- Physical Review Journals
All JournalsPhysics Magazine

Physical Review Research

Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Letter
  • Open Access

Thermal activation signatures of the Anderson insulator and the Wigner solid forming near ν=1

S. A. Myers1,*, Haoyun Huang1,*, Waseem Hussain1, L. N. Pfeiffer2, K. W. West2, and G. A. Csáthy1,†

  • *These authors contributed equally to this work.
  • †Corresponding author: gcsathy@purdue.edu
PDF

Phys. Rev. Research 6, L022056 – Published 10 June, 2024

DOI: https://doi.org/10.1103/PhysRevResearch.6.L022056

Abstract

When interactions overcome disorder, integer quantum Hall plateaus support topological phases with different bulk insulators. In the center of the ν=1 plateau the bulk is an Anderson-type insulator, while in the flanks of the plateau the bulk is the integer quantum Hall Wigner solid. We find that the activation energy along the ν=1 plateau exhibits a very dramatic nonmonotonic dependence on the magnetic field, a dependence that is strongly correlated with the stability regions of the two phases. Furthermore, the activation energy has an unexpected minimum at the boundary between the Anderson insulator and the Wigner solid. Our findings constrain the theory of the integer quantum Hall Wigner solid, determine its thermodynamic properties, and reveal unusual behavior at the boundary between the Anderson insulator and the Wigner solid.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (71)

