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Phase transitions in 2D materials

Nature Reviews Materials volume 6, pages 829–846 (2021)Cite this article

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Abstract

The discovery and control of new phases of matter is a central endeavour in materials research. The emergence of atomically thin 2D materials, such as transition-metal dichalcogenides and monochalcogenides, has allowed the study of diffusive, displacive and quantum phase transitions in 2D. In this Review, we discuss the thermodynamic and kinetic features of 2D phase transitions arising from dimensionality confinement, elasticity, electrostatics, defects and chemistry unique to 2D materials. We highlight polymorphic, ferroic and high-temperature diffusive phase changes, and examine the technological potential of controlled 2D phase transitions. Finally, we give an outlook to future opportunities in the study and applications of 2D phase transitions, and identify key challenges that remain to be addressed.

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Fig. 1: Timeline of key developments in the study of 2D phase transitions.
Fig. 2: Distinct features of phase transitions in 2D materials.
Fig. 3: Polymorphic transitions in 2D transition-metal dichalcogenides.
Fig. 4: Ferroic phase transitions in 2D materials.
Fig. 5: 2D or 2D-templated diffusive phase transitions.
Fig. 6: New device applications of 2D phase-change materials.

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References

  1. Ma, S. Modern Theory of Critical Phenomena (W. A. Benjamin, Advanced Book Program, 1976).

  2. Goldenfeld, N. Lectures on Phase Transitions and the Renormalization Group (Addison-Wesley, 1992).

  3. Christian, J. W. The Theory of Transformations in Metals and Alloys 3rd edn (Pergamon, 2002).

  4. Sachdev, S. Quantum Phase Transitions 2nd edn (Cambridge Univ. Press, 2011).

  5. Fradkin, E. Field Theories of Condensed Matter Physics 2nd edn (Cambridge Univ. Press, 2013).

  6. Novoselov, K. S. et al. Two-dimensional atomic crystals. Proc. Natl Acad. Sci. USA 102, 10451–10453 (2005).

    Article  CAS  Google Scholar 

  7. Wang, Q. H., Kalantar-Zadeh, K., Kis, A., Coleman, J. N. & Strano, M. S. Electronics and optoelectronics of two-dimensional transition metal dichalcogenides. Nat. Nanotechnol. 7, 699–712 (2012).

    Article  CAS  Google Scholar 

  8. Novoselov, K. S., Mishchenko, A., Carvalho, A. & Castro Neto, A. H. 2D materials and van der Waals heterostructures. Science 353, aac9439 (2016).

    Article  CAS  Google Scholar 

  9. Manzeli, S., Ovchinnikov, D., Pasquier, D., Yazyev, O. V. & Kis, A. 2D transition metal dichalcogenides. Nat. Rev. Mater. 2, 17033 (2017).

    Article  CAS  Google Scholar 

  10. Yang, H., Kim, S. W., Chhowalla, M. & Lee, Y. H. Structural and quantum-state phase transitions in van der Waals layered materials. Nat. Phys. 13, 931–937 (2017).

    Article  CAS  Google Scholar 

  11. Onsager, L. Crystal statistics. I. A two-dimensional model with an order-disorder transition. Phys. Rev. 65, 117–149 (1944).

    Article  CAS  Google Scholar 

  12. Hohenberg, P. C. Existence of long-range order in one and two dimensions. Phys. Rev. 158, 383–386 (1967).

    Article  CAS  Google Scholar 

  13. Mermin, N. D. & Wagner, H. Absence of ferromagnetism or antiferromagnetism in one- or two-dimensional isotropic heisenberg models. Phys. Rev. Lett. 17, 1133–1136 (1966).

    Article  CAS  Google Scholar 

  14. Kosterlitz, J. M. & Thouless, D. J. Long range order and metastability in two dimensional solids and superfluids. (Application of dislocation theory). J. Phys. C Solid State Phys. 5, L124–L126 (1972).

    Article  CAS  Google Scholar 

  15. Kosterlitz, J. M. & Thouless, D. J. Ordering, metastability and phase transitions in two-dimensional systems. J. Phys. C Solid State Phys. 6, 1181–1203 (1973).

    Article  CAS  Google Scholar 

  16. Klitzing, K. V., 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 (1980).

    Article  Google Scholar 

  17. 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 

  18. Binnig, G., Rohrer, H., Gerber, C. & Weibel, E. Surface studies by scanning tunneling microscopy. Phys. Rev. Lett. 49, 57–61 (1982).

    Article  Google Scholar 

  19. Binnig, G., Quate, C. F. & Gerber, C. Atomic force microscope. Phys. Rev. Lett. 56, 930–933 (1986).

    Article  CAS  Google Scholar 

  20. Binnig, G., Rohrer, H., Gerber, C. & Weibel, E. 7 × 7 reconstruction on Si(111) resolved in real space. Phys. Rev. Lett. 50, 120–123 (1983).

    Article  CAS  Google Scholar 

  21. Zhang, J., Liu, J., Huang, J. L., Kim, P. & Lieber, C. M. Creation of nanocrystals through a solid-solid phase transition induced by an STM tip. Science 274, 757–760 (1996).

    Article  CAS  Google Scholar 

  22. Kaganer, V. M., Möhwald, H. & Dutta, P. Structure and phase transitions in Langmuir monolayers. Rev. Mod. Phys. 71, 779–819 (1999).

