Floquet–Bloch states are known to form in solids under periodic driving of electrons. We visualize their ultrafast build-up with angle-resolved photoemission spectroscopy and subcycle time resolution. We drive the Dirac surface state of a topological insulator with mid-infrared fields in the MV/cm range. 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.
As conventional electronics approaches its ultimate limits, novel concepts of fast quantum control have been sought after. Lightwave electronics – the foundation of attosecond science – has opened a new arena by utilizing the oscillating carrier wave of intense light pulses to control electrons faster than a cycle of light. We employ atomically strong terahertz electromagnetic pulses to accelerate electrons through the entire Brillouin zone of solids, drive quasiparticle collisions, and generate high-harmonic radiation as well as high-order sidebands. The unique band structures of topological insulators allow for all-ballistic and quasi-relativistic acceleration of Dirac quasiparticles over distances as large as 0.5 μm. In monolayers of transition metal dichalcogenides, we switch the electrons’ valley pseudospin, opening the door to subcycle valleytronics. Finally, we show that lightwave electronics can be combined with ultimate atomic spatial resolution in state-selective ultrafast scanning tunneling microscopy.
The Dirac-cone surface states of topological insulators are characterized by a chiral spin texture in k-space with the electron spin locked to its parallel momentum. Mid-infrared pump pulses can induce spin-polarized photocurrents in such a topological surface state by optical transitions between the occupied and unoccupied part of the Dirac cone. We monitor the ultrafast dynamics of the corresponding asymmetric electron population in momentum space directly by time- and angle-resolved two-photon photoemission (2PPE). The elastic scattering times of 2.5 ps deduced for Sb2Te3 corresponds to a mean-fee path of 0.75 μm in real space.
We report the development of an experimental technique to measure the dynamics of electrical currents on
the femtosecond timescale. The technique combines methods of coherent control with time- and angle-resolved
photoelectron spectroscopy. Direct snapshots of the momentum distribution of the excited electrons as function
of time are then determined by photoelectron spectroscopy. In this way we gain information on the generation and
decay of ultrashort current pulses in unprecedented detail. In particular, this technique allows the observation
of elastic electron scattering in terms of an incoherent population dynamics in momentum space. We have
applied this optical current generation and detection scheme to electrons in so-called image-potential states
which represent a prototype of two-dimensional electronic surface states. Electrons in these states are bound
perpendicular to the metal surface by the Coulombic image potential whereas they can move almost freely parallel
to the surface. For the (n=1) image-potential state of Cu(100) we find a decay time of 10 fs due to electron
scattering with steps and surface defects.
The ultrafast dynamics of electrons in image-potential states on a Cu(100) surface is studied by means of femtosecond time-resolved two-photon photoemission (2PPE). By coherently exciting several eigenstates of the Rydberg series we observe periodic oscillations of the 2PPE signal as a function of the delay time between pump and probe pulses. These quantum beats allow us to determine the spacing of high-order states (quantum number n >= 4) that are difficult to resolve by conventional electron spectroscopy. The superposition of several states around n equals 7 creates an electron wave packet that describes the quasi-classical periodic motion of weakly bound electrons. Its distance from the surface is reflected in the strength of the photoemission signal. The electron is observed to move about 100 atomic distances away from the surface and oscillates back and forth with a period of 800 femtoseconds. The results demonstrate the power of coherent laser spectroscopy for surface studies.
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