  1. K. von Klitzing, G. Dorda, and M. Pepper, New method for high-accuracy determination of the fine-structure constant based on quantized Hall resistance, Phys. Rev. Lett. 45, 494 (1980).
  2. D. C. Tsui, H. L. Stormer, and A. C. Gossard, Two-dimensional magnetotransport in the extreme quantum limit, Phys. Rev. Lett. 48, 1559 (1982).
  3. J. K. Jain, Incompressible quantum Hall states, Phys. Rev. B 40, 8079(R) (1989).
  4. A. A. Koulakov, M. M. Fogler, and B. I. Shklovskii, Charge density wave in two-dimensional electron liquid in weak magnetic field, Phys. Rev. Lett. 76, 499 (1996).
  5. R. Moessner and J. T. Chalker, Exact results for interacting electrons in high Landau levels, Phys. Rev. B 54, 5006 (1996).
  6. M. P. Lilly, K. B. Cooper, J. P. Eisenstein, L. N. Pfeiffer, and K. W. West, Evidence for an anisotropic state of two-dimensional electrons in high Landau levels, Phys. Rev. Lett. 82, 394 (1999).
  7. R. R. Du, D. C. Tsui, H. L. Stormer, L. N. Pfeiffer, K. W. Baldwin, and K. W. West, Strongly anisotropic transport in higher two-dimensional Landau levels, Solid State Commun. 109, 389 (1999).
  8. K. B. Cooper, M. P. Lilly, J. P. Eisenstein, L. N. Pfeiffer, and K. W. West, Insulating phases of two-dimensional electrons in high Landau levels: Observation of sharp thresholds to conduction, Phys. Rev. B 60, R11285(R) (1999).
  9. J. P. Eisenstein, K. B. Cooper, L. N. Pfeiffer, and K. W. West, Insulating and fractional quantum Hall states in the first excited Landau level, Phys. Rev. Lett. 88, 076801 (2002).
  10. X. Fu, Q. Shi, M. A. Zudov, G. C. Gardner, J. D. Watson, and M. J. Manfra, Two- and three-electron bubbles in AlxGa1−xAs/Al0.24Ga0.76As quantum wells, Phys. Rev. B 99, 161402(R) (2019).
  11. D. Ro, S. A. Myers, N. Deng, J. D. Watson, M. J. Manfra, L. N. Pfeiffer, K. W. West, and G. A. Csáthy, Stability of multielectron bubbles in high Landau levels, Phys. Rev. B 102, 115303 (2020).
  12. Y. P. Chen, R. M. Lewis, L. W. Engel, D. C. Tsui, P. D. Ye, L. N. Pfeiffer, and K. W. West, Microwave resonance of the 2D Wigner crystal around integer Landau fillings, Phys. Rev. Lett. 91, 016801 (2003).
  13. K. S. Kim and S. A. Kivelson, The quantum Hall effect in the absence of disorder, npj Quantum Mater. 6, 22 (2021).
  14. R. E. Prange, Quantized Hall resistance and the measurement of the fine-structure constant, Phys. Rev. B 23, 4802(R) (1981).
  15. H. Aoki and T. Ando, Effect of localization on the Hall conductivity in the two-dimensional system in strong magnetic fields, Solid State Commun. 38, 1079 (1981).
  16. Y. Liu, C. G. Pappas, M. Shayegan, L. N. Pfeiffer, K. W. West, and K. W. Baldwin, Observation of reentrant integer quantum Hall states in the lowest Landau level, Phys. Rev. Lett. 109, 036801 (2012).
  17. Y. Liu, D. Kamburov, S. Hasdemir, M. Shayegan, L. N. Pfeiffer, K. W. West, and K. W. Baldwin, Fractional quantum Hall effect and Wigner crystal of interacting composite fermions, Phys. Rev. Lett. 113, 246803 (2014).
  18. S. A. Myers, H. Huang, L. N. Pfeiffer, K. W. West, and G. A. Csáthy, Magnetotransport patterns of collective localization near ν=1 in a high-mobility two-dimensional electron gas, Phys. Rev. B 104, 045311 (2021).
  19. L. Tiemann, T. D. Rhone, N. Shibata, and K. Muraki, NMR profiling of quantum electron solids in high magnetic fields, Nat. Phys. 10, 648 (2014).
  20. D. Zhang, X. Huang, W. Dietsche, K. von Klitzing, and J. H. Smet, Signatures for Wigner crystal formation in the chemical potential of a two-dimensional electron system, Phys. Rev. Lett. 113, 076804 (2014).
  21. I. L. Drichko, I. Y. Smirnov, A. V. Suslov, L. N. Pfeiffer, K. W. West, and Y. M. Galperin, Crossover between localized states and pinned Wigner crystal in high-mobility n-GaAs/AlGaAs heterostructures near filling factor ν=1, Phys. Rev. B 92, 205313 (2015).
  22. J. Jang, B. M. Hunt, L. N. Pfeiffer, K. W. West, and R. C. Ashoori, Sharp tunnelling resonance from the vibrations of an electronic Wigner crystal, Nat. Phys. 13, 340 (2017).
  23. L. Zhao, W. Lin, Y. J. Chung, K. W. Baldwin, L. N. Pfeiffer, and Y. Liu, Finite capacitive response at the quantum Hall plateau, Chinese Phys. Lett. 39, 097301 (2022).
  24. H. Zhou, H. Polshyn, T. Taniguchi, K. Watanabe, and A. F. Young, Solids of quantum Hall skyrmions in graphene, Nat. Phys. 16, 154 (2020).
  25. R. L. Willett, H. L. Stormer, D. C. Tsui, L. N. Pfeiffer, K. W. West, and K. W. Baldwin, Termination of the series of fractional quantum Hall states at small filling factors, Phys. Rev. B 38, 7881(R) (1988).
