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Ito S, Schüler M, Meierhofer M, Schlauderer S, Freudenstein J, Reimann J, Afanasiev D, Kokh KA, Tereshchenko OE, Güdde J, Sentef MA, Höfer U, Huber R. Build-up and dephasing of Floquet-Bloch bands on subcycle timescales. Nature 2023; 616:696-701. [PMID: 37046087 DOI: 10.1038/s41586-023-05850-x] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/21/2022] [Accepted: 02/15/2023] [Indexed: 04/14/2023]
Abstract
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.
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Affiliation(s)
- S Ito
- Department of Physics, Philipps-University of Marburg, Marburg, Germany
| | - M Schüler
- Laboratory for Materials Simulations, Paul Scherrer Institute, Villigen PSI, Switzerland
- Department of Physics, University of Fribourg, Fribourg, Switzerland
| | - M Meierhofer
- Department of Physics, University of Regensburg, Regensburg, Germany
| | - S Schlauderer
- Department of Physics, University of Regensburg, Regensburg, Germany
| | - J Freudenstein
- Department of Physics, University of Regensburg, Regensburg, Germany
| | - J Reimann
- Department of Physics, Philipps-University of Marburg, Marburg, Germany
| | - D Afanasiev
- Department of Physics, University of Regensburg, Regensburg, Germany
| | - K A Kokh
- A.V. Rzhanov Institute of Semiconductor Physics and V.S. Sobolev Institute of Geology and Mineralogy SB RAS, Novosibirsk, Russian Federation
| | - O E Tereshchenko
- A.V. Rzhanov Institute of Semiconductor Physics and V.S. Sobolev Institute of Geology and Mineralogy SB RAS, Novosibirsk, Russian Federation
| | - J Güdde
- Department of Physics, Philipps-University of Marburg, Marburg, Germany
| | - M A Sentef
- Max Planck Institute for the Structure and Dynamics of Matter, Hamburg, Germany.
| | - U Höfer
- Department of Physics, Philipps-University of Marburg, Marburg, Germany.
- Department of Physics, University of Regensburg, Regensburg, Germany.
| | - R Huber
- Department of Physics, University of Regensburg, Regensburg, Germany.
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Schmid CP, Weigl L, Grössing P, Junk V, Gorini C, Schlauderer S, Ito S, Meierhofer M, Hofmann N, Afanasiev D, Crewse J, Kokh KA, Tereshchenko OE, Güdde J, Evers F, Wilhelm J, Richter K, Höfer U, Huber R. Tunable non-integer high-harmonic generation in a topological insulator. Nature 2021; 593:385-390. [PMID: 34012087 DOI: 10.1038/s41586-021-03466-7] [Citation(s) in RCA: 28] [Impact Index Per Article: 9.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/28/2020] [Accepted: 03/17/2021] [Indexed: 02/04/2023]
Abstract
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.
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Affiliation(s)
- C P Schmid
- Institute of Experimental and Applied Physics, University of Regensburg, Regensburg, Germany
| | - L Weigl
- Institute of Experimental and Applied Physics, University of Regensburg, Regensburg, Germany
| | - P Grössing
- Institute of Theoretical Physics, University of Regensburg, Regensburg, Germany
| | - V Junk
- Institute of Theoretical Physics, University of Regensburg, Regensburg, Germany
| | - C Gorini
- Institute of Theoretical Physics, University of Regensburg, Regensburg, Germany.,Université Paris-Saclay, CEA, CNRS, SPEC, Gif-sur-Yvette, France
| | - S Schlauderer
- Institute of Experimental and Applied Physics, University of Regensburg, Regensburg, Germany
| | - S Ito
- Department of Physics, Philipps-University of Marburg, Marburg, Germany
| | - M Meierhofer
- Institute of Experimental and Applied Physics, University of Regensburg, Regensburg, Germany
| | - N Hofmann
- Institute of Experimental and Applied Physics, University of Regensburg, Regensburg, Germany
| | - D Afanasiev
- Institute of Experimental and Applied Physics, University of Regensburg, Regensburg, Germany
| | - J Crewse
- Institute of Theoretical Physics, University of Regensburg, Regensburg, Germany
| | - K A Kokh
- V.S. Sobolev Institute of Geology and Mineralogy SB RAS, Novosibirsk, Russia.,Novosibirsk State University, Novosibirsk, Russia
| | - O E Tereshchenko
- Novosibirsk State University, Novosibirsk, Russia.,A.V. Rzhanov Institute of Semiconductor Physics SB RAS, Novosibirsk, Russia
| | - J Güdde
- Department of Physics, Philipps-University of Marburg, Marburg, Germany
| | - F Evers
- Institute of Theoretical Physics, University of Regensburg, Regensburg, Germany
| | - J Wilhelm
- Institute of Theoretical Physics, University of Regensburg, Regensburg, Germany.
| | - K Richter
- Institute of Theoretical Physics, University of Regensburg, Regensburg, Germany.
| | - U Höfer
- Department of Physics, Philipps-University of Marburg, Marburg, Germany
| | - R Huber
- Institute of Experimental and Applied Physics, University of Regensburg, Regensburg, Germany.
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