{"id":1034100,"date":"2026-06-18T07:39:23","date_gmt":"2026-06-18T07:39:23","guid":{"rendered":"https:\/\/www.europesays.com\/uk\/1034100\/"},"modified":"2026-06-18T07:39:23","modified_gmt":"2026-06-18T07:39:23","slug":"visualizing-the-impact-of-quenched-disorder-on-2d-electron-wigner-solids","status":"publish","type":"post","link":"https:\/\/www.europesays.com\/uk\/1034100\/","title":{"rendered":"Visualizing the impact of quenched disorder on 2D electron Wigner solids"},"content":{"rendered":"
  • \n

    Chui, S. & Tanatar, B. Impurity effect on the two-dimensional-electron fluid-solid transition in zero field. Phys. Rev. Lett. 74<\/b>, 458 (1995).<\/p>\n

    Article<\/a>\u00a0
    \n     ADS<\/a>\u00a0
    \n     CAS<\/a>\u00a0
    \n     PubMed<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Thakur, J. & Neilson, D. Frozen electron solid in the presence of small concentrations of defects. Phys. Rev. B 54<\/b>, 7674 (1996).<\/p>\n

    Article<\/a>\u00a0
    \n     ADS<\/a>\u00a0
    \n     CAS<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Chakravarty, S., Kivelson, S., Nayak, C. & Voelker, K. Wigner glass, spin liquids and the metal-insulator transition. Philos. Mag. B 79<\/b>, 859\u2013868 (1999).<\/p>\n

    Article<\/a>\u00a0
    \n     ADS<\/a>\u00a0
    \n     CAS<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Chitra, R., Giamarchi, T. & Le Doussal, P. Pinned Wigner crystals. Phys. Rev. B 65<\/b>, 035312 (2001).<\/p>\n

    Article<\/a>\u00a0
    \n     ADS<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Giamarchi, T. in Strongly Correlated Fermions and Bosons in Low-Dimensional Disordered Systems (eds Lerner, I. V., Althsuler, B. L., Fal\u2019ko, V. I. & Giamarchi, T.) 165\u2013183 (Springer, 2002).<\/p>\n<\/li>\n

  • \n

    Kravchenko, S. & Sarachik, M. P. Metal\u2013insulator transition in two-dimensional electron systems. Rep. Prog. Phys. 67<\/b>, 1 (2003).<\/p>\n

    Article<\/a>\u00a0
    \n     ADS<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Chitra, R. & Giamarchi, T. Zero field Wigner crystal. Eur. Phys. J. B 44<\/b>, 455\u2013467 (2005).<\/p>\n

    Article<\/a>\u00a0
    \n     ADS<\/a>\u00a0
    \n     CAS<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Spivak, B., Kravchenko, S., Kivelson, S. & Gao, X. Colloquium: Transport in strongly correlated two dimensional electron fluids. Rev. Mod. Phys. 82<\/b>, 1743\u20131766 (2010).<\/p>\n

    Article<\/a>\u00a0
    \n     ADS<\/a>\u00a0
    \n     CAS<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Vu, D. & Das Sarma, S. Thermal melting of a quantum electron solid in the presence of strong disorder: Anderson localization versus the Wigner crystal. Phys. Rev. B 106<\/b>, L121103 (2022).<\/p>\n

    Article<\/a>\u00a0
    \n     ADS<\/a>\u00a0
    \n     CAS<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Ahn, S. & Das Sarma, S. Density-tuned effective metal-insulator transitions in two-dimensional semiconductor layers: Anderson localization or Wigner crystallization. Phys. Rev. B 107<\/b>, 195435 (2023).<\/p>\n

    Article<\/a>\u00a0
    \n     ADS<\/a>\u00a0
    \n     CAS<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Reichhardt, C. & Reichhardt, C. Melting, reentrant ordering and peak effect for Wigner crystals with quenched and thermal disorder. New J. Phys. 25<\/b>, 043016 (2023).<\/p>\n

    Article<\/a>\u00a0
    \n     ADS<\/a>\u00a0
    \n     CAS<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Huang, Y. & Das Sarma, S. Electronic transport, metal-insulator transition, and Wigner crystallization in transition metal dichalcogenide monolayers. Phys. Rev. B 109<\/b>, 245431 (2024).<\/p>\n