  26. V. J. Goldman, M. Santos, M. Shayegan, and J. E. Cunningham, Evidence for two-dimentional quantum Wigner crystal, Phys. Rev. Lett. 65, 2189 (1990).
  27. H. W. Jiang, R. L. Willett, H. L. Stormer, D. C. Tsui, L. N. Pfeiffer, and K. W. West, Quantum liquid versus electron solid around ν=1/5 Landau-level filling, Phys. Rev. Lett. 65, 633 (1990).
  28. C. Reichhardt and C. J. Olson Reichhardt, Depinning and nonequilibrium dynamic phases of particle assemblies driven over random and ordered substrates: A review, Rep. Prog. Phys. 80, 026501 (2017).
  29. D. Maryenko, A. McCollam, J. Falson, Y. Kozuka, J. Bruin, U. Zeitler, and M. Kawasaki, Composite fermion liquid to Wigner solid transition in the lowest Landau level of zinc oxide, Nat. Commun. 9, 4356 (2018).
  30. H. Deng, L. N. Pfeiffer, K. W. West, K. W. Baldwin, L. W. Engel, and M. Shayegan, Probing the melting of a two-dimensional quantum Wigner crystal via its screening efficiency, Phys. Rev. Lett. 122, 116601 (2019).
  31. A. T. Hatke, H. Deng, Y. Liu, L. W. Engel, L. N. Pfeiffer, K. W. West, K. W. Baldwin, and M. Shayegan, Wigner solid pinning modes tuned by fractional quantum Hall states of a nearby layer, Sci. Adv. 5, eaao2848 (2019).
  32. M. K. Ma, K. A. Villegas Rosales, H. Deng, Y. J. Chung, L. N. Pfeiffer, K. W. West, K. W. Baldwin, R. Winkler, and M. Shayegan, Thermal and quantum melting phase diagrams for a magnetic-field-induced Wigner solid, Phys. Rev. Lett. 125, 036601 (2020).
  33. K. A. Villegas Rosales, S. K. Singh, M. K. Ma, Md. S. Hossain, Y. J. Chung, L. N. Pfeiffer, K. W. West, K. W. Baldwin, and M. Shayegan, Competition between fractional quantum Hall liquid and Wigner solid at small fillings: Role of layer thickness and Landau level mixing, Phys. Rev. Res. 3, 013181 (2021).
  34. Y. Zhou, J. Sung, E. Brutschea, I. Esterlis, Y. Wang, G. Scuri, R. Gelly, H. Heo, T. Taniguchi, K. Watanabe, G. Zaránd, M. Lukin, P. Kim, E. Demler, and H. Park, Bilayer Wigner crystals in a transition metal dichalcogenide heterostructure, Nature (London) 595, 48 (2021).
  35. T. Smoleński, P. E. Dolgirev, C. Kuhlenkamp, A. Popert, Y. Shimazaki, P. Back, X. Lu, M. Kroner, K. Watanabe, T. Taniguchi, I. Esterlis, E. Demler, and A. Imamoğlu, Signatures of Wigner crystal of electrons in a monolayer semiconductor, Nature (London) 595, 53 (2021).
  36. H. Li, S. Li, E. C. Regan, D. Wang, W. Zhao, S. Kahn, K. Yumigeta, M. Blei, T. Taniguchi, K. Watanabe, S. Tongay, A. Zettl, M. F. Crommie, and F. Wang, Imaging two-dimensional generalized Wigner crystals, Nature (London) 597, 650 (2021).
  37. V. Shingla, S. A. Myers, L. N. Pfeiffer, K. W. Baldwin, and G. A. Csáthy, Particle-hole symmetry and the reentrant integer quantum Hall Wigner solid, Commun. Phys. 4, 204 (2021).
  38. J. Falson, I. Sodemann, B. Skinner, D. Tabrea, Y. Kozuka, A. Tsukazaki, M. Kawasaki, K. von Klitzing, and J. H. Smet, Competing correlated states around the zero-field Wigner crystallization transition of electrons in two dimensions, Nat. Mater. 21, 311 (2022).
  39. S. L. Sondhi, A. Karlhede, S. A. Kivelson, and E. H. Rezayi, Skyrmions and the crossover from the integer to fractional quantum Hall effect at small Zeeman energies, Phys. Rev. B 47, 16419 (1993).
  40. H. A. Fertig, L. Brey, R. Côté, and A. H. MacDonald, Charged spin-texture excitations and the Hartree-Fock approximation in the quantum Hall effect, Phys. Rev. B 50, 11018 (1994).
  41. S. E. Barrett, G. Dabbagh, L. N. Pfeiffer, K. W. West, and R. Tycko, Optically pumped NMR evidence for finite-size skyrmions in GaAs quantum wells near Landau level filling ν=1, Phys. Rev. Lett. 74, 5112 (1995).
  42. R. Tycko, S. E. Barrett, G. Dabbagh, L. N. Pfeiffer, and K. W. West, Electronic states in gallium arsenide quantum wells probed by optically pumped NMR, Science 268, 1460 (1995).
  43. E. H. Aifer, B. B. Goldberg, and D. A. Broido, Evidence of skyrmion excitations about ν=1 in n-modulation-doped single quantum wells by interband optical transmission, Phys. Rev. Lett. 76, 680 (1996).
  44. B. A. Piot, W. Desrat, D. K. Maude, D. Kazazis, A. Cavanna, and U. Gennser, Disorder-induced stabilization of the quantum Hall ferromagnet, Phys. Rev. Lett. 116, 106801 (2016).
  45. H. M. Yoo, K. W. Baldwin, K. West, L. Pfeiffer, and R. C. Ashoori, Spin phase diagram of the interacting quantum Hall liquid, Nat. Phys. 16, 1022 (2020).
  46. A. Schmeller, J. P. Eisenstein, L. N. Pfeiffer, and K. W. West, Evidence for skyrmions and single spin flips in the integer quantized Hall effect, Phys. Rev. Lett. 75, 4290 (1995).
