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Real-space imaging of fractional quantum Hall liquids


Electrons in semiconductors usually behave like a gas—as independent particles. However, when confined to two dimensions under a perpendicular magnetic field at low temperatures, they condense into an incompressible quantum liquid. This phenomenon, known as the fractional quantum Hall (FQH) effect1, is a quantum-mechanical manifestation of the macroscopic behaviour of correlated electrons that arises when the Landau-level filling factor is a rational fraction. However, the diverse microscopic interactions responsible for its emergence1,2 have been hidden by its universality and macroscopic nature3,4,5,6,7,8,9. Here, we report real-space imaging of FQH liquids, achieved with polarization-sensitive scanning optical microscopy using trions (charged excitons)10,11,12,13,14,15 as a local probe for electron spin polarization. When the FQH ground state is spin-polarized, the triplet/singlet intensity map exhibits a spatial pattern that mirrors the intrinsic disorder potential, which is interpreted as a mapping of compressible and incompressible electron liquids. In contrast, when FQH ground states with different spin polarization coexist, domain structures with spontaneous quasi-long-range order emerge, which can be reproduced remarkably well from the disorder patterns using a two-dimensional random-field Ising model16. Our results constitute the first reported real-space observation of quantum liquids in a class of broken symmetry state known as the quantum Hall ferromagnet17,18,19,20,21,22,23,24,25.

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Figure 1: Schematic diagram, transport and optical properties of the sample.
Figure 2: Real-space images of fully spin-polarized (ferromagnetic) FQH liquid around ν = 2/5.
Figure 3: Real-space images of the phase transition between non-magnetic and ferromagnetic FQH liquids around ν = 2/3.
Figure 4: Spatial patterns calculated by the Monte Carlo method using a two-dimensional random field Ising model.

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  1. Tsui, D. C., Stormer, H. L. & Gossard, A. C. Two-dimensional magnetotransport in the extreme quantum limit. Phys. Rev. Lett. 48, 1559–1562 (1982).

    Article  CAS  Google Scholar 

  2. Von Klitzing, K., Dorda, G. & Pepper, M. New method for high-accuracy determination of the fine-structure constant based on quantized Hall resistance. Phys. Rev. Lett. 45, 494–497 (1982).

    Article  Google Scholar 

  3. Yacoby, A., Hess, H. F., Fulton, T. A., Pfeiffer, L. N. & West, K. W. Electrical imaging of the quantum Hall state. Solid State Commun. 111, 1–13 (1999).

    Article  CAS  Google Scholar 

  4. Morgenstern, M., Klijn, J., Meyer, C. & Wiesendanger, R. Real-space observation of drift states in a two-dimensional electron system at high magnetic fields. Phys. Rev. Lett. 90, 056804 (2003).

    Article  CAS  Google Scholar 

  5. Niimi, Y., Kambara, H., Matsui, T., Yoshioka, D. & Fukuyama, H. Real-space imaging of alternate localization and extension of quasi-two-dimensional electronic states at graphite surfaces in magnetic fields. Phys. Rev. Lett. 97, 236804 (2006).

    Article  CAS  Google Scholar 

  6. Hashimoto, K. et al. Quantum Hall transition in real space: from localized to extended states. Phys. Rev. Lett. 101, 256802 (2008).

    Article  CAS  Google Scholar 

  7. Song, Y. J. et al. High-resolution tunnelling spectroscopy of a graphene quartet Nature 467, 185–198 (2010).

    Article  CAS  Google Scholar 

  8. Ilani, S. et al. The microscopic nature of localization in the quantum Hall effect. Nature 427, 328–332 (2004).

    Article  CAS  Google Scholar 

  9. Martin, J. et al. Localization of fractionally charged quasi-particles. Science 305, 980–983 (2004).

    Article  CAS  Google Scholar 

  10. Kheng, K. et al. Observation of negatively charged excitons X in semiconductor quantum wells. Phys. Rev. Lett. 71, 1752–1755 (1993).

    Article  CAS  Google Scholar 

  11. Finkelstein, G., Shtrikman, H. & Bar-Joseph, I. Optical spectroscopy of a two-dimensional electron gas near the metal–insulator transition. Phys. Rev. Lett. 74, 976–979 (1995).

    Article  CAS  Google Scholar 

  12. Shields, A. J., Pepper, M., Simmons, M. Y. & Ritchie, D. A. Spin-triplet negatively charged excitons in GaAs quantum wells. Phys. Rev. B 52, 7841–7844 (1995).

    Article  CAS  Google Scholar 

  13. Yusa, G., Shtrikman, H. & Bar-Joseph, I. Charged excitons in the fractional quantum Hall regime. Phys. Rev. Lett. 87, 216402 (2001).

