Direct observation of a magnetic-field-induced Wigner crystal

  • Wigner, E. On the interaction of electrons in metals. Phys. Rev. 46, 1002–1011 (1934).

    Article 
    ADS 
    CAS 

    Google Scholar
     

  • Grimes, C. C. & Adams, G. Evidence for a liquid-to-crystal phase transition in a classical, two-dimensional sheet of electrons. Phys. Rev. Lett. 42, 795–798 (1979).

    Article 
    ADS 
    CAS 

    Google Scholar
     

  • Lozovik, Y. E. & Yudson, V. I. Crystallization of a two-dimensional electron gas in a magnetic field. J. Exp. Theor. Phys. Lett. 22, 11–12 (1975).


    Google Scholar
     

  • Andrei, E. Y. et al. Observation of a magnetically induced Wigner solid. Phys. Rev. Lett. 60, 2765–2768 (1988).

    Article 
    ADS 
    CAS 
    PubMed 

    Google Scholar
     

  • Santos, M. B. et al. Observation of a reentrant insulating phase near the 1/3 fractional quantum Hall liquid in a two-dimensional hole system. Phys. Rev. Lett. 68, 1188–1191 (1991).

    Article 
    ADS 

    Google Scholar
     

  • Yoon, J., Li, C. C., Shahar, D., Tsui, D. C. & Shayegan, M. Wigner crystallization and metal-insulator transition of two-dimensional holes in GaAs at B = 0. Phys. Rev. Lett. 82, 1744–1747 (1999).

    Article 
    ADS 
    CAS 

    Google Scholar
     

  • Hossain, M. S. et al. Observation of spontaneous ferromagnetism in a two-dimensional electron system. Proc. Natl Acad. Sci. USA 117, 32244–32250 (2020).

    Article 
    ADS 
    CAS 
    PubMed 
    PubMed Central 

    Google Scholar
     

  • Smoleński, T. et al. Signatures of Wigner crystal of electrons in a monolayer semiconductor. Nature 595, 53–57 (2021).

    Article 
    ADS 
    PubMed 

    Google Scholar
     

  • Zhou, Y. et al. Bilayer Wigner crystals in a transition metal dichalcogenide heterostructure. Nature 595, 48–52 (2021).

    Article 
    ADS 
    CAS 
    PubMed 

    Google Scholar
     

  • Yang, F. et al. Experimental determination of the energy per particle in partially filled Landau levels. Phys. Rev. Lett. 126, 156802 (2021).

    Article 
    ADS 
    CAS 
    PubMed 

    Google Scholar
     

  • Falson, J. et al. Competing correlated states around the zero-field Wigner crystallization transition of electrons in two dimensions. Nat. Mater. 21, 311–316 (2022).

    Article 
    ADS 
    CAS 
    PubMed 

    Google Scholar
     

  • Tanatar, B. & Ceperley, D. M. Ground state of the two-dimensional electron gas. Phys. Rev. B 39, 5005–5016 (1988).

    Article 
    ADS 

    Google Scholar
     

  • Levesque, D., Weis, J. J. & MacDonald, A. H. Crystallization of the incompressible quantum-fluid state of a two-dimensional electron gas in a strong magnetic field. Phys. Rev. B 30, 1056–1058 (1984).

    Article 
    ADS 
    CAS 

    Google Scholar
     

  • Lam, P. K. & Girvin, S. M. Liquid-solid transition and the fractional quantum-Hall effect. Phys. Rev. B 30, 473–475 (1984).

    Article 
    ADS 
    CAS 

    Google Scholar
     

  • Tiemann, L., Rhone, T. D., Shibata, N. & Muraki, K. NMR profiling of quantum electron solids in high magnetic fields. Nat. Phys. 10, 648–652 (2014).

    Article 
    CAS 

    Google Scholar
     

  • Willett, R. L. et al. Termination of the series of fractional quantum hall states at small filling factors. Phys. Rev. B 38, 7881–7884 (1988).

    Article 
    ADS 
    CAS 

    Google Scholar
     

  • Goldman, V. J., Santos, M., Shayegan, M. & Cunningham, J. E. Evidence for two-dimensional quantum Wigner crystal. Phys. Rev. Lett. 65, 2189–2192 (1990).