    Article  CAS  Google Scholar 

  23. Novoselov, K. S. et al. Electric field effect in atomically thin carbon films. Science 306, 666–669 (2004).

    Article  CAS  Google Scholar 

  24. Zhang, Y. B., Tan, Y. W., Stormer, H. L. & Kim, P. Experimental observation of the quantum Hall effect and Berry’s phase in graphene. Nature 438, 201–204 (2005).

    Article  CAS  Google Scholar 

  25. Bolotin, K. I., Ghahari, F., Shulman, M. D., Stormer, H. L. & Kim, P. Observation of the fractional quantum Hall effect in graphene. Nature 462, 196–199 (2009).

    Article  CAS  Google Scholar 

  26. Du, X., Skachko, I., Duerr, F., Luican, A. & Andrei, E. Y. Fractional quantum Hall effect and insulating phase of Dirac electrons in graphene. Nature 462, 192–195 (2009).

    Article  CAS  Google Scholar 

  27. Cao, Y. et al. Correlated insulator behaviour at half-filling in magic-angle graphene superlattices. Nature 556, 80–84 (2018).

    Article  CAS  Google Scholar 

  28. Xi, X. X. et al. Ising pairing in superconducting NbSe2 atomic layers. Nat. Phys. 12, 139–143 (2016).

    Article  CAS  Google Scholar 

  29. Saito, Y., Nojima, T. & Iwasa, Y. Highly crystalline 2D superconductors. Nat. Rev. Mater. 2, 16094 (2017).

    Article  CAS  Google Scholar 

  30. Cao, Y. et al. Unconventional superconductivity in magic-angle graphene superlattices. Nature 556, 43–50 (2018).

    Article  CAS  Google Scholar 

  31. Kane, C. L. & Mele, E. J. Quantum spin Hall effect in graphene. Phys. Rev. Lett. 95, 226801 (2005).

    Article  CAS  Google Scholar 

  32. Konig, M. et al. Quantum spin hall insulator state in HgTe quantum wells. Science 318, 766–770 (2007).

    Article  CAS  Google Scholar 

  33. Qian, X. F., Liu, J. W., Fu, L. & Li, J. Quantum spin Hall effect in two-dimensional transition metal dichalcogenides. Science 346, 1344–1347 (2014). This paper predicts that several group 6 transition-metal dichalcogenide monolayers in 1T′ phase are quantum spin Hall insulators competing with the trivial semiconducting 1H phase and metallic 1T phase.

    Article  CAS  Google Scholar 

  34. Tang, S. J. et al. Quantum spin Hall state in monolayer 1T′-WTe2. Nat. Phys. 13, 683–687 (2017).

    Article  CAS  Google Scholar 

  35. Wu, S. F. et al. Observation of the quantum spin Hall effect up to 100 kelvin in a monolayer crystal. Science 359, 76–79 (2018).

    Article  CAS  Google Scholar 

  36. Chen, G. et al. Tunable correlated Chern insulator and ferromagnetism in a moiré superlattice. Nature 579, 56–61 (2020).

    Article  CAS  Google Scholar 

  37. Serlin, M. et al. Intrinsic quantized anomalous Hall effect in a moiré heterostructure. Science 367, 900–903 (2020).

    Article  CAS  Google Scholar 

  38. Polshyn, H. et al. Electrical switching of magnetic order in an orbital Chern insulator. Nature 588, 66–70 (2020).

    Article  CAS  Google Scholar 

  39. Huang, B. et al. Layer-dependent ferromagnetism in a van der Waals crystal down to the monolayer limit. Nature 546, 270–273 (2017). The first demonstration that intrinsic ferromagnetism can be present in monolayer CrI3.

    Article  CAS  Google Scholar 

  40. Gong, C. et al. Discovery of intrinsic ferromagnetism in two-dimensional van der Waals crystals. Nature 546, 265–269 (2017). The first demonstration of layer-dependent ferromagnetic transition in 2D Cr2Ge2Te6.

    Article  CAS  Google Scholar 

  41. Burch, K. S., Mandrus, D. & Park, J. G. Magnetism in two-dimensional van der Waals materials. Nature 563, 47–52 (2018).

    Article  CAS  Google Scholar 

  42. Gong, C. & Zhang, X. Two-dimensional magnetic crystals and emergent heterostructure devices. Science 363, eaav4450 (2019).

    Article  CAS  Google Scholar 

  43. Gibertini, M., Koperski, M., Morpurgo, A. F. & Novoselov, K. S. Magnetic 2D materials and heterostructures. Nat. Nanotechnol. 14, 408–419 (2019).

    Article  CAS  Google Scholar 

  44. Mak, K. F., Shan, J. & Ralph, D. C. Probing and controlling magnetic states in 2D layered magnetic materials. Nat. Rev. Phys. 1, 646–661 (2019).

    Article  Google Scholar 

  45. Huang, B. et al. Emergent phenomena and proximity effects in two-dimensional magnets and heterostructures. Nat. Mater. 19, 1276–1289 (2020).

    Article  CAS  Google Scholar 

  46. Eda, G. et al. Coherent atomic and electronic heterostructures of single-layer MoS2. ACS Nano 6, 7311–7317 (2012).

    Article  CAS  Google Scholar 

  47. Kappera, R. et al. Phase-engineered low-resistance contacts for ultrathin MoS2 transistors. Nat. Mater. 13, 1128–1134 (2014).

