Инд. авторы:	Schmid C.P., Weigl L., Grossing P., Junk V., Gorini C., Schlauderer S., Ito S., Meierhofer M., Hofmann N., Afanasiev D., Crewse J., Kokh K.A., Tereshchenko O.E., Gudde J., Evers F., Wilhelm J., Richter K., Hofer U., Huber R.
Заглавие:	Tunable non-integer high-harmonic generation in a topological insulator
Библ. ссылка:	Schmid C.P., Weigl L., Grossing P., Junk V., Gorini C., Schlauderer S., Ito S., Meierhofer M., Hofmann N., Afanasiev D., Crewse J., Kokh K.A., Tereshchenko O.E., Gudde J., Evers F., Wilhelm J., Richter K., Hofer U., Huber R. Tunable non-integer high-harmonic generation in a topological insulator // Nature. - 2021. - Vol.593. - Iss. 7859. - P.385-+. - ISSN 0028-0836. - EISSN 1476-4687.
Внешние системы:	DOI: 10.1038/s41586-021-03466-7; РИНЦ: 46075620; PubMed: 34012087; WoS: 000652278400016;
Реферат:	eng: When intense lightwaves accelerate electrons through a solid, the emerging high-order harmonic (HH) radiation offers key insights into the material(1-11). Sub-optical-cycle dynamics-such as dynamical Bloch oscillations(2-5), quasiparticle collisions(6,12), valley pseudospin switching(13) and heating of Dirac gases(10)-leave fingerprints in the HH spectra of conventional solids. Topologically non-trivial matter(14,15) with invariants that are robust against imperfections has been predicted to support unconventional HH generation(16-20). 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 locking(17) 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.
Ключевые слова:	BLOCH; STATES; SURFACE;
Издано:	2021
Физ. характеристика:	с.385
Цитирование:	1. Chin, A. H., Calderón, O. G. & Kono, J. Extreme midinfrared nonlinear optics in semiconductors. Phys. Rev. Lett. 86, 3292–3295 (2001). 2. Ghimire, S. et al. Observation of high-order harmonic generation in a bulk crystal. Nat. Phys. 7, 138–141 (2011). 3. Schubert, O. et al. Sub-cycle control of terahertz high-harmonic generation by dynamical Bloch oscillations. Nat. Photon. 8, 119–123 (2014). 4. Hohenleutner, M. et al. Real-time observation of interfering crystal electrons in high-harmonic generation. Nature 523, 572–575 (2015). 5. Luu, T. T. et al. Extreme ultraviolet high-harmonic spectroscopy of solids. Nature 521, 498–502 (2015). 6. Vampa, G. et al. Linking high harmonics from gases and solids. Nature 522, 462–464 (2015); corrigendum 542, 260 (2017). 7. Garg, M. et al. Multi-petahertz electronic metrology. Nature 538, 359–363 (2016). 8. Yoshikawa, N., Tamaya, T. & Tanaka, K. High-harmonic generation in graphene enhanced by elliptically polarized light excitation. Science 356, 736–738 (2017). 9. Sivis, M. et al. Tailored semiconductors for high-harmonic optoelectronics. Science 357, 303–306 (2017). 10. Hafez, H. A. et al. Extremely efficient terahertz high-harmonic generation in graphene by hot Dirac fermions. Nature 561, 507–511 (2018). 11. Floss, I. et al. Ab initio multiscale simulation of high-order harmonic generation in solids. Phys. Rev A. 97, 011401(R) (2018). 12. Langer, F. et al. Lightwave-driven quasiparticle collisions on a subcycle timescale. Nature 533, 225–229 (2016). 13. Langer, F. et al. Lightwave valleytronics in a monolayer of tungsten diselenide. Nature 557, 76–80 (2018). 14. Chen, Y. L. et al. Experimental realization of a three-dimensional topological insulator, Bi2Te3. Science 325, 178–181 (2009). 15. Giorgianni, F. et al. Strong nonlinear terahertz response induced by Dirac surface states in Bi2Se3 topological insulator. Nat. Commun. 7, 11421 (2016). 16. Bauer, D. & Hansen, K. K. High-harmonic generation in solids with and without topological edge states. Phys. Rev. Lett. 120, 177401 (2018). 17. Reimann, J. et al. Subcycle observation of lightwave-driven Dirac currents in a topological surface band. Nature 562, 396–400 (2018). 