    Article 
    ADS 
    CAS 
    PubMed 

    Google Scholar
     

  • Buhmann, H. et al. Novel magneto-optical behavior in the Wigner-solid regime. Phys. Rev. Lett. 66, 926–929 (1990).

    Article 
    ADS 

    Google Scholar
     

  • Jiang, H. W. et al. Quantum liquid versus electron solid around ν = 1/5 Landau-level filling. Phys. Rev. Lett. 65, 633–636 (1990).

    Article 
    ADS 
    CAS 
    PubMed 

    Google Scholar
     

  • Li, Y. P., Sajoto, T., Engel, L. W., Tsui, D. C. & Shayegan, M. Low-frequency noise in the reentrant insulating phase around the 1/5 fractional quantum Hall liquid. Phys. Rev. Lett. 67, 1630–1633 (1991).

    Article 
    ADS 
    CAS 
    PubMed 

    Google Scholar
     

  • Paalanen, M. A. et al. rf conductivity of a two-dimensional electron system at small Landau-level filling factors. Phys. Rev. B 45, 11342–11345 (1992).

    Article 
    ADS 
    CAS 

    Google Scholar
     

  • Ye, P. D. et al. Correlation lengths of the Wigner-crystal order in a two-dimensional electron system at high magnetic fields. Phys. Rev. Lett. 89, 176802 (2002).

    Article 
    ADS 
    CAS 
    PubMed 

    Google Scholar
     

  • Chen, Y. P. et al. Melting of a 2D quantum electron solid in high magnetic field. Nat. Phys. 2, 452–455 (2006).

    Article 
    CAS 

    Google Scholar
     

  • Zhang, D., Huang, X., Dietsche, W., Klitzing, Kvon & Smet, J. H. Signatures for Wigner crystal formation in the chemical potential of a two-dimensional electron system. Phys. Rev. Lett. 113, 076804 (2014).

    Article 
    ADS 
    CAS 
    PubMed 

    Google Scholar
     

  • Deng, H. et al. Commensurability oscillations of composite fermions induced by the periodic potential of a Wigner crystal. Phys. Rev. Lett. 117, 096601 (2016).

    Article 
    ADS 
    CAS 
    PubMed 

    Google Scholar
     

  • Jang, J., Hunt, B. M., Pfeiffer, L. N., West, K. W. & Ashoori, R. C. Sharp tunnelling resonance from the vibrations of an electronic Wigner crystal. Nat. Phys. 13, 340–344 (2017).

    Article 
    CAS 

    Google Scholar
     

  • Shapir, I. et al. Imaging the electronic Wigner crystal in one dimension. Science 364, 870–875 (2019).

    Article 
    ADS 
    CAS 
    PubMed 

    Google Scholar
     

  • Li, H. et al. Imaging two-dimensional generalized Wigner crystals. Nature 597, 650–654 (2021).

    Article 
    ADS 
    CAS 
    PubMed 

    Google Scholar
     

  • Li, S.-Y., Zhang, Y., Yin, L.-J. & He, L. Scanning tunneling microscope study of quantum Hall isospin ferromagnetic states in the zero Landau level in a graphene monolayer. Phys. Rev. B 100, 085437 (2019).

    Article 
    ADS 
    CAS 

    Google Scholar
     

  • Liu, X. et al. Visualizing broken symmetry and topological defects in a quantum Hall ferromagnet. Science 375, 321–326 (2021).

    Article 
    ADS 
    PubMed 

    Google Scholar
     

  • Coissard, A. et al. Imaging tunable quantum Hall broken-symmetry orders in graphene. Nature 605, 51–56 (2022).

    Article 
    ADS 
    CAS 
    PubMed 

    Google Scholar
     

  • Farahi, G. et al. Broken symmetries and excitation spectra of interacting electrons in partially filled Landau levels. Nat. Phys. 19, 1482–1488 (2023).

    Article 
    CAS 

    Google Scholar
     

  • Hu, Y. et al. High-resolution tunneling spectroscopy of fractional quantum Hall states. Preprint at arxiv.org/abs/2308.05789 (2023).