  47. D. K. Maude, M. Potemski, J. C. Portal, M. Henini, L. Eaves, G. Hill, and M. A. Pate, Spin excitations of a two-dimensional electron gas in the limit of vanishing landé g Factor, Phys. Rev. Lett. 77, 4604 (1996).
  48. L. Brey, H. A. Fertig, R. Côté, and A. H. MacDonald, Skyrme crystal in a two-dimensional electron gas, Phys. Rev. Lett. 75, 2562 (1995).
  49. A. G. Green, I. I. Kogan, and A. M. Tsvelik, Skyrmions in the quantum Hall effect at finite Zeeman coupling, Phys. Rev. B 54, 16838 (1996).
  50. R. Côté, A. H. MacDonald, L. Brey, H. A. Fertig, S. M. Girvin, and H. T. C. Stoof, Collective excitations, NMR, and phase transitions in skyrme crystals, Phys. Rev. Lett. 78, 4825 (1997).
  51. M. Rao, S. Sengupta, and R. Shankar, Shape-deformation-driven structural transitions in quantum Hall skyrmions, Phys. Rev. Lett. 79, 3998 (1997).
  52. V. Bayot, E. Grivei, S. Melinte, M. B. Santos, and M. Shayegan, Giant low temperature heat capacity of GaAs quantum wells near Landau level filling ν=1, Phys. Rev. Lett. 76, 4584 (1996).
  53. V. Bayot, E. Grivei, J. M. Beuken, S. Melinte, and M. Shayegan, Critical behavior of nuclear-spin diffusion in GaAs/AlGaAs heterostructures near Landau level filling ν=1, Phys. Rev. Lett. 79, 1718 (1997)
  54. W. Desrat, D. K. Maude, M. Potemski, J. C. Portal, Z. R. Wasilewski, and G. Hill, Resistively detected nuclear magnetic resonance in the quantum Hall regime: Possible evidence for a skyrme crystal, Phys. Rev. Lett. 88, 256807 (2002).
  55. K. Hashimoto, K. Muraki, T. Saku, and Y. Hirayama, Electrically controlled nuclear spin polarization and relaxation by quantum-Hall states, Phys. Rev. Lett. 88, 176601 (2002).
  56. G. Gervais, H. L. Stormer, D. C. Tsui, P. L. Kuhns, W. G. Moulton, A. P. Reyes, L. N. Pfeiffer, K. W. Baldwin, and K. W. West, Evidence for skyrmion crystallization from NMR relaxation experiments, Phys. Rev. Lett. 94, 196803 (2005).
  57. Y. Gallais, J. Yan, A. Pinczuk, L. N. Pfeiffer, and K. W. West, Soft spin wave near ν=1: Evidence for a magnetic instability in skyrmion systems, Phys. Rev. Lett. 100, 086806 (2008).
  58. H. Zhu, G. Sambandamurthy, Y. P. Chen, P. Jiang, L. W. Engel, D. C. Tsui, L. N. Pfeiffer, and K. W. West, Pinning-mode resonance of a skyrme crystal near Landau-level filling factor ν=1, Phys. Rev. Lett. 104, 226801 (2010).
  59. J. Oswald and R. A. Römer, Manifestation of many-body interactions in the integer quantum Hall effect regime, Phys. Rev. B 96, 125128 (2017).
  60. D. Werner and J. Oswald, Size scaling of the exchange interaction in the quantum Hall effect regime, Phys. Rev. B 102, 235305 (2020).
  61. J. Oswald and R. A. Römer, Microscopic details of stripes and bubbles in the quantum Hall regime, Phys. Rev. B 102, 121305(R) (2020).
  62. J. Oswald, Revision of the edge channel picture for the integer quantum Hall effect, Results Phys. 47, 106381 (2023).
  63. Y. J. Chung, K. A. Villegas Rosales, K. W. Baldwin, P. T. Madathil, K. W. West, M. Shayegan, and L. N. Pfeiffer, Ultra-high-quality two-dimensional electron systems, Nat. Mater. 20, 632 (2021).
  64. N. Samkharadze, A. Kumar, M. J. Manfra, L. N. Pfeiffer, K. W. West, and G. A. Csáthy, Integrated electronic transport and thermometry at milliKelvin temperatures and in strong magnetic fields, Rev. Sci. Instrum. 82, 053902 (2011).
  65. H. Fukuyama and P. A. Lee, Pinning and conductivity of two-dimensional charge-density waves in magnetic fields, Phys. Rev. B 18, 6245 (1978).
  66. I. M. Ruzin, S. Marianer, and B. I. Shklovskii, Pinning of a two-dimensional Wigner crystal by charged impurities, Phys. Rev. B 46, 3999 (1992).
  67. M. C. Cha and H. A. Fertig, Disorder-induced phase transitions in two-dimensional crystals, Phys. Rev. Lett. 74, 4867 (1995).
  68. E. Stahl, D. Weiss, G. Weimann, K. von Klitzing, and K. Ploog, Density of states of a two-dimensional electron gas in a strong magnetic field, J. Phys. C: Solid State Phys. 18, L783 (1985).
  69. H. P. Wei, A. M. Chang, D. C. Tsui, and M. Razeghi, Temperature dependence of the quantized Hall effect, Phys. Rev. B 32, 7016(R) (1985).
  70. J. Sinova, A. H. MacDonald, and S. M. Girvin, Disorder and interactions in quantum Hall ferromagnets near ν=1, Phys. Rev. B 62, 13579 (2000).
  71. A. J. Nederveen and Y. V. Nazarov, Skyrmions in disordered heterostructures, Phys. Rev. Lett. 82, 406 (1999).

Outline

Information

Phys. Rev. Research 6, L022056– Published 10 June, 2024
  • Received 1 October 2023
  • Accepted 7 May 2024
Crossmark - Check for updates button
Creative Commons Logo

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation