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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Essmann, U. & Träuble, H. The direct observation of individual flux lines in type II superconductors. Phys. Lett. A 24, 526–527 (1967)
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)
Madison, K. W., Chevy, F., Wohlleben, W. & Dalibard, J. Vortex formation is stirred Bose-Einstein condensate. Phys. Rev. Lett. 84, 806–809 (2000)
Abo-Shaeer, J. R., Raman, C., Vogels, J. M. & Ketterle, W. Observation of vortex lattices in Bose-Einstein condensates. Science 292, 476–479 (2001)
Keldysh, L. V. & Kozlov, A. N. Collective properties of excitons in semiconductors. Sov. Phys. JETP 27, 521–528 (1968)
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)
Perakis, I. E. Exciton developments. Nature 417, 33–35 (2002)
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)
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)
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)
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)
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)
Yoshioka, D. & MacDonald, A. H. Double quantum well electron-hole systems in strong magnetic fields. J. Phys. Soc. Jpn 59, 4211–4214 (1990)
Zhu, X., Littlewood, P. B., Hybertsen, M. & Rice, T. Exciton condensate in semiconductor quantum well structures. Phys. Rev. Lett. 74, 1633–1636 (1995)
Leggett, A. J. Bose-Einstein condensation in the alkali gases: Some fundamental concepts. Rev. Mod. Phys. 73, 307–356 (2001)
Popov, V. N. On the theory of the superfluidity of two- and one-dimensional Bose systems. Theor. Math. Phys. 11, 565–573 (1972)
Kosterlitz, J. M. & Thouless, D. J. Ordering, metastability and phase transitions in two-dimensional systems. J. Phys. C 6, 1181–1203 (1973)
Feldmann, J. et al. Linewidth dependence of radiative exciton lifetimes in quantum wells. Phys. Rev. Lett. 59, 2337–2340 (1987)
Topinka, M. A. et al. Coherent branched flow in a two-dimensional electron gas. Nature 410, 183–186 (2001)
Taylor, G. I. Stability of a viscous liquid contained between two rotating cylinders. Phil. Trans. R. Soc. Lond. A 223, 289–343 (1923)
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)
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).
The authors declare that they have no competing financial interests.
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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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