    Article  CAS  Google Scholar 

  48. Duerloo, K.-A. N., Li, Y. & Reed, E. J. Structural phase transitions in two-dimensional Mo- and W-dichalcogenide monolayers. Nat. Commun. 5, 4214 (2014). This paper reports the first comprehensive theoretical study of structural phase transitions in monolayer transition-metal dichalcogenides.

    Article  CAS  Google Scholar 

  49. Keum, D. H. et al. Bandgap opening in few-layered monoclinic MoTe2. Nat. Phys. 11, 482–486 (2015).

    Article  CAS  Google Scholar 

  50. Cho, S. et al. Phase patterning for ohmic homojunction contact in MoTe2. Science 349, 625–628 (2015).

    Article  CAS  Google Scholar 

  51. Wang, Y. et al. Structural phase transition in monolayer MoTe2 driven by electrostatic doping. Nature 550, 487–491 (2017).

    Article  CAS  Google Scholar 

  52. Zhang, F. et al. Electric-field induced structural transition in vertical MoTe2- and Mo1−xWxTe2-based resistive memories. Nat. Mater. 18, 55–61 (2019).

    Article  CAS  Google Scholar 

  53. Sie, E. J. et al. An ultrafast symmetry switch in a Weyl semimetal. Nature 565, 61–66 (2019).

    Article  CAS  Google Scholar 

  54. Xiao, J. et al. Berry curvature memory through electrically driven stacking transitions. Nat. Phys. 16, 1028–1034 (2020). The first experimental demonstration of the theoretically predicted ferroelectric nonlinear Hall effect and Berry curvature memory in 2D semimetals.

    Article  CAS  Google Scholar 

  55. Chang, K. et al. Discovery of robust in-plane ferroelectricity in atomic-thick SnTe. Science 353, 274–278 (2016). The first experimental report of in-plane ferroelectricity in an atomically thin material.

    Article  CAS  Google Scholar 

  56. Ding, W. et al. Prediction of intrinsic two-dimensional ferroelectrics in In2Se3 and other III2-VI3 van der Waals materials. Nat. Commun. 8, 14956 (2017). The first theoretical prediction of simultaneous out-of-plane and in-plane ferroelectricity in monolayer α-In2Se3.

    Article  CAS  Google Scholar 

  57. Li, W. B. & Li, J. Ferroelasticity and domain physics in two-dimensional transition metal dichalcogenide monolayers. Nat. Commun. 7, 10843 (2016). One of the earliest studies of ferroelasticity and ferroelastic transitions in 2D materials.

    Article  CAS  Google Scholar 

  58. Wang, H. & Qian, X. Two-dimensional multiferroics in monolayer group IV monochalcogenides. 2D Mater. 4, 015042 (2017).

    Article  Google Scholar 

  59. Zhou, J., Xu, H. W., Li, Y. F., Jaramillo, R. & Li, J. Opto-mechanics driven fast martensitic transition in two-dimensional materials. Nano Lett. 18, 7794–7800 (2018).

    Article  CAS  Google Scholar 

  60. Xu, H., Zhou, J., Li, Y., Jaramillo, R. & Li, J. Optomechanical control of stacking patterns of h-BN bilayer. Nano Res. 12, 2634–2639 (2019).

    Article  CAS  Google Scholar 

  61. Mishin, Y., Asta, M. & Li, J. Atomistic modeling of interfaces and their impact on microstructure and properties. Acta Mater. 58, 1117–1151 (2010).

    Article  CAS  Google Scholar 

  62. Mermin, N. D. Crystalline order in two dimensions. Phys. Rev. 176, 250–254 (1968).

    Article  Google Scholar 

  63. Splendiani, A. et al. Emerging photoluminescence in monolayer MoS2. Nano Lett. 10, 1271–1275 (2010).

    Article  CAS  Google Scholar 

  64. Mak, K. F., Lee, C., Hone, J., Shan, J. & Heinz, T. F. Atomically thin MoS2: a new direct-gap semiconductor. Phys. Rev. Lett. 105, 136805 (2010).

    Article  CAS  Google Scholar 

  65. Sohier, T., Gibertini, M., Calandra, M., Mauri, F. & Marzari, N. Breakdown of optical phonons’ splitting in two-dimensional materials. Nano Lett. 17, 3758–3763 (2017).

    Article  CAS  Google Scholar 

  66. Cudazzo, P., Tokatly, I. V. & Rubio, A. Dielectric screening in two-dimensional insulators: implications for excitonic and impurity states in graphane. Phys. Rev. B 84, 085406 (2011).

    Article  CAS  Google Scholar 

  67. Xi, X. X. et al. Strongly enhanced charge-density-wave order in monolayer NbSe2. Nat. Nanotechnol. 10, 765–769 (2015).

    Article  CAS  Google Scholar 

  68. Ye, J. T. et al. Superconducting dome in a gate-tuned band insulator. Science 338, 1193–1196 (2012).

    Article  CAS  Google Scholar 

  69. Li, L. J. et al. Controlling many-body states by the electric-field effect in a two-dimensional material. Nature 529, 185–189 (2016).

