoretically investigate the photocurrents injected in gapped graphene by the orthogonally polarized two-color laser field. Depending on the relative phase, the photocurrents can be coherently controlled by deforming the electron trajectory in the reciprocal space. Under the same field strength, the peak photocurrent in the orthogonally polarized two-color field is about 20 times larger than that for linearly polarized light, and about 3.6 times for elliptically polarized light. The enhancement of the photocurrent can be attributed to an obvious asymmetric distribution of the real population in the reciprocal space, which is sensitive to the waveform of the laser field and related to the quantum interference between the electron trajectories. Our work provides a noncontact method to effectively enhance the injected current in graphene.

Tunable non-integer high-harmonic generation in a topological insulator

When intense lightwaves accelerate electrons through a solid, the emerging high-order harmonic (HH) radiation offers key insights into the material^1-11. Sub-optical-cycle dynamics-such as dynamical Bloch oscillations^2-5, quasiparticle collisions^6,12, valley pseudospin switching¹³ and heating of Dirac gases¹⁰-leave fingerprints in the HH spectra of conventional solids. Topologically non-trivial matter^14,15 with invariants that are robust against imperfections has been predicted to support unconventional HH generation^16-20. Here we experimentally demonstrate HH generation in a three-dimensional topological insulator-bismuth telluride. The frequency of the terahertz driving field sharply discriminates between HH generation from the bulk and from the topological surface, where the unique combination of long scattering times owing to spin-momentum locking¹⁷ and the quasi-relativistic dispersion enables unusually efficient HH generation. Intriguingly, all observed orders can be continuously shifted to arbitrary non-integer multiples of the driving frequency by varying the carrier-envelope phase of the driving field-in line with quantum theory. The anomalous Berry curvature warranted by the non-trivial topology enforces meandering ballistic trajectories of the Dirac fermions, causing a hallmark polarization pattern of the HH emission. Our study provides a platform to explore topology and relativistic quantum physics in strong-field control, and could lead to non-dissipative topological electronics at infrared frequencies.

Schrödinger-Cat States in Landau-Zener-Stückelberg-Majorana Interferometry: A Multiple Davydov Ansatz Approach

Employing the time-dependent variational principle combined with the multiple Davydov D₂ Ansatz, we investigate Landau-Zener (LZ) transitions in a qubit coupled to a photon mode with various initial photon states at zero temperature. Thanks to the multiple Davydov trial states, exact photonic dynamics taking place in the course of the LZ transition is also studied efficiently. With the qubit driven by a linear external field and the photon mode initialized with Schrödinger-cat states, asymptotic behavior of the transition probability beyond the rotating-wave approximation is uncovered for a variety of initial states. Using a sinusoidal external driving field, we also explore the photon-assisted dynamics of Landau-Zener-Stückelberg-Majorana interferometry. Transition pathways involving multiple energy levels are unveiled by analyzing the photon dynamics.

Super-resolution lightwave tomography of electronic bands in quantum materials

Searching for quantum functionalities requires access to the electronic structure, constituting the foundation of exquisite spin-valley-electronic, topological, and many-body effects. All-optical band-structure reconstruction could directly connect electronic structure with the coveted quantum phenomena if strong lightwaves transported localized electrons within preselected bands. Here, we demonstrate that harmonic sideband (HSB) generation in monolayer tungsten diselenide creates distinct electronic interference combs in momentum space. Locating these momentum combs in spectroscopy enables super-resolution tomography of key band-structure details in situ. We experimentally tuned the optical-driver frequency by a full octave and show that the predicted super-resolution manifests in a critical intensity and frequency dependence of HSBs. Our concept offers a practical, all-optical, fully three-dimensional tomography of electronic structure even in microscopically small quantum materials, band by band.

Plasmonic topological quasiparticle on the nanometre and femtosecond scales

At the interface of classical and quantum physics, the Maxwell and Schrödinger equations describe how optical fields drive and control electronic phenomena to enable lightwave electronics at terahertz or petahertz frequencies and on ultrasmall scales^1-5. The electric field of light striking a metal interacts with electrons and generates light-matter quasiparticles, such as excitons⁶ or plasmons⁷, on an attosecond timescale. Here we create and image a quasiparticle of topological plasmonic spin texture in a structured silver film. The spin angular momentum components of linearly polarized light interacting with an Archimedean coupling structure with a designed geometric phase generate plasmonic waves with different orbital angular momenta. These plasmonic fields undergo spin-orbit interaction and their superposition generates an array of plasmonic vortices. Three of these vortices can form spin textures that carry non-trivial topological charge⁸ resembling magnetic meron quasiparticles⁹. These spin textures are localized within a half-wavelength of light, and exist on the timescale of the plasmonic field. We use ultrafast nonlinear coherent photoelectron microscopy to generate attosecond videos of the spatial evolution of the vortex fields; electromagnetic simulations and analytic theory confirm the presence of plasmonic meron quasiparticles. The quasiparticles form a chiral field, which breaks the time-reversal symmetry on a nanometre spatial scale and a 20-femtosecond timescale (the 'nano-femto scale'). This transient creation of non-trivial spin angular momentum topology pertains to cosmological structure creation and topological phase transitions in quantum matter^10-12, and may transduce quantum information on the nano-femto scale^13,14.