  • Aoki, H. Effect of coexistence of random potential and electron-electron interaction in two-dimensional systems: Wigner glass. J. Phys. C Solid State Phys. 12, 633 (2001).

    Article 
    ADS 

    Google Scholar
     

  • Spivak, B. & Kivelson, S. A. Phases intermediate between a two-dimensional electron liquid and Wigner crystal. Phys. Rev. B 70, 155114 (2004).

    Article 
    ADS 

    Google Scholar
     

  • Zhu, X. & Louie, S. G. Wigner crystallization in the fractional quantum Hall regime: a variational quantum Monte Carlo study. Phys. Rev. Lett. 70, 335–338 (1993).

    Article 
    ADS 
    CAS 
    PubMed 

    Google Scholar
     

  • Halperin, B. I., Lee, P. A. & Read, N. Theory of the half-filled Landau level. Phys. Rev. B 47, 7312–7343 (1993).

    Article 
    ADS 
    CAS 

    Google Scholar
     

  • Girvin, S. M., MacDonald, A. H. & Platzman, P. M. Magneto-roton theory of collective excitations in the fractional quantum Hall effect. Phys. Rev. B 33, 2481–2494 (1986).

    Article 
    ADS 
    CAS 

    Google Scholar
     

  • Falakshahi, H. & Waintal, X. Hybrid phase at the quantum melting of the Wigner crystal. Phys. Rev. Lett. 94, 046801 (2005).

    Article 
    ADS 
    PubMed 

    Google Scholar
     

  • Ma, M. K. et al. Thermal and quantum melting phase diagrams for a magnetic-field-induced Wigner solid. Phys. Rev. Lett. 125, 036601 (2020).

    Article 
    ADS 
    CAS 
    PubMed 

    Google Scholar
     

  • Zou, K., Hong, X. & Zhu, J. Effective mass of electrons and holes in bilayer graphene: electron-hole asymmetry and electron-electron interaction. Phys. Rev. B 84, 085408 (2011).

    Article 
    ADS 

    Google Scholar
     

  • Koulakov, A. A., Fogler, M. M. & Shklovskii, B. I. Charge density wave in two-dimensional electron liquid in weak magnetic field. Phys. Rev. Lett. 76, 499–502 (1995).

    Article 
    ADS 

    Google Scholar
     

  • Fradkin, E. & Kivelson, S. A. Liquid-crystal phases of quantum Hall systems. Phys. Rev. B 59, 8065–8072 (1999).

    Article 
    ADS 
    CAS 

    Google Scholar
     

  • Lilly, M. P., Cooper, K. B., Eisenstein, J. P., Pfeiffer, L. N. & West, K. W. Evidence for an anisotropic state of two-dimensional electrons in high Landau levels. Phys. Rev. Lett. 82, 394–397 (1999).

    Article 
    ADS 
    CAS 

    Google Scholar
     

  • Du, R. R. et al. Strongly anisotropic transport in higher two-dimensional Landau levels. Solid State Commun. 109, 389–394 (1999).

    Article 
    ADS 
    CAS 

    Google Scholar
     

  • Kerelsky, A. et al. Maximized electron interactions at the magic angle in twisted bilayer graphene. Nature 572, 95–100 (2019).

    Article 
    ADS 
    CAS 
    PubMed 

    Google Scholar
     

  • Cazorla, C. & Boronat, J. Simulation and understanding of atomic and molecular quantum crystals. Rev. Mod. Phys. 89, 035003 (2017).

    Article 
    ADS 
    MathSciNet 

    Google Scholar
     

  • Lindemann, F. About the calculation of molecular own frequencies. Z. Phys. 11, 609–612 (1910).

    CAS 

    Google Scholar
     

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

    Article 
    ADS 
    CAS 

    Google Scholar
     

  • Halperin, B. I. & Nelson, D. R. Theory of two-dimensional melting. Phys. Rev. Lett. 41, 121–124 (1978).

    Article 
    ADS 
    MathSciNet 
    CAS 

    Google Scholar
     


  • Source link

    Total
    0
    Shares
    Leave a Reply

    Your email address will not be published. Required fields are marked *

    Related Posts