    Article<\/a>\u00a0
    \n     ADS<\/a>\u00a0
    \n     CAS<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Wigner, E. On the interaction of electrons in metals. Phys. Rev. 46<\/b>, 1002 (1934).<\/p>\n

    Article<\/a>\u00a0
    \n     ADS<\/a>\u00a0
    \n     CAS<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Tanatar, B. & Ceperley, D. M. Ground state of the two-dimensional electron gas. Phys. Rev. B 39<\/b>, 5005 (1989).<\/p>\n

    Article<\/a>\u00a0
    \n     ADS<\/a>\u00a0
    \n     CAS<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Spivak, B. & Kivelson, S. A. Phases intermediate between a two-dimensional electron liquid and Wigner crystal. Phys. Rev. B 70<\/b>, 155114 (2004).<\/p>\n

    Article<\/a>\u00a0
    \n     ADS<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Drummond, N. & Needs, R. Phase diagram of the low-density two-dimensional homogeneous electron gas. Phys. Rev. Lett. 102<\/b>, 126402 (2009).<\/p>\n

    Article<\/a>\u00a0
    \n     ADS<\/a>\u00a0
    \n     CAS<\/a>\u00a0
    \n     PubMed<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Smith, C. et al. Unified variational approach description of ground-state phases of the two-dimensional electron gas. Phys. Rev. Lett. 133<\/b>, 266504 (2024).<\/p>\n

    Article<\/a>\u00a0
    \n     ADS<\/a>\u00a0
    \n     MathSciNet<\/a>\u00a0
    \n     CAS<\/a>\u00a0
    \n     PubMed<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Dolgopolov, V. T. Quantum melting of a two-dimensional Wigner crystal. Phys. Uspekhi 60<\/b>, 731\u2013742 (2017).<\/p>\n

    Article<\/a>\u00a0
    \n     ADS<\/a>\u00a0
    \n     CAS<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Yoon, J., Li, C., Shahar, D., Tsui, D. & Shayegan, M. Wigner crystallization and metal-insulator transition of two-dimensional holes in GaAs at B = 0. Phys. Rev. Lett. 82<\/b>, 1744 (1999).<\/p>\n

    Article<\/a>\u00a0
    \n     ADS<\/a>\u00a0
    \n     CAS<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Smole\u0144ski, T. et al. Signatures of Wigner crystal of electrons in a monolayer semiconductor. Nature 595<\/b>, 53\u201357 (2021).<\/p>\n

    Article<\/a>\u00a0
    \n     ADS<\/a>\u00a0
    \n     PubMed<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Pack, J. et al. Charge-transfer contacts for the measurement of correlated states in high-mobility WSe2. Nat. Nanotechnol. 19<\/b>, 948\u2013954 (2024).<\/p>\n

    Article<\/a>\u00a0
    \n     ADS<\/a>\u00a0
    \n     CAS<\/a>\u00a0
    \n     PubMed<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Sung, J. et al. An electronic microemulsion phase emerging from a quantum crystal-to-liquid transition. Nat. Phys. 21<\/b>, 437\u2013443 (2025).<\/p>\n

    Article<\/a>\u00a0
    \n     CAS<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Das Sarma, S. et al. Two-dimensional metal-insulator transition as a percolation transition in a high-mobility electron system. Phys. Rev. Lett. 94<\/b>, 136401 (2005).<\/p>\n

    Article<\/a>\u00a0
    \n     ADS<\/a>\u00a0
    \n     PubMed<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Li, H. et al. Imaging two-dimensional generalized Wigner crystals. Nature 597<\/b>, 650\u2013654 (2021).<\/p>\n

    Article<\/a>\u00a0
    \n     ADS<\/a>\u00a0
    \n     CAS<\/a>\u00a0
    \n     PubMed<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Li, H. et al. Wigner molecular crystals from multielectron moir\u00e9 artificial atoms. Science 385<\/b>, 86\u201391 (2024).<\/p>\n

    Article<\/a>\u00a0
    \n     ADS<\/a>\u00a0
    \n     CAS<\/a>\u00a0
    \n     PubMed<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Li, H. et al. Imaging tunable Luttinger liquid systems in van der Waals heterostructures. Nature 631<\/b>, 765\u2013770 (2024).<\/p>\n

    Article<\/a>\u00a0
    \n     ADS<\/a>\u00a0
    \n     CAS<\/a>\u00a0
    \n     PubMed<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Tsui, Y.-C. et al. Direct observation of a magnetic-field-induced Wigner crystal. Nature 628<\/b>, 287\u2013292 (2024).<\/p>\n

