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Ultrafast terahertz probes of transient conducting and insulating phases in an electron–hole gas


Many-body systems in nature exhibit complexity and self-organization arising from seemingly simple laws. For example, the long-range Coulomb interaction between electrical charges has a simple form, yet is responsible for a plethora of bound states in matter, ranging from the hydrogen atom to complex biochemical structures. Semiconductors form an ideal laboratory for studying many-body interactions of electronic quasiparticles among themselves and with lattice vibrations and light1,2,3,4. Oppositely charged electron and hole quasiparticles can coexist in an ionized but correlated plasma, or form bound hydrogen-like pairs called excitons5,6. The pathways between such states, however, remain elusive in near-visible optical experiments that detect a subset of excitons with vanishing centre-of-mass momenta. In contrast, transitions between internal exciton levels, which occur in the far-infrared at terahertz (1012 s-1) frequencies7,8,9, are independent of this restriction, suggesting10 their use as a probe of electron–hole pair dynamics. Here we employ an ultrafast terahertz probe to investigate directly the dynamical interplay of optically-generated excitons and unbound electron–hole pairs in GaAs quantum wells. Our observations reveal an unexpected quasi-instantaneous excitonic enhancement, the formation of insulating excitons on a 100-ps timescale, and the conditions under which excitonic populations prevail.

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Figure 1: Experimental scheme.
Figure 2: Near-infrared and THz properties of GaAs multiple quantum wells.
Figure 3: Temperature dependence of THz dynamics.
Figure 4: Exciton formation.


  1. Shah, J. Ultrafast Spectroscopy of Semiconductors and Semiconductor Nanostructures (Springer, Berlin, 1999)

    Book  Google Scholar 

  2. Chemla, D. S. & Shah, J. Many-body and correlation effects in semiconductors. Nature 411, 549–557 (2001)

    Article  ADS  CAS  Google Scholar 

  3. Rashba, E. I. Excitons (North-Holland, Amsterdam, 1982)

    Google Scholar 

  4. Perakis, I. Exciton developments. Nature 417, 33–35 (2002)

    Article  ADS  CAS  Google Scholar 

  5. Lundstrom, T., Schoenfeld, W., Lee, H. & Petroff, P. M. Exciton storage in semiconductor self-assembled quantum dots. Science 286, 2312–2314 (1999)

    Article  CAS  Google Scholar 

  6. Bayer, M., Stern, O., Hawrylak, P., Fafard, S. & Forchel, A. Hidden symmetries in the energy levels of excitonic ‘artificial atoms’. Nature 405, 923–926 (2000)

    Article  ADS  CAS  Google Scholar 

  7. Groeneveld, R. H. M. & Grischkowsky, D. Picosecond time-resolved far-infrared experiments on carriers and excitons in GaAs–AlGaAs multiple quantum wells. J. Opt. Soc. Am. B 11, 2502–2507 (1994)

    Article  ADS  CAS  Google Scholar 

  8. Timusk, T. Far-infrared absorption study of exciton ionization in germanium. Phys. Rev. B 13, 3511–3514 (1976)

    Article  ADS  CAS  Google Scholar 

  9. Černe, J. et al. Terahertz dynamics of excitons in GaAs/AlGaAs quantum wells. Phys. Rev. Lett. 77, 1131–1134 (1996)

    Article  ADS  Google Scholar 

  10. Kira, M., Hoyer, W., Stroucken, T. & Koch, S. W. Exciton formation in semiconductors and the influence of a photonic environment. Phys. Rev. Lett 87, 176401 (2001)

    Article  ADS  CAS  Google Scholar 

  11. Huber, R. et al. How many-particle interactions develop after ultrafast excitation of an electron–hole plasma. Nature 414, 286–289 (2001)

    Article  ADS  CAS  Google Scholar 

  12. Beard, M. C., Turner, G. M. & Schmuttenmaer, C. A. Transient photoconductivity in GaAs as measured by time-resolved terahertz spectroscopy. Phys. Rev. B 62, 15764–15777 (2000)

    Article  ADS  CAS  Google Scholar 

  13. Lövenich, R., Lai, C. W., Hägele, D., Chemla, D. S. & Schäfer, W. Semiconductor polarization dynamics from the coherent to the incoherent regime: Theory and experiment. Phys. Rev. B 66, 045306 (2002)

