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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.The build-up and dephasing of Floquet-–Bloch bands is visualized in both subcycle band-structure videography and quantum theory, revealing the interplay of strong-field intraband and interband excitations in a non-equilibrium Floquet picture. [ABSTRACT FROM AUTHOR]

We study ultrafast population dynamics in the topological surface state of Sb 2 Te 3 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 Γ ¯ – M ¯ directions and results in a macroscopic photocurrent when the plane of incidence is aligned along a Γ ¯ – K ¯ 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 2 Te 3 by vanadium atoms strongly enhances inelastic electron scattering to lower energies, but only scarcely affects elastic scattering around the Dirac cone. [ABSTRACT FROM AUTHOR]

When intense lightwaves accelerate electrons through a solid, the emerging high-order harmonic (HH) radiation offers key insights into the material1–11. Sub-optical-cycle dynamics—such as dynamical Bloch oscillations2–5, quasiparticle collisions6,12, valley pseudospin switching13 and heating of Dirac gases10—leave fingerprints in the HH spectra of conventional solids. Topologically non-trivial matter14,15 with invariants that are robust against imperfections has been predicted to support unconventional HH generation16–20. 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.High-harmonic generation from the Dirac-like surface state of a topological insulator is separated from bulk contributions and continuously tuned by the carrier-envelope phase of the driving lightwave. [ABSTRACT FROM AUTHOR]

Harnessing the carrier wave of light as an alternating-current bias may enable electronics at optical clock rates1. Lightwave-driven currents have been assumed to be essential for high-harmonic generation in solids2-6, charge transport in nanostructures7,8, attosecond-streaking experiments9-16 and atomic-resolution ultrafast microscopy17,18. However, in conventional semiconductors and dielectrics, the finite effective mass and ultrafast scattering of electrons limit their ballistic excursion and velocity. The Dirac-like, quasi-relativistic band structure of topological insulators19-29 may allow these constraints to be lifted and may thus open a new era of lightwave electronics. To understand the associated, complex motion of electrons, comprehensive experimental access to carrier-wave-driven currents is crucial. Here we report angle-resolved photoemission spectroscopy with subcycle time resolution that enables us to observe directly how the carrier wave of a terahertz light pulse accelerates Dirac fermions in the band structure of the topological surface state of Bi2Te3. While terahertz streaking of photoemitted electrons traces the electromagnetic field at the surface, the acceleration of Dirac states leads to a strong redistribution of electrons in momentum space. The inertia-free surface currents are protected by spin-momentum locking and reach peak densities as large as two amps per centimetre, with ballistic mean free paths of several hundreds of nanometres, opening up a realistic parameter space for all-coherent lightwave-driven electronic devices. Furthermore, our subcycle-resolution analysis of the band structure may greatly improve our understanding of electron dynamics and strong-field interaction in solids. [ABSTRACT FROM AUTHOR]

The electron transfer processes at the interface between 3,4,9,10-perylene-tetracarboxylic acid dianhydride (PTCDA) and Ag(111) have been studied using time- and angle-resolved two-photon photo-emission (2PPE). For this system a dispersing unoccupied interface state can be identified that is located 0.6 eV above the Fermi level with an effective electron mass of 0.39 me at the $\overline{\Gamma}$-point. The lifetime of 54 fs for the interface state is relatively short indicating a large penetration of the wavefunction into the metal. Supported by model calculations this interface state is interpreted as predominantly arising from an upshift of the occupied Shockley surface state of the clean metal substrate due to the interaction with the PTCDA overlayer. Coverage dependent measurements show a second long-lived component in the time-resolved measurements for higher PTCDA coverages that can be associated to charge transfer processes from the PTCDA multilayers into the metal substrate. Additionally the influence of the PTCDA adlayers on the image-potential states is studied indicating that the n = 1 image-potential state is localized in the first two monolayers of the PTCDA film. [ABSTRACT FROM AUTHOR]

Buried interface states in Ar/Cu(100) were studied by means of one- and two-photon photoemission experiments. With increasing Ar overlayer thickness, a transition from broad electron scattering resonances in the Ar conduction band into a hydrogen-like series of quasi-bound states at the Ar/Cu interface was observed. The thickness dependence of energies and lifetimes is compared to theoretical resonance positions and linewidths derived from a parameterized one-dimensional potential. [ABSTRACT FROM AUTHOR]