18. Silva, R. E. F., Jiménez-Galán, A., Amorim, B., Smirnova, O. & Ivanov, M. Topological strong field physics on sub-laser cycle timescale. Nat. Photon. 13, 849–854 (2019). 19. Baykusheva, D. et al. Strong-field physics in three-dimensional topological insulators. Phys. Rev. A 103, 023101 (2021). 20. Wilhelm, J. et al. Semiconductor-Bloch formalism: derivation and application to high-harmonic generation from Dirac fermions. Phys. Rev. B 103, 125419 (2021). 21. Higuchi, T., Heide, C., Ullmann, K., Weber, H. B. & Hommelhoff, P. Light-field-driven currents in graphene. Nature 550, 224–228 (2017). 22. McIver, J. W. et al. Light-induced anomalous Hall effect in graphene. Nat. Phys. 16, 38–41 (2020). 23. Kuroda, K., Reimann, J., Güdde, J. & Höfer, U. Generation of transient photocurrents in the topological surface state of Sb2Te3 by direct optical excitation with midinfrared pulses. Phys. Rev. Lett. 116, 076801 (2016). 24. Wu, L. et al. Quantized Faraday and Kerr rotation and axion electrodynamics of a 3D topological insulator. Science 354, 1124–1127 (2016). 25. Mahmood, F. et al. Selective scattering between Floquet–Bloch and Volkov states in a topological insulator. Nat. Phys. 12, 306–310 (2016). 26. Braun, L. et al. Ultrafast photocurrents at the surface of the three-dimensional topological insulator Bi2Se3. Nat. Commun. 7, 13259 (2016). 27. Berry, M. V. Quantal phase factors accompanying adiabatic changes. Proc. R. Soc. Lond. A 392, 45–57 (1984). 28. Luu, T. T. & Wörner, H. J. Measurement of the Berry curvature of solids using high-harmonic spectroscopy. Nat. Commun. 9, 916 (2018). 29. Banks, H. B. et al. Dynamical birefringence: electron–hole recollisions as probes of Berry curvature. Phys. Rev. X 7, 041042 (2017). 30. Cheng, B. et al. Efficient terahertz harmonic generation with coherent acceleration of electrons in the Dirac semimetal Cd3As2. Phys. Rev. Lett. 124, 117402 (2020). 31. Sell, A., Leitenstorfer, A. & Huber, R. Phase-locked generation and field-resolved detection of widely tunable terahertz pulses with amplitudes exceeding 100 MV/cm. Opt. Lett. 33, 2767–2769 (2008). 32. Michiardi, M. et al. Bulk band structure of Bi2Te3. Phys. Rev. B 90, 075105 (2014). 33. Austin. I. G. The optical properties of bismuth telluride. Proc. Phys. Soc. 72, 545–552 (1958). 34. Kokh, K. A. et al. Melt growth of bulk Bi2Te3 crystals with a natural p–n junction. CrystEngComm 16, 581–584 (2014). 35. Liu, C.-X. et al. Model Hamiltonian for topological insulators. Phys. Rev. B 82, 045122 (2010). 36. Xiao, D., Chang, M.-C. & Niu, Q. Berry phase effects on electronic properties. Rev. Mod. Phys. 82, 1959–2007 (2010). 37. Gradhand, M. et al. First-principle calculations of the Berry curvature of Bloch states for charge and spin transport of electrons. J. Phys. Condens. Matter 24, 213202 (2012). 38. Kane, E. O. Zener tunneling in semiconductors. J. Phys. Chem. Solids 12, 181–188 (1960). 39. Lange, C. et al. Extremely nonperturbative nonlinearities in GaAs driven by atomically strong terahertz fields in gold metamaterials. Phys. Rev. Lett. 113, 227401 (2014). 40. Junginger, F. et al. Nonperturbative interband response of a bulk InSb semiconductor driven off resonantly by terahertz electromagnetic few-cycle pulses. Phys. Rev. Lett. 109, 147403 (2012). 41. Kira, M. & Koch, S. W. Semiconductor Quantum Optics (Cambridge Univ. Press, 2012). 42. Mikhailov, S. A. Non-linear electromagnetic response of graphene. Europhys. Lett. 79, 27002 (2007). 43. Huard, S. Polarization of Light (Wiley, 1997). 44. Junk, V., Reck, P., Gorini, C. & Richter, K. Floquet oscillations in periodically driven Dirac systems. Phys. Rev. B 101, 134302 (2020). 45. Krückl, V. Wave Packets in Mesoscopic Systems: From Time-dependent Dynamics to Transport Phenomena in Graphene and Topological Insulators. PhD thesis, Univ. Regensburg (2013).