    Article  CAS  Google Scholar 

  70. Fei, Z. Y. et al. Ferroelectric switching of a two-dimensional metal. Nature 560, 336–339 (2018).

    Article  CAS  Google Scholar 

  71. Yang, Q., Wu, M. & Li, J. Origin of two-dimensional vertical ferroelectricity in WTe2 bilayer and multilayer. J. Phys. Chem. Lett. 9, 7160–7164 (2018).

    Article  CAS  Google Scholar 

  72. Feng, J., Qi, L., Huang, J. Y. & Li, J. Geometric and electronic structure of graphene bilayer edges. Phys. Rev. B 80, 165407 (2009).

    Article  CAS  Google Scholar 

  73. Kushima, A., Qian, X. F., Zhao, P., Zhang, S. L. & Li, J. Ripplocations in van der Waals layers. Nano Lett. 15, 1302–1308 (2015).

    Article  CAS  Google Scholar 

  74. Britnell, L. et al. Strong light-matter interactions in heterostructures of atomically thin films. Science 340, 1311–1314 (2013).

    Article  CAS  Google Scholar 

  75. Elias, D. C. et al. Control of graphene’s properties by reversible hydrogenation: evidence for graphane. Science 323, 610–613 (2009).

    Article  CAS  Google Scholar 

  76. Lin, Y. C., Dumcencon, D. O., Huang, Y. S. & Suenaga, K. Atomic mechanism of the semiconducting-to-metallic phase transition in single-layered MoS2. Nat. Nanotechnol. 9, 391–396 (2014).

    Article  CAS  Google Scholar 

  77. Franklin, B. Of the stilling of waves by means of oil. Philos. Trans. R. Soc. Lond. 64, 445–460 (1774).

    Google Scholar 

  78. Lord Rayleigh Measurements of the amount of oil necessary in order to check the motions of camphor upon water. Proc. R. Soc. Lond. 47, 364–367 (1890).

    Article  Google Scholar 

  79. Nair, R. R. et al. Fine structure constant defines visual transparency of graphene. Science 320, 1308–1308 (2008).

    Article  CAS  Google Scholar 

  80. Rehn, D. A., Li, Y., Pop, E. & Reed, E. J. Theoretical potential for low energy consumption phase change memory utilizing electrostatically-induced structural phase transitions in 2D materials. NPJ Comput. Mater. 4, 2 (2018).

    Article  CAS  Google Scholar 

  81. Simpson, R. E. et al. Interfacial phase-change memory. Nat. Nanotechnol. 6, 501–505 (2011).

    Article  CAS  Google Scholar 

  82. Gu, X. K., Wei, Y. J., Yin, X. B., Li, B. W. & Yang, R. G. Colloquium: Phononic thermal properties of two-dimensional materials. Rev. Mod. Phys. 90, 041002 (2018).

    Article  CAS  Google Scholar 

  83. Li, J. The mechanics and physics of defect nucleation. MRS Bull. 32, 151–159 (2007).

    Article  CAS  Google Scholar 

  84. Zhu, T. & Li, J. Ultra-strength materials. Prog. Mater. Sci. 55, 710–757 (2010).

    Article  Google Scholar 

  85. Yakobson, B. I. Mechanical relaxation and “intramolecular plasticity” in carbon nanotubes. Appl. Phys. Lett. 72, 918–920 (1998).

    Article  CAS  Google Scholar 

  86. Lee, C., Wei, X., Kysar, J. W. & Hone, J. Measurement of the elastic properties and intrinsic strength of monolayer graphene. Science 321, 385–388 (2008).

    Article  CAS  Google Scholar 

  87. Bertolazzi, S., Brivio, J. & Kis, A. Stretching and breaking of ultrathin MoS2. ACS Nano 5, 9703–9709 (2011).

    Article  CAS  Google Scholar 

  88. Li, J., Shan, Z. W. & Ma, E. Elastic strain engineering for unprecedented materials properties. MRS Bull. 39, 108–117 (2014).

    Article  CAS  Google Scholar 

  89. Song, S. et al. Room temperature semiconductor–metal transition of MoTe2 thin films engineered by strain. Nano Lett. 16, 188–193 (2015).

    Article  CAS  Google Scholar 

  90. Hou, W. et al. Strain-based room-temperature non-volatile MoTe2 ferroelectric phase change transistor. Nat. Nanotechnol. 14, 668–673 (2019).

    Article  CAS  Google Scholar 

  91. Bausch, A. R. et al. Grain boundary scars and spherical crystallography. Science 299, 1716–1718 (2003).

    Article  CAS  Google Scholar 

  92. Masel, R. I. Principles of Adsorption and Reaction on Solid Surfaces (Wiley, 1996).

  93. Geim, A. K. & Grigorieva, I. V. Van der Waals heterostructures. Nature 499, 419–425 (2013).

    Article  CAS  Google Scholar 

  94. Jones, D. A. Principles and Prevention of Corrosion 2nd edn (Prentice Hall, 1996).

  95. Dean, C. R. et al. Boron nitride substrates for high-quality graphene electronics. Nat. Nanotechnol. 5, 722–726 (2010). This work shows that hexagonal boron nitride is an excellent material for protecting the properties of 2D materials.

