Data archive of "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 rates(1). Lightwave-driven currents have been assumed to be essential for high-harmonic generation in solids(2-6), charge transport in nanostructures(7-8), attosecond-streaking experiments(9-16) and atomic-resolution ultrafast microscopy(17-18). 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 insulators(19-29) 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

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

Strong light fields have created opportunities to tailor novel functionalities of solids1,2,3,4,5. Floquet–Bloch states can form under periodic driving of electrons and enable exotic quantum phases6,7,8,9,10,11,12,13,14,15. On subcycle timescales, lightwaves can simultaneously drive intraband currents16,17,18,19,20,21,22,23,24,25,26,27,28,29 and interband transitions18,19,30,31, which enable high-harmonic generation16,18,19,21,22,25,28,29,30 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

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 material1,2,3,4,5,6,7,8,9,10,11. Sub-optical-cycle dynamics—such as dynamical Bloch oscillations2,3,4,5, 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 generation16,17,18,19,20. 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