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.

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.

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 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.

Tracing orbital images on ultrafast time scales.

Frontier orbitals determine fundamental molecular properties such as chemical reactivities. Although electron distributions of occupied orbitals can be imaged in momentum space by photoemission tomography, it has so far been impossible to follow the momentum-space dynamics of a molecular orbital in time, for example, through an excitation or a chemical reaction. Here, we combined time-resolved photoemission using high laser harmonics and a momentum microscope to establish a tomographic, femtosecond pump-probe experiment of unoccupied molecular orbitals. We measured the full momentum-space distribution of transiently excited electrons, connecting their excited-state dynamics to real-space excitation pathways. Because in molecules this distribution is closely linked to orbital shapes, our experiment may, in the future, offer the possibility of observing ultrafast electron motion in time and space.

Second-harmonic generation as a probe for structural and electronic properties of buried GaP/Si(0 0 1) interfaces.

Optical second-harmonic generation is demonstrated to be a sensitive probe of the buried interface between the lattice-matched semiconductors gallium phosphide and silicon with (0 0 1) orientation. Ex situ rotational anisotropy measurements on GaP/Si heterostructures show a strong isotropic component of the second-harmonic response not present for pure Si(0 0 1) or GaP(0 0 1). The strength of the overlaying anisotropic response directly correlates with the quality of the interface as determined by atomically resolved scanning transmission electron microscopy. Systematic comparison of samples fabricated under different growth conditions in metal-organic vapor phase epitaxy reveals that the anisotropy for different polarization combinations can be used as a selective fingerprint for the occurrence of anti-phase domains and twins. This all-optical technique can be applied as an in situ and non-invasive monitor even during growth.

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

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.

Spectroscopy and Dynamics of a Two-Dimensional Electron Gas on Ultrathin Helium Films on Cu(111).

Electrons in image-potential states on the surface of bulk helium represent a unique model system of a two-dimensional electron gas. Here, we investigate their properties in the extreme case of reduced film thickness: a monolayer of helium physisorbed on a single-crystalline (111)-oriented Cu surface. For this purpose we have utilized a customized setup for time-resolved two-photon photoemission at very low temperatures under ultrahigh vacuum conditions. We demonstrate that the highly polarizable metal substrate increases the binding energy of the first (n=1) image-potential state by more than 2 orders of magnitude as compared to the surface of liquid helium. An electron in this state is still strongly decoupled from the metal surface due to the large negative electron affinity of helium and we find that even 1 monolayer of helium increases its lifetime by 1 order of magnitude compared to the bare Cu(111) surface.

Generation of Transient Photocurrents in the Topological Surface State of Sb_{2}Te_{3} by Direct Optical Excitation with Midinfrared Pulses.

We combine tunable midinfrared (mid-IR) pump pulses with time- and angle-resolved two-photon photoemission to study ultrafast photoexcitation of the topological surface state (TSS) of Sb_{2}Te_{3}. It is revealed that mid-IR pulses permit a direct excitation from the occupied to the unoccupied part of the TSS across the Dirac point. The novel optical coupling induces asymmetric transient populations of the TSS at ±k_{∥}, which reflects a macroscopic photoexcited electric surface current. By observing the decay of the asymmetric population, we directly investigate the dynamics of the long-lived photocurrent in the time domain. Our discovery promises important advantages of photoexcitation by mid-IR pulses for spintronic applications.

Time-resolved two-photon photoemission of unoccupied electronic states of periodically rippled graphene on Ru(0001).

The unoccupied electronic states of epitaxially grown graphene on Ru(0001) have been explored by time- and angle-resolved two-photon photoemission. We identify a Ru derived resonance and a Ru/graphene interface state at 0.91 and 2.58 eV above the Fermi level, as well as three image-potential derived states close to the vacuum level. The most strongly bound, short-lived, and least dispersing image-potential state is suggested to have some quantum-well character with a large amplitude below the graphene hills. The two other image-potential states are attributed to a series of slightly decoupled states. Their lifetimes and dispersions are indicative of electrons moving almost freely above the valley areas of the moiré superstructure of graphene.

Spectrally resolved maker fringes in high-order harmonic generation.

We investigate macroscopic interference effects in high-order harmonic generation using a Ti:sapphire laser operating at a 100 kHz repetition rate. The structure and behavior of spectral and spatial interference fringes are explained and analytically described by transient phase matching of the long electron trajectory contribution. Time-frequency mapping due to the temporal chirp of the harmonic emission allows us to observe Maker fringes directly in the spectral domain.

Time-resolved investigation of coherently controlled electric currents at a metal surface.

Studies of current dynamics in solids have been hindered by insufficiently brief trigger signals and electronic detection speeds. By combining a coherent control scheme with photoelectron spectroscopy, we generated and detected lateral electron currents at a metal surface on a femtosecond time scale with a contact-free experimental setup. We used coherent optical excitation at the light frequencies omega(a) and omega(a)/2 to induce the current, whose direction was controlled by the relative phase between the phase-locked laser excitation pulses. Time- and angle-resolved photoelectron spectroscopy afforded a direct image of the momentum distribution of the excited electrons as a function of time. For the first (n = 1) image-potential state of Cu(100), we found a decay time of 10 femtoseconds, attributable to electron scattering with steps and surface defects.

Time-resolved measurement of surface diffusion induced by femtosecond laser pulses.

Diffusion of atomic oxygen on a vicinal Pt111 surface induced by femtosecond laser pulses has been studied using optical second-harmonic generation as a sensitive in situ probe of the step coverage. Time-resolved studies of the hopping rate for step-terrace diffusion with a two-pulse correlation scheme reveal a time constant of 1.5 ps for the energy transfer from the electronic excitation of the substrate to the frustrated translations of the adsorbate.

Time-resolved two-photon photoemission of buried interface states in Ar/Cu(100).

We demonstrate the existence of buried image-potential states at the interface between thick Ar films and a Cu(100) substrate. The electron dynamics of these solid-solid interface states, energetically located above the vacuum level in the band gaps of both materials, could be investigated with time-resolved two-photon photoemission for an Ar layer thickness up to 200 A. Relaxation on time scales between 40 and 200 fs occurs via two distinct channels, resonant tunneling through the insulating layer into the vacuum and electron-hole pair decay in the metal.