    Article  CAS  Google Scholar 

  96. Nine, M. J., Cole, M. A., Tran, D. N. H. & Losic, D. Graphene: a multipurpose material for protective coatings. J. Mater. Chem. A 3, 12580–12602 (2015).

    Article  CAS  Google Scholar 

  97. Su, C. et al. Waterproof molecular monolayers stabilize 2D materials. Proc. Natl Acad. Sci. USA 116, 20844–20849 (2019).

    Article  CAS  Google Scholar 

  98. Levy, N. et al. Strain-induced pseudo-magnetic fields greater than 300 tesla in graphene nanobubbles. Science 329, 544–547 (2010).

    Article  CAS  Google Scholar 

  99. Feng, J., Qian, X. F., Huang, C. W. & Li, J. Strain-engineered artificial atom as a broad-spectrum solar energy funnel. Nat. Photonics 6, 865–871 (2012).

    Article  CAS  Google Scholar 

  100. Voiry, D. et al. Enhanced catalytic activity in strained chemically exfoliated WS2 nanosheets for hydrogen evolution. Nat. Mater. 12, 850–855 (2013).

    Article  CAS  Google Scholar 

  101. Voiry, D., Mohite, A. & Chhowalla, M. Phase engineering of transition metal dichalcogenides. Chem. Soc. Rev. 44, 2702–2712 (2015).

    Article  CAS  Google Scholar 

  102. Wang, J., Wei, Y., Li, H., Huang, X. & Zhang, H. Crystal phase control in two-dimensional materials. Sci. China Chem. 61, 1227–1242 (2018).

    Article  CAS  Google Scholar 

  103. Xiao, Y., Zhou, M., Liu, J., Xu, J. & Fu, L. Phase engineering of two-dimensional transition metal dichalcogenides. Sci. China Mater. 62, 759–775 (2019).

    Article  CAS  Google Scholar 

  104. Wang, X. et al. Potential 2D materials with phase transitions: structure, synthesis, and device applications. Adv. Mater. 31, 1804682 (2019).

    Article  CAS  Google Scholar 

  105. Sokolikova, M. S. & Mattevi, C. Direct synthesis of metastable phases of 2D transition metal dichalcogenides. Chem. Soc. Rev. 49, 3952–5980 (2020).

    Article  CAS  Google Scholar 

  106. Bergeron, H., Lebedev, D. & Hersam, M. C. Polymorphism in post-dichalcogenide two-dimensional materials. Chem. Rev. 121, 2713–2775 (2021).

    Article  CAS  Google Scholar 

  107. Wilson, J. A. & Yoffe, A. D. The transition metal dichalcogenides discussion and interpretation of the observed optical, electrical and structural properties. Adv. Phys. 18, 193–335 (1969).

    Article  CAS  Google Scholar 

  108. Xia, F., Wang, H., Xiao, D., Dubey, M. & Ramasubramaniam, A. Two-dimensional material nanophotonics. Nat. Photonics 8, 899–907 (2014).

    Article  CAS  Google Scholar 

  109. Fei, Z. et al. Edge conduction in monolayer WTe2. Nat. Phys. 13, 677–682 (2017).

    Article  CAS  Google Scholar 

  110. Zheng, F. et al. On the quantum spin Hall gap of monolayer 1T′-WTe2. Adv. Mater. 28, 4845–4851 (2016).

    Article  CAS  Google Scholar 

  111. Sajadi, E. et al. Gate-induced superconductivity in a monolayer topological insulator. Science 362, 922–925 (2018).

    Article  CAS  Google Scholar 

  112. Duerloo, K.-A. N. & Reed, E. J. Structural phase transitions by design in monolayer alloys. ACS Nano 10, 289–297 (2015).

    Article  CAS  Google Scholar 

  113. Li, Y., Duerloo, K.-A. N., Wauson, K. & Reed, E. J. Structural semiconductor-to-semimetal phase transition in two-dimensional materials induced by electrostatic gating. Nat. Commun. 7, 10671 (2016).

    Article  CAS  Google Scholar 

  114. Py, M. A. & Haering, R. R. Structural destabilization induced by lithium intercalation in MoS2 and related compounds. Can. J. Phys. 61, 76–84 (1983).

    Article  CAS  Google Scholar 

  115. Gordon, R. A., Yang, D., Crozier, E. D., Jiang, D. T. & Frindt, R. F. Structures of exfoliated single layers of WS2, MoS2, and MoSe2 in aqueous suspension. Phys. Rev. B 65, 125407 (2002).

    Article  CAS  Google Scholar 

  116. Chhowalla, M. et al. The chemistry of two-dimensional layered transition metal dichalcogenide nanosheets. Nat. Chem. 5, 263–275 (2013).

    Article  Google Scholar 

  117. Wadhawan, V. K. Introduction to Ferroic Materials (Gordon & Breach, 2000).

  118. Wang, G.-Y. et al. Formation mechanism of twin domain boundary in 2D materials: The case for WTe2. Nano Res. 12, 569–573 (2019).

    Article  CAS  Google Scholar 

  119. Pedramrazi, Z. et al. Manipulating topological domain boundaries in the single-layer quantum spin Hall insulator 1T′–WSe2. Nano Lett. 19, 5634–5639 (2019).

    Article  CAS  Google Scholar 

  120. Kim, H. W. et al. Symmetry dictated grain boundary state in a two-dimensional topological insulator. Nano Lett. 20, 5837–5843 (2020).

    Article  CAS  Google Scholar 

  121. Seixas, L., Rodin, A. S., Carvalho, A. & Castro Neto, A. H. Multiferroic two-dimensional materials. Phys. Rev. Lett. 116, 206803 (2016).

    Article  CAS  Google Scholar 

  122. Dawber, M., Rabe, K. M. & Scott, J. F. Physics of thin-film ferroelectric oxides. Rev. Mod. Phys. 77, 1083–1130 (2005).

    Article  CAS  Google Scholar 

  123. Ahn, C. H., Rabe, K. M. & Triscone, J.-M. Ferroelectricity at the nanoscale: local polarization in oxide thin films and heterostructures. Science 303, 488–491 (2004).

    Article  CAS  Google Scholar 

  124. Wu, M. & Zeng, X. C. Intrinsic ferroelasticity and/or multiferroicity in two-dimensional phosphorene and phosphorene analogues. Nano Lett. 16, 3236–3241 (2016).

    Article  CAS  Google Scholar 

  125. Fei, R., Kang, W. & Yang, L. Ferroelectricity and phase transitions in monolayer group-IV monochalcogenides. Phys. Rev. Lett. 117, 097601 (2016).

    Article  CAS  Google Scholar 

  126. Hanakata, P. Z., Carvalho, A., Campbell, D. K. & Park, H. S. Polarization and valley switching in monolayer group-IV monochalcogenides. Phys. Rev. B 94, 035304 (2016).

    Article  CAS  Google Scholar 

  127. Mehboudi, M. et al. Structural phase transition and material properties of few-layer monochalcogenides. Phys. Rev. Lett. 117, 246802 (2016).

    Article  Google Scholar 

  128. Mehboudi, M. et al. Two-dimensional disorder in black phosphorus and monochalcogenide monolayers. Nano Lett. 16, 1704–1712 (2016).

    Article  CAS  Google Scholar 

  129. Zhou, Y. et al. Out-of-plane piezoelectricity and ferroelectricity in layered α-In2Se3 nanoflakes. Nano Lett. 17, 5508–5513 (2017).

    Article  CAS  Google Scholar 

  130. Cui, C. et al. Intercorrelated in-plane and out-of-plane ferroelectricity in ultrathin two-dimensional layered semiconductor In2Se3. Nano Lett. 18, 1253–1258 (2018).

    Article  CAS  Google Scholar 

  131. Xiao, J. et al. Intrinsic two-dimensional ferroelectricity with dipole locking. Phys. Rev. Lett. 120, 227601 (2018).

    Article  CAS  Google Scholar 

  132. Zheng, C. et al. Room temperature in-plane ferroelectricity in van der Waals In2Se3. Sci. Adv. 4, eaar7720 (2018).

    Article  CAS  Google Scholar 

  133. Belianinov, A. et al. CuInP2S6 room temperature layered ferroelectric. Nano Lett. 15, 3808–3814 (2015).

    Article  CAS  Google Scholar 

  134. Liu, F. et al. Room-temperature ferroelectricity in CuInP2S6 ultrathin flakes. Nat. Commun. 7, 12357 (2016).

    Article  CAS  Google Scholar 

  135. Yuan, S. et al. Room-temperature ferroelectricity in MoTe2 down to the atomic monolayer limit. Nat. Commun. 10, 1775 (2019).

    Article  CAS  Google Scholar 

  136. Shirodkar, S. N. & Waghmare, U. V. Emergence of ferroelectricity at a metal-semiconductor transition in a 1T monolayer of MoS2. Phys. Rev. Lett. 112, 157601 (2014).

    Article  CAS  Google Scholar 

  137. Soluyanov, A. A. et al. Type-II Weyl semimetals. Nature 527, 495–498 (2015).

    Article  CAS  Google Scholar 

  138. Brown, B. E. The crystal structures of WTe2 and high-temperature MoTe2. Acta Crystallogr. 20, 268–274 (1966).

    Article  CAS  Google Scholar 

  139. Cochran, W. Crystal stability and the theory of ferroelectricity. Adv. Phys. 9, 387–423 (1960).

    Article  CAS  Google Scholar 

  140. Wang, H. & Qian, X. Ferroelectric nonlinear anomalous Hall effect in few-layer WTe2. NPJ Comput. Mater. 5, 119 (2019).

    Article  CAS  Google Scholar 

  141. Herring, C. & Kittel, C. On the theory of spin waves in ferromagnetic media. Phys. Rev. 81, 869–880 (1951).

    Article  Google Scholar 

  142. Fröhlich, J. & Lieb, E. H. Existence of phase transitions for anisotropic Heisenberg models. Phys. Rev. Lett. 38, 440–442 (1977).

    Article  Google Scholar 

  143. Li, W. et al. High temperature ferromagnetism in π-conjugated two-dimensional metal–organic frameworks. Chem. Sci. 8, 2859–2867 (2017).

    Article  CAS  Google Scholar 

  144. Wang, H., Qi, J. & Qian, X. Electrically tunable high Curie temperature two-dimensional ferromagnetism in van der Waals layered crystals. Appl. Phys. Lett. 117, 083102 (2020).

