Subcycle observation of lightwave-driven Dirac currents in a topological surface band

Intercalation in 2D materials and in situ studies

Intercalation of atoms, ions and molecules is a powerful tool for altering or tuning the properties - interlayer interactions, in-plane bonding configurations, Fermi-level energies, electronic band structures and spin-orbit coupling - of 2D materials. Intercalation can induce property changes in materials related to photonics, electronics, optoelectronics, thermoelectricity, magnetism, catalysis and energy storage, unlocking or improving the potential of 2D materials in present and future applications. In situ imaging and spectroscopy technologies are used to visualize and trace intercalation processes. These techniques provide the opportunity for deciphering important and often elusive intercalation dynamics, chemomechanics and mechanisms, such as the intercalation pathways, reversibility, uniformity and speed. In this Review, we discuss intercalation in 2D materials, beginning with a brief introduction of the intercalation strategies, then we look into the atomic and intrinsic effects of intercalation, followed by an overview of their in situ studies, and finally provide our outlook.

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.

Valleytronics in bulk MoS2 with a topologic optical field

The valley degree of freedom1-4 of electrons in materials promises routes towards energy-efficient information storage with enticing prospects for quantum information processing5-7. Current challenges in utilizing valley polarization are symmetry conditions that require monolayer structures8,9 or specific material engineering10-13, non-resonant optical control to avoid energy dissipation and the ability to switch valley polarization at optical speed. We demonstrate all-optical and non-resonant control over valley polarization using bulk MoS2, a centrosymmetric material without Berry curvature at the valleys. Our universal method utilizes spin angular momentum-shaped trefoil optical control pulses14,15 to switch the material's electronic topology and induce valley polarization by transiently breaking time and space inversion symmetry16 through a simple phase rotation. We confirm valley polarization through the transient generation of the second harmonic of a non-collinear optical probe pulse, depending on the trefoil phase rotation. The investigation shows that direct optical control over the valley degree of freedom is not limited to monolayer structures. Indeed, such control is possible for systems with an arbitrary number of layers and for bulk materials. Non-resonant valley control is universal and, at optical speeds, unlocks the possibility of engineering efficient multimaterial valleytronic devices operating on quantum coherent timescales.

Perspectives: Light Control of Magnetism and Device Development

Accurately controlling magnetic and spin states presents a significant challenge in spintronics, especially as demands for higher data storage density and increased processing speeds grow. Approaches such as light control are gradually supplanting traditional magnetic field methods. Traditionally, the modulation of magnetism was predominantly achieved through polarized light with the help of ultrafast light technologies. With the growing demand for energy efficiency and multifunctionality in spintronic devices, integrating photovoltaic materials into magnetoelectric systems has introduced more physical effects. This development suggests that sunlight will play an increasingly pivotal role in manipulating spin orientation in the future. This review introduces and concludes the influence of various light types on magnetism, exploring mechanisms such as magneto-optical (MO) effects, light-induced magnetic phase transitions, and spin photovoltaic effects. This review briefly summarizes recent advancements in the light control of magnetism, especially sunlight, and their potential applications, providing an optimistic perspective on future research directions in this area.

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.

Topological spin textures in electronic non-Hermitian systems

Non-Hermitian systems have been discussed mostly in the context of open systems and nonequilibrium. Recent experimental progress is much from optical, cold-atomic, and classical platforms due to the vast tunability and clear identification of observables. However, their counterpart in solid-state electronic systems in equilibrium remains unmasked although highly desired, where a variety of materials are available, calculations are solidly founded, and accurate spectroscopic techniques can be applied. We demonstrate that, in the surface state of a topological insulator with spin-dependent relaxation due to magnetic impurities, highly nontrivial topological soliton spin textures appear in momentum space. Such spin-channel phenomena are delicately related to the type of non-Hermiticity and correctly reveal the most robust non-Hermitian features detectable spectroscopically. Moreover, the distinct topological soliton objects can be deformed to each other, mediated by topological transitions driven by tuning across a critical direction of doped magnetism. These results not only open a solid-state avenue to exotic spin patterns via spin- and angle-resolved photoemission spectroscopy, but also inspire non-Hermitian dissipation engineering of spins in solids.

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.

Electron- versus Spin-Phonon Coupling Governs the Temperature-Dependent Carrier Dynamics in the Topological Insulator Bi2Te3

Ultrafast charge and spin dynamics have immense effects on the applications of topological insulators (TIs). By performing spin-adiabatic nonadiabatic molecular dynamics simulations in the presence of electron-phonon (e-ph) and spin-phonon couplings, we investigate temperature-dependent intra- and interband charge and spin relaxation dynamics via the bulk and surface paths in the three-dimensional TI Bi2Te3. The e-ph coupling dominates charge relaxation in the bulk path, and the relaxation rate is positively correlated with temperature due to the large energy gaps and weak spin polarization. Conversely, the relaxation dynamics exhibits an opposite temperature dependence in the surface path because of electron re-excitation and spin mismatching induced by spin-phonon coupling, which arises from small energy gaps and strong spin polarization. The two mechanisms rationalize the charge carriers being long-lived in the bulk and surface phases at low and room temperature, respectively. Additionally, strong thermal fluctuations of the topological states' magnetic moments destroy the spin-momentum locking and trigger backscattering at room temperature.

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.

Symmetry-aware deep neural networks for high harmonic spectroscopy in solids

Neural networks are a prominent tool for identifying and modeling complex patterns, which are otherwise hard to detect and analyze. While machine learning and neural networks have been finding applications across many areas of science and technology, their use in decoding ultrafast dynamics of quantum systems driven by strong laser fields has been limited so far. Here we use standard deep neural networks to analyze simulated noisy spectra of highly nonlinear optical response of a 2-dimensional gapped graphene crystal to intense few-cycle laser pulses. We show that a computationally simple 1-dimensional system provides a useful "nursery school" for our neural network, allowing it to be retrained to treat more complex 2D systems, recovering the parametrized band structure and spectral phases of the incident few-cycle pulse with high accuracy, in spite of significant amplitude noise and phase jitter. Our results offer a route for attosecond high harmonic spectroscopy of quantum dynamics in solids with a simultaneous, all-optical, solid-state based complete characterization of few-cycle pulses, including their nonlinear spectral phase and the carrier envelope phase.

Coulomb enhancement of high harmonic generation in monolayer transition metal dichalcogenides

High harmonic generation (HHG) in monolayer MoS₂ is studied using fully microscopic many-body models based on the semiconductor Bloch equations and density functional theory. It is shown that Coulomb correlations lead to a dramatic enhancement of HHG. In particular, near the bandgap, enhancements of two orders of magnitude or more are observed for a wide range of excitation wavelengths and intensities. For excitation at excitonic resonances, strong absorption leads to spectrally broad sub-floors of the harmonics that is absent without Coulomb interaction. The widths of these sub-floors depend strongly on the dephasing time for polarizations. For times of the order of 10 fs the broadenings are comparable to the Rabi energies and reach one electronvolt at fields of approximately 50 MV/cm. The intensities of these contributions are approximately four to six orders below the peaks of the harmonics.

Ultrafast electron dynamics in a topological surface state observed in two-dimensional momentum space

We study ultrafast population dynamics in the topological surface state of Sb[Formula: see text]Te[Formula: see text] in two-dimensional momentum space with time- and angle-resolved two-photon photoemission spectroscopy. Linearly polarized mid-infrared pump pulses are used to permit a direct optical excitation across the Dirac point. We show that this resonant excitation is strongly enhanced within the Dirac cone along three of the six [Formula: see text]-[Formula: see text] directions and results in a macroscopic photocurrent when the plane of incidence is aligned along a [Formula: see text]-[Formula: see text] direction. Our experimental approach makes it possible to disentangle the decay of transiently excited population and photocurent by elastic and inelastic electron scattering within the full Dirac cone in unprecedented detail. This is utilized to show that doping of Sb[Formula: see text]Te[Formula: see text] by vanadium atoms strongly enhances inelastic electron scattering to lower energies, but only scarcely affects elastic scattering around the Dirac cone.

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.

Detecting Majorana Zero Modes via Strong Field Dynamics

We propose a protocol to detect topological phase transitions of one-dimensional p-wave superconductors from their harmonic emission spectra in strong fields. Specifically, we identify spectral features due to radiating edge modes, which characterize the spectrum and the density of states in the topological phase and are absent in the trivial phase. These features allow us to define a measurable signature, obtained from emission measurements, that unambiguously differentiates between the two phases. Local probing provides insight into the localized and topologically protected nature of the modes. The presented results establish that high-harmonic spectroscopy can be used as an all-optical tool for the detection of Majorana zero modes.

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.

Attosecond clocking of correlations between Bloch electrons

Delocalized Bloch electrons and the low-energy correlations between them determine key optical¹, electronic² and entanglement³ functionalities of solids, all the way through to phase transitions^4,5. To directly capture how many-body correlations affect the actual motion of Bloch electrons, subfemtosecond (1 fs = 10^-15 s) temporal precision^6-15 is desirable. Yet, probing with attosecond (1 as = 10^-18 s) high-energy photons has not been energy-selective enough to resolve the relevant millielectronvolt-scale interactions of electrons^1-5,16,17 near the Fermi energy. Here, we use multi-terahertz light fields to force electron-hole pairs in crystalline semiconductors onto closed trajectories, and clock the delay between separation and recollision with 300 as precision, corresponding to 0.7% of the driving field's oscillation period. We detect that strong Coulomb correlations emergent in atomically thin WSe₂ shift the optimal timing of recollisions by up to 1.2 ± 0.3 fs compared to the bulk material. A quantitative analysis with quantum-dynamic many-body computations in a Wigner-function representation yields a direct and intuitive view on how the Coulomb interaction, non-classical aspects, the strength of the driving field and the valley polarization influence the dynamics. The resulting attosecond chronoscopy of delocalized electrons could revolutionize the understanding of unexpected phase transitions and emergent quantum-dynamic phenomena for future electronic, optoelectronic and quantum-information technologies.

Ultrafast Momentum-Resolved Hot Electron Dynamics in the Two-Dimensional Topological Insulator Bismuthene

Two-dimensional quantum spin Hall (QSH) insulators are a promising material class for spintronic applications based on topologically protected spin currents in their edges. Yet, they have not lived up to their technological potential, as experimental realizations are scarce and limited to cryogenic temperatures. These constraints have also severely restricted characterization of their dynamical properties. Here, we report on the electron dynamics of the novel room-temperature QSH candidate bismuthene after photoexcitation using time- and angle-resolved photoemission spectroscopy. We map the transiently occupied conduction band and track the full relaxation pathway of hot photocarriers. Intriguingly, we observe photocarrier lifetimes much shorter than those in conventional semiconductors. This is ascribed to the presence of topological in-gap states already established by local probes. Indeed, we find spectral signatures consistent with these earlier findings. Demonstration of the large band gap and the view into photoelectron dynamics mark a critical step toward optical control of QSH functionalities.

Scalable high-repetition-rate sub-half-cycle terahertz pulses from spatially indirect interband transitions

Intense phase-locked terahertz (THz) pulses are the bedrock of THz lightwave electronics, where the carrier field creates a transient bias to control electrons on sub-cycle time scales. Key applications such as THz scanning tunnelling microscopy or electronic devices operating at optical clock rates call for ultimately short, almost unipolar waveforms, at megahertz (MHz) repetition rates. Here, we present a flexible and scalable scheme for the generation of strong phase-locked THz pulses based on shift currents in type-II-aligned epitaxial semiconductor heterostructures. The measured THz waveforms exhibit only 0.45 optical cycles at their centre frequency within the full width at half maximum of the intensity envelope, peak fields above 1.1 kV cm^-1 and spectral components up to the mid-infrared, at a repetition rate of 4 MHz. The only positive half-cycle of this waveform exceeds all negative half-cycles by almost four times, which is unexpected from shift currents alone. Our detailed analysis reveals that local charging dynamics induces the pronounced positive THz-emission peak as electrons and holes approach charge neutrality after separation by the optical pump pulse, also enabling ultrabroadband operation. Our unipolar emitters mark a milestone for flexibly scalable, next-generation high-repetition-rate sources of intense and strongly asymmetric electric field transients.

Ultra-broadband THz pulses with electric field amplitude exceeding 100 kV/cm at a 200 kHz repetition rate

We demonstrate a table-top source delivering ultra-broadband THz pulses with electric field strength exceeding 100 kV/cm at a repetition rate of 200 kHz. The source is based on optical rectification of 23 fs pulses at 1030 nm delivered by a ytterbium-doped fiber laser followed by a nonlinear temporal compression stage. We generate THz pulses with a conversion efficiency of up to 0.11 % with a spectrum extending to 11 THz using a 1 mm thick GaP crystal and a conversion efficiency of 0.016 % with a spectrum extending to 30 THz using a 30 µm thick GaSe crystal. The essential features of the emitted THz pulse spectra are well captured by simulations of the optical rectification process relying on coupled nonlinear equations. Our ultrafast laser-based source uniquely satisfies an important requirement of nonlinear THz experiments, namely the emission of ultra-broadband THz pulses with high electric field amplitudes at high repetition rates, opening a route towards nonlinear time-resolved THz experiments with high signal-to-noise ratios.

Role of Majorana fermions in high-harmonic generation from Kitaev chain

The observation of Majorana fermions as collective excitations in condensed-matter systems is an ongoing quest, and several state-of-the-art experiments have been performed in the last decade. As a potential avenue in this direction, we simulate the high-harmonic spectrum of Kitaev's superconducting chain model that hosts Majorana edge modes in its topological phase. It is well-known that this system exhibits a topological-trivial superconducting phase transition. We demonstrate that high-harmonic spectroscopy is sensitive to the phase transition in presence of open boundary conditions due to the presence or absence of these edge modes. The population dynamics of the Majorana edge modes are different from the bulk modes, which is the underlying reason for the distinct harmonic profile of both the phases. On the contrary, in presence of periodic boundary conditions with only bulk modes, high-harmonic spectroscopy becomes insensitive to the phase transition with similar harmonic profiles in both phases.

Spintronic terahertz emission with manipulated polarization (STEMP)

Highly efficient generation and arbitrary manipulation of spin-polarized terahertz (THz) radiation will enable chiral lightwave driven quantum nonequilibrium state regulation, induce new electronic structures, consequently provide a powerful experimental tool for investigation of nonlinear THz optics and extreme THz science and applications. THz circular dichromic spectroscopy, ultrafast electron bunch manipulation, as well as THz imaging, sensing, and telecommunication, also need chiral THz waves. Here we review optical generation of circularly-polarized THz radiation but focus on recently emerged polarization tunable spintronic THz emission techniques, which possess many advantages of ultra-broadband, high efficiency, low cost, easy for integration and so on. We believe that chiral THz sources based on the combination of electron spin, ultrafast optical techniques and material structure engineering will accelerate the development of THz science and applications.

Attosecond Transient Absorption Below the Excited States

In this study, the attosecond transient absorption (ATA) spectrum below the excited states of the helium atom was investigated by numerically solving the fully three-dimensional time-dependent Schrödinger equation. Under single-active electron approximation, the helium atom was illuminated by a combined field comprising of extreme ultraviolet (XUV) and delayed infrared (IR) fields. The response function demonstrates that the absorption near the central frequency (ωX) of the XUV field is periodically modulated during the overlapping between the XUV and IR pulses. Using the time-dependent perturbation, the absorption near ωX is attributed to the wavepacket excited by the XUV pulse. The wave function oscillating at the frequency of the XUV pulse was obtained. Furthermore, the chirp-dependent absorption spectrum near ωX potentially provides an all-optical method for characterizing the attosecond pulse duration. Finally, these results can extend to other systems, such as solids or liquids, indicating a potential for application in photonic devices, and they may be meaningful for quantum manipulation.

Multiphoton Resonance in Attosecond Transient Absorption

We present the theory and simulation of attosecond transient absorption in helium atoms under the single-active-electron approximation. This study investigates the attosecond dynamics of intrinsic atomic states that interact with a field comprising vacuum ultraviolet (VUV) and extreme ultraviolet (XUV) fields. The absorption spectrum of the helium atom is obtained from the response function, which is constructed by numerically solving the three-dimensional time-dependent Schrödinger equation. We observe a fine structure near the intrinsic atomic level, which is modulated with a 0.2 fs period. Based on high-order time-dependent perturbation theory, the frequency-dependent phase of the dipole response induced by the VUV and XUV fields is analytically obtained, and the fine structure is well explained by the phase difference. In addition, the absorption fringes are dependent on the chirp of the VUV field. This study investigates the features of the attosecond transient absorption in the VUV region, which may have valuable applications in the study of ultrafast phenomena in atoms, molecules, and solids.

Nonequilibrium topological spin textures in momentum space

Optically excited systems can host unprecedented phenomena and reveal key information. The spin-channel physics in the photoexcited dynamics of quantum matter remains largely unexplored. This study finds the topological surface state under contemporary time-resolved pump-probe spectroscopy an exceptionally capable platform in this regard. Spin signals exhibit interesting tornado-like spiral patterns, and the unusual topological optical activity can be indicative of spintronic applications. This exemplifies a purely nonequilibrium topological winding phenomenon, where all the hidden helicity factors in the light–matter-coupled system are robustly encoded. These results open a direction of nonequilibrium topological spin states in quantum materials.

Nonequilibrium quantum dynamics of many-body systems is the frontier of condensed matter physics; recent advances in various time-resolved spectroscopic techniques continue to reveal rich phenomena. Angle-resolved photoemission spectroscopy (ARPES) as one powerful technique can resolve electronic energy, momentum, and spin along the time axis after excitation. However, dynamics of spin textures in momentum space remains mostly unexplored. Here, we demonstrate theoretically that the photoexcited surface state of genuine or magnetically doped topological insulators shows intriguing topological spin textures (i.e., tornado-like patterns) in the spin-resolved ARPES. We systematically reveal its origin as a unique nonequilibrium photoinduced topological winding phenomenon. As all intrinsic and extrinsic topological helicity factors of both material and light are embedded in a robust and delicate manner, the tornado patterns not only allow a remarkable tomography of such important system information, but also enable various unique dichroic topological switchings of the momentum-space spin texture. These results open a direction of nonequilibrium topological spin states in quantum materials.

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.

Ultrafast time- and angle-resolved photoemission spectroscopy with widely tunable probe photon energy of 5.3-7.0 eV for investigating dynamics of three-dimensional materials

Time- and angle-resolved photoemission spectroscopy (TrARPES) is a powerful technique for capturing the ultrafast dynamics of charge carriers and revealing photo-induced phase transitions in quantum materials. However, the lack of widely tunable probe photon energy, which is critical for accessing the dispersions at different out-of-plane momentum k_z in TrARPES measurements, has hindered the ultrafast dynamics investigation of 3D quantum materials, such as Dirac or Weyl semimetals. Here, we report the development of a TrARPES system with a highly tunable probe photon energy from 5.3 to 7.0 eV. The tunable probe photon energy is generated by the fourth harmonic generation of a tunable wavelength femtosecond laser source by combining a β-BaB₂O₄ crystal and a KBe₂BO₃F₂ crystal. A high energy resolution of 29-48 meV and time resolution of 280-320 fs are demonstrated on 3D topological materials ZrTe₅ and Sb₂Te₃. Our work opens up new opportunities for exploring ultrafast dynamics in 3D quantum materials.

Field-resolved high-order sub-cycle nonlinearities in a terahertz semiconductor laser

The exploitation of ultrafast electron dynamics in quantum cascade lasers (QCLs) holds enormous potential for intense, compact mode-locked terahertz (THz) sources, squeezed THz light, frequency mixers, and comb-based metrology systems. Yet the important sub-cycle dynamics have been notoriously difficult to access in operational THz QCLs. Here, we employ high-field THz pulses to perform the first ultrafast two-dimensional spectroscopy of a free-running THz QCL. Strong incoherent and coherent nonlinearities up to eight-wave mixing are detected below and above the laser threshold. These data not only reveal extremely short gain recovery times of 2 ps at the laser threshold, they also reflect the nonlinear polarization dynamics of the QCL laser transition for the first time, where we quantify the corresponding dephasing times between 0.9 and 1.5 ps with increasing bias currents. A density-matrix approach reproducing the emergence of all nonlinearities and their ultrafast evolution, simultaneously, allows us to map the coherently induced trajectory of the Bloch vector. The observed high-order multi-wave mixing nonlinearities benefit from resonant enhancement in the absence of absorption losses and bear potential for a number of future applications, ranging from efficient intracavity frequency conversion, mode proliferation to passive mode locking.

All-Optical Probe of Three-Dimensional Topological Insulators Based on High-Harmonic Generation by Circularly Polarized Laser Fields

We report the observation of an anomalous nonlinear optical response of the prototypical three-dimensional topological insulator bismuth selenide through the process of high-order harmonic generation. We find that the generation efficiency increases as the laser polarization is changed from linear to elliptical, and it becomes maximum for circular polarization. With the aid of a microscopic theory and a detailed analysis of the measured spectra, we reveal that such anomalous enhancement encodes the characteristic topology of the band structure that originates from the interplay of strong spin-orbit coupling and time-reversal symmetry protection. The implications are in ultrafast probing of topological phase transitions, light-field driven dissipationless electronics, and quantum computation.

Survival of Floquet-Bloch States in the Presence of Scattering

Floquet theory has spawned many exciting possibilities for electronic structure control with light, with enormous potential for future applications. The experimental demonstration in solids, however, remains largely unrealized. In particular, the influence of scattering on the formation of Floquet-Bloch states remains poorly understood. Here we combine time- and angle-resolved photoemission spectroscopy with time-dependent density functional theory and a two-level model with relaxation to investigate the survival of Floquet-Bloch states in the presence of scattering. We find that Floquet-Bloch states will be destroyed if scattering-activated by electronic excitations-prevents the Bloch electrons from following the driving field coherently. The two-level model also shows that Floquet-Bloch states reappear at high field intensities where energy exchange with the driving field dominates over energy dissipation to the bath. Our results clearly indicate the importance of long scattering times combined with strong driving fields for the successful realization of various Floquet phenomena.

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.

A light-induced phononic symmetry switch and giant dissipationless topological photocurrent in ZrTe5

Dissipationless currents from topologically protected states are promising for disorder-tolerant electronics and quantum computation. Here, we photogenerate giant anisotropic terahertz nonlinear currents with vanishing scattering, driven by laser-induced coherent phonons of broken inversion symmetry in a centrosymmetric Dirac material ZrTe₅. Our work suggests that this phononic terahertz symmetry switching leads to formation of Weyl points, whose chirality manifests in a transverse, helicity-dependent current, orthogonal to the dynamical inversion symmetry breaking axis, via circular photogalvanic effect. The temperature-dependent topological photocurrent exhibits several distinct features: Berry curvature dominance, particle-hole reversal near conical points and chirality protection that is responsible for an exceptional ballistic transport length of ~10 μm. These results, together with first-principles modelling, indicate two pairs of Weyl points dynamically created by B_1u phonons of broken inversion symmetry. Such phononic terahertz control breaks ground for coherent manipulation of Weyl nodes and robust quantum transport without application of static electric or magnetic fields.

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.

A quantitative comparison of time-of-flight momentum microscopes and hemispherical analyzers for time- and angle-resolved photoemission spectroscopy experiments

Time-of-flight-based momentum microscopy has a growing presence in photoemission studies, as it enables parallel energy- and momentum-resolved acquisition of the full photoelectron distribution. Here, we report table-top extreme ultraviolet time- and angle-resolved photoemission spectroscopy (trARPES) featuring both a hemispherical analyzer and a momentum microscope within the same setup. We present a systematic comparison of the two detection schemes and quantify experimentally relevant parameters, including pump- and probe-induced space-charge effects, detection efficiency, photoelectron count rates, and depth of focus. We highlight the advantages and limitations of both instruments based on exemplary trARPES measurements of bulk WSe₂. Our analysis demonstrates the complementary nature of the two spectrometers for time-resolved ARPES experiments. Their combination in a single experimental apparatus allows us to address a broad range of scientific questions with trARPES.

Ultrafast terahertz saturable absorbers using tailored intersubband polaritons

Semiconductor heterostructures have enabled a great variety of applications ranging from GHz electronics to photonic quantum devices. While nonlinearities play a central role for cutting-edge functionality, they require strong field amplitudes owing to the weak light-matter coupling of electronic resonances of naturally occurring materials. Here, we ultrastrongly couple intersubband transitions of semiconductor quantum wells to the photonic mode of a metallic cavity in order to custom-tailor the population and polarization dynamics of intersubband cavity polaritons in the saturation regime. Two-dimensional THz spectroscopy reveals strong subcycle nonlinearities including six-wave mixing and a collapse of light-matter coupling within 900 fs. This collapse bleaches the absorption, at a peak intensity one order of magnitude lower than previous all-integrated approaches and well achievable by state-of-the-art QCLs, as demonstrated by a saturation of the structure under cw-excitation. We complement our data by a quantitative theory. Our results highlight a path towards passively mode-locked QCLs based on polaritonic saturable absorbers in a monolithic single-chip design.