    Article  CAS  Google Scholar 

  14. Plochocka, P. et al. Optical absorption to probe the quantum Hall ferromagnet at filling factor ν = 1. Phys. Rev. Lett. 102, 126806 (2009).

    Article  CAS  Google Scholar 

  15. Wojs, A. & Quinn, J. J. Energy spectra of fractional quantum Hall systems in the presence of a valence hole. Phys. Rev. B 63, 045303 (2000).

    Article  Google Scholar 

  16. Pelissetto, A. & Vicari, E. Critical phenomena and renormalization-group theory. Phys. Rep. 368, 549–727 (2002).

    Article  CAS  Google Scholar 

  17. Jungwirth, T. & MacDonald, A. H. Pseudospin anisotropy classification of quantum Hall ferromagnets. Phys. Rev. B 63, 035305 (2000).

    Article  Google Scholar 

  18. Nomura, K. & MacDonald, A. H. Quantum Hall ferromagnetism in graphene. Phys. Rev. Lett. 96, 256602 (2006).

    Article  Google Scholar 

  19. Piazza, V. et al. First-order phase transitions in a quantum Hall ferromagnet. Nature 402, 638–641 (1999).

    Article  CAS  Google Scholar 

  20. Eom, J. et al. Quantum Hall ferromagnetism in a two-dimensional electron system. Science 289, 2320–2323 (2000).

    Article  CAS  Google Scholar 

  21. Smet, J. H., Deutschmann, R. A., Wegscheider, W., Abstreiter, G. & von Klitzing, K. Ising ferromagnetism and domain morphology in the fractional quantum Hall regime. Phys. Rev. Lett. 86, 2412–2415 (2001).

    Article  CAS  Google Scholar 

  22. De Poortere, E. P., Tutuc, E., Papadakis, S. J. & Shayegan, M. Resistance spikes at transitions between quantum Hall ferromagnets. Science 290, 1546–1549 (2000).

    Article  CAS  Google Scholar 

  23. Kumada, N., Muraki, K. & Hirayama, Y. Low-frequency spin dynamics in a canted antiferromagnet. Science 313, 329–332 (2006).

    Article  CAS  Google Scholar 

  24. Weitz, R. T., Allen, M. T., Feldman, B. E., Martin, J. & Yacoby, A. Broken-symmetry states in doubly gated suspended bilayer graphene. Science 330, 812–816 (2010).

    Article  CAS  Google Scholar 

  25. Verdene, B. et al. Microscopic manifestation of the spin phase transition at filling factor 2/3. Nature Phys. 3, 392–396 (2007).

    Article  CAS  Google Scholar 

  26. Chklovskii, D. B. & Lee, P. A. Transport properties between quantum Hall plateaus. Phys. Rev. B 48, 18060–18078 (1993).

    Article  CAS  Google Scholar 

  27. Eytan, G., Yayon, Y., Rappaport, M., Strikman, H. & Bar-Joseph, I. Near-field spectroscopy of a gated electron gas: a direct evidence for electron localization. Phys. Rev. Lett. 81, 1666–1669 (1998).

    Article  CAS  Google Scholar 

  28. Shibata, N. & Nomura, K. Phase separation in ν = 2/3 Fractional quantum Hall systems. J. Phys. Soc. Jpn 76, 103711 (2007).

    Article  Google Scholar 

  29. Jain, J. Composite Fermions (Cambridge Univ. Press, 2007).

    Book  Google Scholar 

  30. Imbrie, J. Z. Lower critical dimension of the random-field Ising model. Phys. Rev. Lett. 53, 1747–1750 (1984).

    Article  Google Scholar 

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The authors thank K. Takashina, H. Akiyama, Y. Toda, K. Akiba, N. Kumada, T. D. Rhone, W. J. Munro, T. Fujisawa, N. Shibata, A. Hosoya and H. Sakaki for fruitful discussions and M. Ueki for experimental support. This work was supported by a Grant-in-Aid for Scientific Research (nos. 21241024 and 24241039) from the Ministry of Education, Culture, Sports, Science and Technology (MEXT), Japan, and by the Japan Science and Technology Agency, PRESTO. J.H. was supported by a Grant in-Aid from the Tohoku University International Advanced Research and Education Organization.

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J.H. contributed to the experimental set-up and measurements. J.H. and G.Y. contributed to data analysis and numerical calculations. K.M contributed to material growth. G.Y. wrote the manuscript, with feedback from all authors.

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Correspondence to Go Yusa.

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Hayakawa, J., Muraki, K. & Yusa, G. Real-space imaging of fractional quantum Hall liquids. Nature Nanotech 8, 31–35 (2013).

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