    Article  CAS  Google Scholar 

  145. Jiang, Z., Wang, P., Xing, J., Jiang, X. & Zhao, J. Screening and design of novel 2D ferromagnetic materials with high Curie temperature above room temperature. ACS Appl. Mater. Interfaces 10, 39032–39039 (2018).

    Article  CAS  Google Scholar 

  146. Telford, E. J. et al. layered antiferromagnetism induces large negative magnetoresistance in the van der Waals semiconductor CrSBr. Adv. Mater. 32, 2003240 (2020).

    Article  CAS  Google Scholar 

  147. Lee, K. et al. Magnetic order and symmetry in the 2D semiconductor CrSBr. Preprint at arXiv https://arxiv.org/abs/2007.10715 (2020).

  148. Zhuang, H. L., Kent, P. R. C. & Hennig, R. G. Strong anisotropy and magnetostriction in the two-dimensional Stoner ferromagnet Fe3GeTe2. Phys. Rev. B 93, 134407 (2016).

    Article  CAS  Google Scholar 

  149. Deng, Y. et al. Gate-tunable room-temperature ferromagnetism in two-dimensional Fe3GeTe2. Nature 563, 94–99 (2018).

    Article  CAS  Google Scholar 

  150. Bogaert, K. et al. Diffusion-mediated synthesis of MoS2/WS2 lateral heterostructures. Nano Lett. 16, 5129–5134 (2016).

    Article  CAS  Google Scholar 

  151. Zhou, J. et al. A library of atomically thin metal chalcogenides. Nature 556, 355–359 (2018).

    Article  CAS  Google Scholar 

  152. Li, X. et al. Surfactant-mediated growth and patterning of atomically thin transition metal dichalcogenides. ACS Nano 6, 6570–6581 (2020).

    Article  CAS  Google Scholar 

  153. Zhu, J. et al. Argon plasma induced phase transition in monolayer MoS2. J. Am. Chem. Soc. 139, 10216–10219 (2017).

    Article  CAS  Google Scholar 

  154. Zhou, L. et al. Large-area synthesis of high-quality uniform few-layer MoTe2. J. Am. Chem. Soc. 137, 11892–11895 (2015).

    Article  CAS  Google Scholar 

  155. Liu, L. N. et al. Phase-selective synthesis of 1T′ MoS2 monolayers and heterophase bilayers. Nat. Mater. 17, 1108–1114 (2018).

    Article  CAS  Google Scholar 

  156. Rao, F. et al. Reducing the stochasticity of crystal nucleation to enable subnanosecond memory writing. Science 358, 1423–1426 (2017).

    Article  CAS  Google Scholar 

  157. Zhang, W., Mazzarello, R., Wuttig, M. & Ma, E. Designing crystallization in phase-change materials for universal memory and neuro-inspired computing. Nat. Rev. Mater. 4, 150–168 (2019).

    Article  CAS  Google Scholar 

  158. Kalikka, J. et al. Strain-engineered diffusive atomic switching in two-dimensional crystals. Nat. Commun. 7, 11983 (2016).

    Article  CAS  Google Scholar 

  159. Ding, K. et al. Phase-change heterostructure enables ultralow noise and drift for memory operation. Science 366, 210–215 (2019).

    Article  CAS  Google Scholar 

  160. Wu, J. et al. High tunnelling electroresistance in a ferroelectric van der Waals heterojunction via giant barrier height modulation. Nat. Electron. 3, 466–472 (2020).

    Article  CAS  Google Scholar 

  161. Shi, G. & Kioupakis, E. Anisotropic spin transport and strong visible-light absorbance in few-layer SnSe and GeSe. Nano Lett. 15, 6926–6931 (2015).

    Article  CAS  Google Scholar 

  162. Zhu, X. J., Li, D., Liang, X. G. & Lu, W. D. Ionic modulation and ionic coupling effects in MoS2 devices for neuromorphic computing. Nat. Mater. 18, 141–148 (2019).

    Article  CAS  Google Scholar 

  163. Zhang, X. et al. Two-dimensional MoS2-enabled flexible rectenna for Wi-Fi-band wireless energy harvesting. Nature 566, 368–372 (2019).

    Article  CAS  Google Scholar 

  164. Wang, H. & Qian, X. Ferroicity-driven nonlinear photocurrent switching in time-reversal invariant ferroic materials. Sci. Adv. 5, eaav9743 (2019).

    Article  CAS  Google Scholar 

  165. Peng, B. et al. Phase transition enhanced superior elasticity in freestanding single-crystalline multiferroic BiFeO3 membranes. Sci. Adv. 6, eaba5847 (2020).

    Article  CAS  Google Scholar 

  166. Jiang, S., Xie, H., Shan, J. & Mak, K. F. Exchange magnetostriction in two-dimensional antiferromagnets. Nat. Mater. 19, 1295–1299 (2020).

    Article  CAS  Google Scholar 

  167. Oganov, A. R., Pickard, C. J., Zhu, Q. & Needs, R. J. Structure prediction drives materials discovery. Nat. Rev. Mater. 4, 331–348 (2019).

    Article  Google Scholar 

  168. Butler, K. T., Davies, D. W., Cartwright, H., Isayev, O. & Walsh, A. Machine learning for molecular and materials science. Nature 559, 547–555 (2018).

    Article  CAS  Google Scholar 

  169. Schmidt, J., Marques, M. R. G., Botti, S. & Marques, M. A. L. Recent advances and applications of machine learning in solid-state materials science. NPJ Comput. Mater. 5, 83 (2019).

