Chui, S. & Tanatar, B. Impurity effect on the two-dimensional-electron fluid-solid transition in zero field. Phys. Rev. Lett. 74, 458 (1995).
Thakur, J. & Neilson, D. Frozen electron solid in the presence of small concentrations of defects. Phys. Rev. B 54, 7674 (1996).
Chakravarty, S., Kivelson, S., Nayak, C. & Voelker, K. Wigner glass, spin liquids and the metal-insulator transition. Philos. Mag. B 79, 859–868 (1999).
Chitra, R., Giamarchi, T. & Le Doussal, P. Pinned Wigner crystals. Phys. Rev. B 65, 035312 (2001).
Giamarchi, T. in Strongly Correlated Fermions and Bosons in Low-Dimensional Disordered Systems (eds Lerner, I. V., Althsuler, B. L., Fal’ko, V. I. & Giamarchi, T.) 165–183 (Springer, 2002).
Kravchenko, S. & Sarachik, M. P. Metal–insulator transition in two-dimensional electron systems. Rep. Prog. Phys. 67, 1 (2003).
Chitra, R. & Giamarchi, T. Zero field Wigner crystal. Eur. Phys. J. B 44, 455–467 (2005).
Spivak, B., Kravchenko, S., Kivelson, S. & Gao, X. Colloquium: Transport in strongly correlated two dimensional electron fluids. Rev. Mod. Phys. 82, 1743–1766 (2010).
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, L121103 (2022).
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, 195435 (2023).
Reichhardt, C. & Reichhardt, C. Melting, reentrant ordering and peak effect for Wigner crystals with quenched and thermal disorder. New J. Phys. 25, 043016 (2023).
Huang, Y. & Das Sarma, S. Electronic transport, metal-insulator transition, and Wigner crystallization in transition metal dichalcogenide monolayers. Phys. Rev. B 109, 245431 (2024).
Wigner, E. On the interaction of electrons in metals. Phys. Rev. 46, 1002 (1934).
Tanatar, B. & Ceperley, D. M. Ground state of the two-dimensional electron gas. Phys. Rev. B 39, 5005 (1989).
Spivak, B. & Kivelson, S. A. Phases intermediate between a two-dimensional electron liquid and Wigner crystal. Phys. Rev. B 70, 155114 (2004).
Drummond, N. & Needs, R. Phase diagram of the low-density two-dimensional homogeneous electron gas. Phys. Rev. Lett. 102, 126402 (2009).
Smith, C. et al. Unified variational approach description of ground-state phases of the two-dimensional electron gas. Phys. Rev. Lett. 133, 266504 (2024).
Dolgopolov, V. T. Quantum melting of a two-dimensional Wigner crystal. Phys. Uspekhi 60, 731–742 (2017).
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, 1744 (1999).
Smoleński, T. et al. Signatures of Wigner crystal of electrons in a monolayer semiconductor. Nature 595, 53–57 (2021).
Pack, J. et al. Charge-transfer contacts for the measurement of correlated states in high-mobility WSe2. Nat. Nanotechnol. 19, 948–954 (2024).
Sung, J. et al. An electronic microemulsion phase emerging from a quantum crystal-to-liquid transition. Nat. Phys. 21, 437–443 (2025).
Das Sarma, S. et al. Two-dimensional metal-insulator transition as a percolation transition in a high-mobility electron system. Phys. Rev. Lett. 94, 136401 (2005).
Li, H. et al. Imaging two-dimensional generalized Wigner crystals. Nature 597, 650–654 (2021).
Li, H. et al. Wigner molecular crystals from multielectron moiré artificial atoms. Science 385, 86–91 (2024).
Li, H. et al. Imaging tunable Luttinger liquid systems in van der Waals heterostructures. Nature 631, 765–770 (2024).
Tsui, Y.-C. et al. Direct observation of a magnetic-field-induced Wigner crystal. Nature 628, 287–292 (2024).
Xiang, Z. et al. Imaging quantum melting in a disordered 2D Wigner solid. Science 388, 736–740 (2025).
Hossain, M. S. et al. Anisotropic two-dimensional disordered Wigner solid. Phys. Rev. Lett. 129, 036601 (2022).
Hatke, A. et al. Wigner solid pinning modes tuned by fractional quantum Hall states of a nearby layer. Sci. Adv. 5, eaao2848 (2019).
Chen, Y. P. et al. Microwave resonance study of melting in high magnetic field Wigner solid. Int. J. Mod. Phys. B 21, 1379–1385 (2007).
Larentis, S. et al. Large effective mass and interaction-enhanced Zeeman splitting of K-valley electrons in MoSe2. Phys. Rev. B 97, 201407 (2018).
Barja, S. et al. Identifying substitutional oxygen as a prolific point defect in monolayer transition metal dichalcogenides. Nat. Commun. 10, 3382 (2019).
Schuler, B. et al. How substitutional point defects in two-dimensional WS2 induce charge localization, spin–orbit splitting, and strain. ACS Nano 13, 10520–10534 (2019).
Aghajanian, M. et al. Resonant and bound states of charged defects in two-dimensional semiconductors. Phys. Rev. B 101, 081201 (2020).
Friedel, J. XIV. The distribution of electrons round impurities in monovalent metals. Lond. Edinb. Dublin Philos. Mag. J. Sci. 43, 153–189 (1952).
Simion, G. E. & Giuliani, G. F. Friedel oscillations in a Fermi liquid. Phys. Rev. B 72, 045127 (2005).
Li, J. & Wei, S.-H. Alignment of isovalent impurity levels: oxygen impurity in II-VI semiconductors. Phys. Rev. B 73, 041201 (2006).
Murphy, S., Lu, H. & Grimes, R. General relationships for isovalent cation substitution into oxides with the rocksalt structure. J. Phys. Chem. Solids 71, 735–738 (2010).
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).
Valenti, A. et al. Quantum geometry driven crystallization: a neural-network variational Monte Carlo study. Preprint at https://arxiv.org/abs/2512.07947 (2025).
Kim, J. et al. Neural-network quantum states for ultra-cold Fermi gases. Commun. Phys. 7, 148 (2024).
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 (2026).
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, 246001 (2025).
Qian, Y. et al. Describing Landau level mixing in fractional quantum Hall states with deep learning. Phys. Rev. Lett. 134, 176503 (2025).
Li, X. et al. Deep learning sheds light on integer and fractional topological insulators. Preprint at https://arxiv.org/abs/2503.11756 (2025).
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 (2025).
Li, X., Qian, Y., Ren, W., Xu, Y. & Chen, J. Emergent Wigner phases in moiré superlattice from deep learning. Commun. Phys. 8, 364 (2025).
Poduval, P. P. & Das Sarma, S. Anderson localization in doped semiconductors. Phys. Rev. B 107, 174204 (2023).
