Macroscopically ordered state in an exciton system

Abstract

There is a rich variety of quantum liquids—such as superconductors, liquid helium and atom Bose–Einstein condensates—that exhibit macroscopic coherence in the form of ordered arrays of vortices1,2,3,4. Experimental observation of a macroscopically ordered electronic state in semiconductors has, however, remained a challenging and relatively unexplored problem. A promising approach for the realization of such a state is to use excitons, bound pairs of electrons and holes that can form in semiconductor systems. At low densities, excitons are Bose-particles5, and at low temperatures, of the order of a few kelvin, excitons can form a quantum liquid—that is, a statistically degenerate Bose gas or even a Bose–Einstein condensate5,6,7. Here we report photoluminescence measurements of a quasi-two-dimensional exciton gas in GaAs/AlGaAs coupled quantum wells and the observation of a macroscopically ordered exciton state. Our spatially resolved measurements reveal fragmentation of the ring-shaped emission pattern into circular structures that form periodic arrays over lengths up to 1 mm.

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Figure 1: Radial dependence of the indirect exciton photoluminescence (PL).
Figure 2: Excitation density dependence of the spatial pattern of the indirect exciton PL intensity.
Figure 3: Temperature dependence of the spatial pattern of the indirect exciton PL intensity.
Figure 4: Schematics demonstrating a reduction of emission intensity for excitons in motion.

References

  1. 1

    Essmann, U. & Träuble, H. The direct observation of individual flux lines in type II superconductors. Phys. Lett. A 24, 526–527 (1967)

    CAS  Article  Google Scholar 

  2. 2

    Yarmchuk, E. J., Gordon, M. J. V. & Packard, R. E. Observation of stationary vortex arrays in rotating superfluid helium. Phys. Rev. Lett. 43, 214–217 (1979)

    CAS  Article  Google Scholar 

  3. 3

    Madison, K. W., Chevy, F., Wohlleben, W. & Dalibard, J. Vortex formation is stirred Bose-Einstein condensate. Phys. Rev. Lett. 84, 806–809 (2000)

    CAS  Article  Google Scholar 

  4. 4

    Abo-Shaeer, J. R., Raman, C., Vogels, J. M. & Ketterle, W. Observation of vortex lattices in Bose-Einstein condensates. Science 292, 476–479 (2001)

    CAS  Article  Google Scholar 

  5. 5

    Keldysh, L. V. & Kozlov, A. N. Collective properties of excitons in semiconductors. Sov. Phys. JETP 27, 521–528 (1968)

    Google Scholar 

  6. 6

    Lozovik, Yu. E. & Yudson, V. I. A new mechanism for superconductivity: pairing between spatially separated electrons and holes. Sov. Phys. JETP 44, 389–397 (1976)

    Google Scholar 

  7. 7

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

    CAS  Article  Google Scholar 

  8. 8

    Fukuzawa, T., Mendez, E. E. & Hong, J. M. Phase transition of an exciton system in GaAs coupled quantum wells. Phys. Rev. Lett. 64, 3066–3069 (1990)

    CAS  Article  Google Scholar 

  9. 9

    Butov, L. V. & Filin, A. I. Anomalous transport and luminescence of indirect excitons in AlAs/GaAs coupled quantum wells as evidence for exciton condensation. Phys. Rev. B 58, 1980–2000 (1998)

    CAS  Article  Google Scholar 

  10. 10

    Butov, L. V. et al. Stimulated scattering of indirect excitons in coupled quantum wells: Signature of a degenerate Bose-gas of excitons. Phys. Rev. Lett. 86, 5608–5611 (2001)

    CAS  Article  Google Scholar 

  11. 11

    Butov, L. V., Lai, C. W., Ivanov, A. L., Gossard, A. C. & Chemla, D. S. Towards Bose-Einstein condensation of excitons in potential traps. Nature 417, 47–52 (2002)

    CAS  Article  Google Scholar 

  12. 12

    Larionov, A. V., Timofeev, V. B., Hvam, J. & Soerensen, K. Collective state of interwell excitons in GaAs/AlGaAs double quantum wells under pulse resonance excitation. JETP Lett. 75, 200–204 (2002)

    CAS  Article  Google Scholar 

  13. 13

    Yoshioka, D. & MacDonald, A. H. Double quantum well electron-hole systems in strong magnetic fields. J. Phys. Soc. Jpn 59, 4211–4214 (1990)

    Article  Google Scholar 

  14. 14

    Zhu, X., Littlewood, P. B., Hybertsen, M. & Rice, T. Exciton condensate in semiconductor quantum well structures. Phys. Rev. Lett. 74, 1633–1636 (1995)

    CAS  Article  Google Scholar 

  15. 15

    Leggett, A. J. Bose-Einstein condensation in the alkali gases: Some fundamental concepts. Rev. Mod. Phys. 73, 307–356 (2001)

    CAS  Article  Google Scholar 

  16. 16

    Popov, V. N. On the theory of the superfluidity of two- and one-dimensional Bose systems. Theor. Math. Phys. 11, 565–573 (1972)

    Article  Google Scholar 

  17. 17

    Kosterlitz, J. M. & Thouless, D. J. Ordering, metastability and phase transitions in two-dimensional systems. J. Phys. C 6, 1181–1203 (1973)

    CAS  Article  Google Scholar 

  18. 18

    Feldmann, J. et al. Linewidth dependence of radiative exciton lifetimes in quantum wells. Phys. Rev. Lett. 59, 2337–2340 (1987)

    CAS  Article  Google Scholar 

  19. 19

    Topinka, M. A. et al. Coherent branched flow in a two-dimensional electron gas. Nature 410, 183–186 (2001)

    CAS  Article  Google Scholar 

  20. 20

    Taylor, G. I. Stability of a viscous liquid contained between two rotating cylinders. Phil. Trans. R. Soc. Lond. A 223, 289–343 (1923)

    Article  Google Scholar 

  21. 21

    Carr, L. D., Clark, C. W. & Reinhardt W. P. Stationary solutions of the one-dimensional nonlinear Schrödinger equation. I. Case of repulsive nonlinearity. Phys. Rev. A 62, 063610-1–063610-10 (2000)

    Google Scholar 

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Acknowledgements

We thank A.L. Ivanov for discussions, C.W. Lai and A.V. Mintsev for help in preparing the experiment and K.L. Campman for growing the high quality CQW samples. This work was supported by the Office of Basic Energy Sciences US Department of Energy and by the Russian Foundation for Basic Research (RFBR).

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Correspondence to L. V. Butov.

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Butov, L., Gossard, A. & Chemla, D. Macroscopically ordered state in an exciton system. Nature 418, 751–754 (2002). https://doi.org/10.1038/nature00943

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