    Article<\/a>\u00a0
    \n     ADS<\/a>\u00a0
    \n     CAS<\/a>\u00a0
    \n     PubMed<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Xiang, Z. et al. Imaging quantum melting in a disordered 2D Wigner solid. Science 388<\/b>, 736\u2013740 (2025).<\/p>\n

    Article<\/a>\u00a0
    \n     ADS<\/a>\u00a0
    \n     CAS<\/a>\u00a0
    \n     PubMed<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Hossain, M. S. et al. Anisotropic two-dimensional disordered Wigner solid. Phys. Rev. Lett. 129<\/b>, 036601 (2022).<\/p>\n

    Article<\/a>\u00a0
    \n     ADS<\/a>\u00a0
    \n     CAS<\/a>\u00a0
    \n     PubMed<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Hatke, A. et al. Wigner solid pinning modes tuned by fractional quantum Hall states of a nearby layer. Sci. Adv. 5<\/b>, eaao2848 (2019).<\/p>\n

    Article<\/a>\u00a0
    \n     ADS<\/a>\u00a0
    \n     CAS<\/a>\u00a0
    \n     PubMed<\/a>\u00a0
    \n     PubMed Central<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Chen, Y. P. et al. Microwave resonance study of melting in high magnetic field Wigner solid. Int. J. Mod. Phys. B 21<\/b>, 1379\u20131385 (2007).<\/p>\n

    Article<\/a>\u00a0
    \n     ADS<\/a>\u00a0
    \n     CAS<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Larentis, S. et al. Large effective mass and interaction-enhanced Zeeman splitting of K-valley electrons in MoSe2. Phys. Rev. B 97<\/b>, 201407 (2018).<\/p>\n

    Article<\/a>\u00a0
    \n     ADS<\/a>\u00a0
    \n     CAS<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Barja, S. et al. Identifying substitutional oxygen as a prolific point defect in monolayer transition metal dichalcogenides. Nat. Commun. 10<\/b>, 3382 (2019).<\/p>\n

    Article<\/a>\u00a0
    \n     ADS<\/a>\u00a0
    \n     PubMed<\/a>\u00a0
    \n     PubMed Central<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Schuler, B. et al. How substitutional point defects in two-dimensional WS2 induce charge localization, spin\u2013orbit splitting, and strain. ACS Nano 13<\/b>, 10520\u201310534 (2019).<\/p>\n

    Article<\/a>\u00a0
    \n     CAS<\/a>\u00a0
    \n     PubMed<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Aghajanian, M. et al. Resonant and bound states of charged defects in two-dimensional semiconductors. Phys. Rev. B 101<\/b>, 081201 (2020).<\/p>\n

    Article<\/a>\u00a0
    \n     ADS<\/a>\u00a0
    \n     CAS<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Friedel, J. XIV. The distribution of electrons round impurities in monovalent metals. Lond. Edinb. Dublin Philos. Mag. J. Sci. 43<\/b>, 153\u2013189 (1952).<\/p>\n

    Article<\/a>\u00a0
    \n     CAS<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Simion, G. E. & Giuliani, G. F. Friedel oscillations in a Fermi liquid. Phys. Rev. B 72<\/b>, 045127 (2005).<\/p>\n

    Article<\/a>\u00a0
    \n     ADS<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Li, J. & Wei, S.-H. Alignment of isovalent impurity levels: oxygen impurity in II-VI semiconductors. Phys. Rev. B 73<\/b>, 041201 (2006).<\/p>\n

    Article<\/a>\u00a0
    \n     ADS<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Murphy, S., Lu, H. & Grimes, R. General relationships for isovalent cation substitution into oxides with the rocksalt structure. J. Phys. Chem. Solids 71<\/b>, 735\u2013738 (2010).<\/p>\n

    Article<\/a>\u00a0
    \n     ADS<\/a>\u00a0
    \n     CAS<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Falson, J. et al. Competing correlated states around the zero-field Wigner crystallization transition of electrons in two dimensions. Nat. Mater. 21<\/b>, 311\u2013316 (2022).<\/p>\n

    Article<\/a>\u00a0
    \n     CAS<\/a>\u00a0
    \n     PubMed<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Valenti, A. et al. Quantum geometry driven crystallization: a neural-network variational Monte Carlo study. Preprint at https:\/\/arxiv.org\/abs\/2512.07947<\/a> (2025).<\/p>\n<\/li>\n

  • \n

    Kim, J. et al. Neural-network quantum states for ultra-cold Fermi gases. Commun. Phys. 7<\/b>, 148 (2024).<\/p>\n

    Article<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Li, C.-T., Ong, T., Geier, M., Lin, H. & Fu, L. Attention is all you need to solve chiral superconductivity. Preprint at https:\/\/arxiv.org\/abs\/2509.03683<\/a> (2026).<\/p>\n<\/li>\n

  • \n

    Linteau, D., Pescia, G., Nys, J., Carleo, G. & Holzmann, M. Phase diagram and crystal melting of helium-4 in two dimensions. Phys. Rev. Lett. 134<\/b>, 246001 (2025).<\/p>\n

    Article<\/a>\u00a0
    \n     ADS<\/a>\u00a0
    \n     CAS<\/a>\u00a0
    \n     PubMed<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Qian, Y. et al. Describing Landau level mixing in fractional quantum Hall states with deep learning. Phys. Rev. Lett. 134<\/b>, 176503 (2025).<\/p>\n

    Article<\/a>\u00a0
    \n     ADS<\/a>\u00a0
    \n     MathSciNet<\/a>\u00a0
    \n     CAS<\/a>\u00a0
    \n     PubMed<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Li, X. et al. Deep learning sheds light on integer and fractional topological insulators. Preprint at https:\/\/arxiv.org\/abs\/2503.11756<\/a> (2025).<\/p>\n<\/li>\n

  • \n

    Luo, D., Zaklama, T. & Fu, L. Solving fractional electron states in twisted MoTe2 with deep neural network. Preprint at https:\/\/arxiv.org\/abs\/2503.13585<\/a> (2025).<\/p>\n<\/li>\n

  • \n

    Li, X., Qian, Y., Ren, W., Xu, Y. & Chen, J. Emergent Wigner phases in moir\u00e9 superlattice from deep learning. Commun. Phys. 8<\/b>, 364 (2025).<\/p>\n

    Article<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Poduval, P. P. & Das Sarma, S. Anderson localization in doped semiconductors. Phys. Rev. B 107<\/b>, 174204 (2023).<\/p>\n

    Article<\/a>\u00a0
    \n     ADS<\/a>\u00a0
    \n     CAS<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n","protected":false},"excerpt":{"rendered":"Chui, S. & Tanatar, B. Impurity effect on the two-dimensional-electron fluid-solid transition in zero field. Phys. Rev. Lett.…\n","protected":false},"author":2,"featured_media":1034101,"comment_status":"","ping_status":"","sticky":false,"template":"","format":"standard","meta":{"footnotes":"","_share_on_mastodon":"0"},"categories":[3845],"tags":[20546,3965,3966,12374,74,22503,134988,70,13811,16,15],"class_list":["post-1034100","post","type-post","status-publish","format-standard","has-post-thumbnail","category-physics","tag-electronic-properties-and-materials","tag-humanities-and-social-sciences","tag-multidisciplinary","tag-phase-transitions-and-critical-phenomena","tag-physics","tag-quantum-fluids-and-solids","tag-scanning-probe-microscopy","tag-science","tag-two-dimensional-materials","tag-uk","tag-united-kingdom"],"share_on_mastodon":{"url":"https:\/\/pubeurope.com\/@uk\/116769978219732322","error":""},"_links":{"self":[{"href":"https:\/\/www.europesays.com\/uk\/wp-json\/wp\/v2\/posts\/1034100","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.europesays.com\/uk\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.europesays.com\/uk\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.europesays.com\/uk\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/www.europesays.com\/uk\/wp-json\/wp\/v2\/comments?post=1034100"}],"version-history":[{"count":0,"href":"https:\/\/www.europesays.com\/uk\/wp-json\/wp\/v2\/posts\/1034100\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.europesays.com\/uk\/wp-json\/wp\/v2\/media\/1034101"}],"wp:attachment":[{"href":"https:\/\/www.europesays.com\/uk\/wp-json\/wp\/v2\/media?parent=1034100"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.europesays.com\/uk\/wp-json\/wp\/v2\/categories?post=1034100"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.europesays.com\/uk\/wp-json\/wp\/v2\/tags?post=1034100"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}