Structures that can enhance the capabilities of quantum cascade lasers are highly sought after to improve their practicality for a range of applications. Here the authors demonstrate such a structure in a saturable absorber that takes advantage of intersubband polaritons in the terahertz range and study coherent nonlinear dynamics in the system.

Ultrafast electron dynamics in monolayer MoS2interacting with optical pulse influenced by exchange field and waveform

In this paper, we investigate the effect of waveform and carrier-envelope phase on the electron dynamics in monolayer MoS2interacting with an ultrashort (few-femtosecond) optical pulse in the presence of magnetic exchange field. The waveform of the zero area pulse is characterized by Hermite-Gaussian polynomials associated with time-dependent and carrier-envelope phases. Because the duration of optical pulse is less than the characteristic electron scattering time (10-100 fs), the electron dynamics is coherent, and can be described by the time-dependent Schrödinger equation. We show, that the electron transition from valence band to conduction band is a deeply irreversible dynamics, which implies quantum electron dynamics is highly nonadiabatic. We study the effect of carrier-envelope phase and exchange field on the conduction band population for two types of waveform. Electron distribution in reciprocal space gives asymmetric hot spots in differentKandK' valleys after the pulse ends (valley polarization effect), which is found to be more sensitive to carrier-envelope phase. The predicted effect provides new opportunities for the improvement of information processing in the petahertz domain and optoelectronics applications.

Enabling high repetition rate nonlinear THz science with a kilowatt-class sub-100 fs laser source

Manipulating the atomic and electronic structure of matter with strong terahertz (THz) fields while probing the response with ultrafast pulses at x-ray free electron lasers (FELs) has offered unique insights into a multitude of physical phenomena in solid state and atomic physics. Recent upgrades of x-ray FEL facilities are pushing to much higher repetition rates, enabling unprecedented signal-to-noise ratio for pump probe experiments. This requires the development of suitable THz pump sources that are able to deliver intense pulses at compatible repetition rates. Here we present a high-power laser-driven THz source based on optical rectification in LiNbO₃ using tilted pulse front pumping. Our source is driven by a kilowatt-level Yb:YAG amplifier system operating at 100 kHz repetition rate and employing nonlinear spectral broadening and recompression to achieve sub-100 fs pulses with pulse energies up to 7 mJ that are necessary for high THz conversion efficiency and peak field strength. We demonstrate a maximum of 144 mW average THz power (1.44 μJ pulse energy), consisting of single-cycle pulses centered at 0.6 THz with a peak electric field strength exceeding 150 kV/cm. These high field pulses open up a range of possibilities for nonlinear time-resolved THz experiments at unprecedented rates.

Coherent multidimensional photoelectron spectroscopy of ultrafast quasiparticle dressing by light

Depending on the applied strength, electromagnetic fields in electronic materials can induce dipole transitions between eigenstates or distort the Coulomb potentials that define them. Between the two regimes, they can also modify the electronic properties in more subtle ways when electron motion becomes governed by time and space-periodic potentials. The optical field introduces new virtual bands through Floquet engineering that under resonant conditions interacts strongly with the preexisting bands. Under such conditions the virtual bands can become real, and real ones become virtual as the optical fields and electronic band dispersions entangle the electronic response. We reveal optical dressing of electronic bands in a metal by exciting four-photon photoemission from the Cu(111) surface involving a three-photon resonant transition from the Shockley surface band to the first image potential band. Attosecond resolved interferometric scanning between identical pump–probe pulses and its Fourier analysis reveal how the optical field modifies the electronic properties of a solid through combined action of dipole excitation and field dressing.

Strong pulses of light can drive materials into nonequilibrium states with distinct physical properties. Here the authors observe the changes in copper’s electronic properties as intense optical fields dress the band structure and quasiparticle mass.