We describe an interferometric time-resolved photoemission technique that makes it possible to simultaneously observe the decay of optical induced polarizations and populations at surfaces in a two-color excitation scheme. In this scheme initially unoccupied electronic surface states are coherently excited by the interaction of laser pulses with frequency ωa and the two-photon polarization which is induced by laser pulses with frequency ωa/2. Interference is observed by changing the delay between both laser pulses using an actively stabilized two-color Mach–Zehnder interferometer. We demonstrate this technique for excitation of the n=1 image-potential state on a Cu(100) surface. [ABSTRACT FROM AUTHOR]

The influence of well-ordered adlayers of Ar, Kr, and Xe on the energetic and dynamical properties of image-potential states on Cu(100) has been investigated in a comprehensive study using time-resolved two-photon photoemission (2PPE). The effect of these insulating films varies systematically with the electron affinity EA of the condensed rare gases and with the film thickness. For the electron-repulsive Ar layers (EA=-0.25 eV), a strong lifetime increase of the n=1 state from 40 fs on clean Cu(100) to as much as 10 ps at a coverage of 5 monolayers is observed. For Kr and Xe layers (EA=+0.3 and +0.5 eV, respectively), decoupling from the metal is less efficient. These layers exhibit quantum-well-like resonances of the n=2 state as a function of layer thickness. The energies of the series of states depend characteristically on the affinity level and the dielectric constant of the films. A microscopic model is developed that includes the discrete atomic structure of the adsorbate layers. It is capable of describing the experimental results to a high degree of quantitative agreement. [ABSTRACT FROM AUTHOR]

Image-potential states in front of a clean Cu (100) surface were investigated by time- and angle-resolved two-photon photo-emission (2PPE). We observe a previously unknown quasi-elastic relaxation channel, which efficiently couples states with different quantum numbers, n, and parallel momenta, k[sub ||] . This process of resonant interband scattering (RIS) is independent of sample temperature and shows a close relationship to the pure dephasing of image-potential states. [ABSTRACT FROM AUTHOR]

Abstract. Ultrafast electronic coherence phenomena of metallic image-potential states and of silicon dangling-bond states are discussed. The image states were investigated on a Cu(100) surface by means of time-resolved two-photon photoemission (2PPE). Spectroscopical and dynamical information about states with high quantum numbers (n Is greater than or equal to 4) were obtained by the coherent excitation of several eigenstates of the Rydberg series and detection of the resulting quantum beats. Electron wave packets that describe the quasi-classical periodic motion of weakly bound electrons at metal surfaces could be created by the superposition of several eigen-functions around n = 7. A surface-sensitive purely optical technique is introduced for the investigation of rapid dephasing processes of excited dangling-bond states of Si(111)7 x 7. The measurement of the diffracted second-harmonic signal from a transient population grating yielded decoherence times of about 5 fs. [ABSTRACT FROM AUTHOR]

Abstract. The dissociative adsorption of molecular hydrogen on vicinal Si(001) and Si(111) surfaces was investigated by means of optical second-harmonic generation (SHG). For temperatures up to 600 K the measured initial sticking coefficients could be decomposed into contributions from step/defect and terrace sites. Whereas the presence of steps on Si(111) leads only to a moderate increase of reactivity, the sticking coefficients for step adsorption on misoriented Si(001) are many orders of magnitude higher than for terrace adsorption and reach values up to 10[sup -4]. Neither the absolute values nor the temperature dependence of adsorption on the terraces are affected by the misorientation. [ABSTRACT FROM AUTHOR]

Abstract. The dynamics of electrons in image-potential states has been studied by means of time- and energy-resolved two-photon photoemission. The loss of coherence in quantum-beat spectroscopy shows directly the influence of pure dephasing which can be determined also from the difference between the results of linewidth and decay rate measurements. We present several examples for the correlation of decay and dephasing with surface defects and disorder. [ABSTRACT FROM AUTHOR]

Reports on the resonant enhancement of optical second-harmonic generation from silicon surfaces by dangling-bond-derived surface states. High diffusion barriers resulting from the covalent nature of hydrogen bonding on silicon surfaces; Dissociative adsorption of molecular hydrogen on silicon; Decisive role of lattice degrees of freedom in the reaction dynamics on semiconductor surfaces.