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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.

We present energy-momentum mapping of surface Dirac photocurrent in the topological insulator Sb$_2$Te$_3$ by means of time- and angle-resolved two-photon photoemission spectroscopy combined with polarization-variable mid-infrared pulse laser. It is demonstrated that the direct optical transition from the occupied to the unoccupied part of the surface Dirac-cone permits the linear and circular photogalvanic effect which thereby enables us to coherently control the surface electric-current by laser polarization. Moreover, the surface current mapping directly visualizes ultrafast current dynamics in the Dirac cone in the time domain. We unravel the ultrafast intraband relaxation dynamics of the inelastic scattering and momentum scattering separately. Our observations pave the pathway for coherent optical control over surface Dirac electrons in topological insulators.

Carrier multiplication by singlet exciton fission enhances photovoltaic conversion efficiencies in organic solids. This decay of one singlet exciton into two triplet states promises to overcome the Shockley-Queisser limit as up to two electrons may be harvested per absorbed photon. Intermolecular coupling is deemed mandatory for both, singlet exciton fission and a band-like transport. Such a coupling is manifested, $e.g.$, by the Davydov-splitting of the lowest-energy exciton transition in crystalline organic solids. For the model system perfluoropentacene, the corresponding transitions in the experimental, polarisation-resolved absorption spectra are identified by theoretical calculations based on the concept of H- and J- aggregation. Optical injection into the first vibronic progression of the fundamental exciton transitions significantly perturbs the higher-energy transitions that are associated to H-type aggregates of the $S_0 \rightarrow S_3$ transition during and following efficient singlet exciton fission. These findings underline the necessity for efficient carrier extraction as triplet accumulation may be detrimental to both, singlet exciton fission and any potentially band like transport. More generally, our observations indicate that electronic excitations can perturb the electronic band structure in organic crystals and highlight their correlated nature by potentially distorting the lattice.