Volt-per-Ångstrom terahertz fields from X-ray free-electron lasers

The electron linear accelerators driving modern X-ray free-electron lasers can emit intense, tunable, quasi-monochromatic terahertz (THz) transients with peak electric fields of V Å-1 and peak magnetic fields in excess of 10 T when a purpose-built, compact, superconducting THz undulator is implemented. New research avenues such as X-ray movies of THz-driven mode-selective chemistry come into reach by making dual use of the ultra-short GeV electron bunches, possible by a rather minor extension of the infrastructure.

High-field mid-infrared pulses derived from frequency domain optical parametric amplification

We present a novel, to the best of our knowledge, approach for scaling the peak power of mid-infrared laser pulses with few-cycle duration and carrier-to-envelope phase stabilization. Using frequency domain optical parametric amplification (FOPA), selective amplification is performed on two spectral slices of broadband pulses centered at 1.8 µm wavelength. In addition to amplification, the Fourier plane is used for specific pulse shaping to control both the relative polarization and the phase/delay between the two spectral slices of the input pulses. At the output of the FOPA, intrapulse difference frequency generation provides carrier-envelope phase stabilized two-cycle pulses centered at 9.5 µm wavelength with 25.5 µJ pulse energy. The control of the carrier-envelope phase is demonstrated through the dependence of high-harmonic generation in solids. This architecture is perfectly adapted to be scaled in the future to high average and high peak powers using picosecond ytterbium laser technologies.

Dimensionality-Driven Photoproduction of Massive Dirac Pairs near Threshold in Gapped Graphene Monolayers

Generation of quasiparticle-hole pairs in gapped graphene monolayers in the combined field of two counterpropagating light waves is studied. The process represents an analog of electron-positron pair production from the vacuum of quantum electrodynamics (QED) by the Breit-Wheeler effect. We show, however, that the two-dimensional structure of graphene causes some striking differences between both scenarios. In particular, contrary to the QED case, it allows for nonzero pair production rates at the energy threshold when the Breit-Wheeler reaction proceeds nonlinearly with absorption of three photons.

Efficient Terahertz Harmonic Generation with Coherent Acceleration of Electrons in the Dirac Semimetal Cd_{3}As_{2}

We report strong terahertz (∼10^{12}  Hz) high harmonic generation at room temperature in thin films of Cd_{3}As_{2}, a three-dimensional Dirac semimetal. Third harmonics are detectable with a tabletop light source and can be as strong as 100  V/cm by applying a fundamental field of 6.5  kV/cm inside the film, demonstrating an unprecedented efficiency for terahertz frequency conversion. Our time-resolved terahertz spectroscopy and calculations also clarify the microscopic mechanism of the nonlinearity originating in the coherent acceleration of Dirac electrons in momentum space. Our results provide clear insights for nonlinear currents of Dirac electrons driven by the terahertz field under the influence of scattering, paving the way toward novel devices for high-speed electronics and photonics based on topological semimetals.

Nanoscale Near-Field Tomography of Surface States on (Bi0.5Sb0.5)2Te3

Three-dimensional topological insulators (TIs) have attracted tremendous interest for their possibility to host massless Dirac Fermions in topologically protected surface states (TSSs), which may enable new kinds of high-speed electronics. However, recent reports have outlined the importance of band bending effects within these materials, which results in an additional two-dimensional electron gas (2DEG) with finite mass at the surface. TI surfaces are also known to be highly inhomogeneous on the nanoscale, which is masked in conventional far-field studies. Here, we use near-field microscopy in the mid-infrared spectral range to probe the local surface properties of custom-tailored (Bi_0.5Sb_0.5)₂Te₃ structures with nanometer precision in all three spatial dimensions. Applying nanotomography and nanospectroscopy, we reveal a few-nanometer-thick layer of high surface conductivity and retrieve its local dielectric function without assuming any model for the spectral response. This allows us to directly distinguish between different types of surface states. An intersubband transition within the massive 2DEG formed by quantum confinement in the bent conduction band manifests itself as a sharp, surface-bound, Lorentzian-shaped resonance. An additional broadband background in the imaginary part of the dielectric function may be caused by the TSS. Tracing the intersubband resonance with nanometer spatial precision, we observe changes of its frequency, likely originating from local variations of doping or/and the mixing ratio between Bi and Sb. Our results highlight the importance of studying the surfaces of these novel materials on the nanoscale to directly access the local optical and electronic properties via the dielectric function.