    Article  ADS  Google Scholar 

  14. Nuss, M. C. & Orenstein, J. in Millimeter and Submillimeter Wave Spectroscopy of Solids (ed. Grüner, G.) 7–50 (Springer, Berlin, 1998)

    Book  Google Scholar 

  15. Dressel, M. & Grüner, G. Electrodynamics in Solids 61–62 (Cambridge Univ. Press, Cambridge, 2002)

    Book  Google Scholar 

  16. Haug, H. & Koch, S. W. Quantum Theory of the Optical and Electronic Properties of Semiconductors (World Scientific, Singapore, 1994)

    Book  Google Scholar 

  17. Gerlach, B., Wüsthoff, J., Dzero, M. O. & Smondyrev, M. A. Exciton binding energy in a quantum well. Phys. Rev. B 58, 10568–10577 (1998)

    Article  ADS  CAS  Google Scholar 

  18. Tzoar, N. & Platzman, P. M. High-frequency conductivity of a two-dimensional, two-component electron gas. Phys. Rev. B 20, 4189–4193 (1979)

    Article  ADS  CAS  Google Scholar 

  19. Wegener, M. et al. Femtosecond dynamics of excitonic absorption in the infrared InxGa1-xAs quantum wells. Phys. Rev. B 39, 12794–12801 (1989)

    Article  ADS  CAS  Google Scholar 

  20. Selbmann, P. E., Gulia, M., Rossi, F., Molinari, E. & Lugli, P. Coupled free-carrier and exciton relaxation in optically excited semiconductors. Phys. Rev. B 54, 4660–4673 (1996)

    Article  ADS  CAS  Google Scholar 

  21. Siantidis, K., Axt, V. M. & Kuhn, T. Dynamics of exciton formation for near band-gap excitations. Phys. Rev. B 65, 035303 (2002)

    Article  ADS  Google Scholar 

  22. Oh, I. K. Exciton formation assisted by LO phonons in quantum wells. Phys. Rev. B 62, 2045–2050 (2000)

    Article  ADS  CAS  Google Scholar 

  23. Betz, M. et al. Nonlinear optical response of highly energetic excitons in GaAs: Microscopic electrodynamics at semiconductor interfaces. Phys. Rev. B 65, 085314 (2002)

    Article  ADS  Google Scholar 

  24. Siarkos, A., Runge, E. & Zimmermann, R. Center of mass properties of the exciton in quantum wells. Phys. Rev. B 61, 10854–10867 (2000)

    Article  ADS  CAS  Google Scholar 

  25. Damen, T. C. et al. Dynamics of exciton formation and relaxation in GaAs quantum wells. Phys. Rev. B 42, 7434–7438 (1990)

    Article  ADS  CAS  Google Scholar 

  26. Blom, P. W. M., van Hall, P. J., Smit, C., Cuypers, J. P. & Wolter, J. H. Selective exciton formation in thin GaAs/AlxGa1-xAs quantum wells. Phys. Rev. Lett. 71, 3878–3881 (1993)

    Article  ADS  CAS  Google Scholar 

  27. Deveaud, B., Sermage, B. & Katzer, D. S. Free exciton versus free carrier luminescence in a quantum well. J. Phys. Colloq. C 5, 11–14 (1993)

    Google Scholar 

  28. Kumar, R., Vengurlekar, A. S., Prabhu, S. S., Shah, J. & Pfeiffer, L. N. Picosecond time evolution of free electron-hole pairs into excitons in GaAs quantum wells. Phys. Rev. B 54, 4891–4897 (1996)

    Article  ADS  CAS  Google Scholar 

  29. Landau, L. & Zeldovich, J. On the relation between the liquid and gaseous states of metals. Acta Physicochim. USSR XVIII 2–3, 194–196 (1943)

    Google Scholar 

  30. Mott, N. F. Metal Insulator Transitions (Taylor and Francis, London, 1990)

    Book  Google Scholar 

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We thank J. Reno for growth of the quantum well samples, and S. L. Chuang for band-structure calculations. We also thank M. Kira, S. W. Koch, M. Woerner, T. Timusk and J. Orenstein for discussions. This work was supported by the Office of Basic Energy Sciences of the US Department of Energy, the Deutsche Forschungsgemeinschaft and the Alexander von Humboldt Foundation.

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Correspondence to R. A. Kaindl.

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Kaindl, R., Carnahan, M., Hägele, D. et al. Ultrafast terahertz probes of transient conducting and insulating phases in an electron–hole gas. Nature 423, 734–738 (2003).

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