    Article  Google Scholar 

  170. Cheon, G. et al. Revealing the spectrum of unknown layered materials with superhuman predictive abilities. J. Phys. Chem. Lett. 9, 6967–6972 (2018).

    Article  CAS  Google Scholar 

  171. Oses, C., Toher, C. & Curtarolo, S. High-entropy ceramics. Nat. Rev. Mater. 5, 295–309 (2020).

    Article  CAS  Google Scholar 

  172. Souvatzis, P., Eriksson, O., Katsnelson, M. I. & Rudin, S. P. Entropy driven stabilization of energetically unstable crystal structures explained from first principles theory. Phys. Rev. Lett. 100, 095901 (2008).

    Article  CAS  Google Scholar 

  173. Lebègue, S., Björkman, T., Klintenberg, M., Nieminen, R. M. & Eriksson, O. Two-dimensional materials from data filtering and ab initio calculations. Phys. Rev. X 3, 031002 (2013).

    Google Scholar 

  174. Ashton, M., Paul, J., Sinnott, S. B. & Hennig, R. G. Topology-scaling identification of layered solids and stable exfoliated 2D materials. Phys. Rev. Lett. 118, 106101 (2017).

    Article  Google Scholar 

  175. Cheon, G. et al. Data mining for new two- and one-dimensional weakly bonded solids and lattice-commensurate heterostructures. Nano Lett. 17, 1915–1923 (2017).

    Article  CAS  Google Scholar 

  176. Mounet, N. et al. Two-dimensional materials from high-throughput computational exfoliation of experimentally known compounds. Nat. Nanotechnol. 13, 246–252 (2018).

    Article  CAS  Google Scholar 

  177. Haastrup, S. et al. The computational 2D materials database: high-throughput modeling and discovery of atomically thin crystals. 2D Mater. 5, 042002 (2018).

    Article  CAS  Google Scholar 

  178. Taheri, M. L. et al. Current status and future directions for in situ transmission electron microscopy. Ultramicroscopy 170, 86–95 (2016).

    Article  CAS  Google Scholar 

  179. Lindenberg, A. M., Johnson, S. L. & Reis, D. A. Visualization of atomic-scale motions in materials via femtosecond X-ray scattering techniques. Annu. Rev. Mater. Res. 47, 425–449 (2017).

    Article  CAS  Google Scholar 

  180. Sciaini, G. & Miller, R. J. D. Femtosecond electron diffraction: heralding the era of atomically resolved dynamics. Rep. Prog. Phys. 74, 096101 (2011).

    Article  CAS  Google Scholar 

  181. Bovensiepen, U. & Kirchmann, P. S. Elementary relaxation processes investigated by femtosecond photoelectron spectroscopy of two-dimensional materials. Laser Photonics Rev. 6, 589–606 (2012).

    Article  Google Scholar 

  182. Raschke, M. B. & Shen, Y. R. Nonlinear optical spectroscopy of solid interfaces. Curr. Opin. Solid State Mater. Sci. 8, 343–352 (2004).

    Article  CAS  Google Scholar 

  183. Danz, T., Domröse, T. & Ropers, C. Ultrafast nanoimaging of the order parameter in a structural phase transition. Science 371, 371–374 (2021).

    Article  CAS  Google Scholar 

  184. Huang, P. Y. et al. Grains and grain boundaries in single-layer graphene atomic patchwork quilts. Nature 469, 389–392 (2011).

    Article  CAS  Google Scholar 

  185. Fasolino, A., Los, J. H. & Katsnelson, M. I. Intrinsic ripples in graphene. Nat. Mater. 6, 858–861 (2007).

    Article  CAS  Google Scholar 

  186. McGilly, L. J. et al. Visualization of moiré superlattices. Nat. Nanotechnol. 15, 580–584 (2020).

    Article  CAS  Google Scholar 

  187. Kim, H.-J., Kang, S.-H., Hamada, I. & Son, Y.-W. Origins of the structural phase transitions in MoTe2 and WTe2. Phys. Rev. B 95, 180101(R) (2017).

    Article  Google Scholar 

  188. Bistritzer, R. & MacDonald, A. H. Moiré bands in twisted double-layer graphene. Proc. Natl Acad. Sci. USA 108, 12233–12237 (2011). This paper predicts the existence of strong-correlation physics in magic-angle twisted bilayer graphene.

    Article  CAS  Google Scholar 

  189. Balents, L., Dean, C. R., Efetov, D. K. & Young, A. F. Superconductivity and strong correlations in moiré flat bands. Nat. Phys. 16, 725–733 (2020).

    Article  CAS  Google Scholar 

  190. Qian, X., Wang, Y., Li, W., Lu, J. & Li, J. Modelling of stacked 2D materials and devices. 2D Mater. 2, 032003 (2015).

    Article  CAS  Google Scholar 

  191. Wang, H. & Qian, X. Electrically and magnetically switchable nonlinear photocurrent in PT-symmetric magnetic topological quantum materials. NPJ Comput. Mater. 6, 199 (2020).

    Article  CAS  Google Scholar 

  192. Salén, P. et al. Matter manipulation with extreme terahertz light: Progress in the enabling THz technology. Phys. Rep. 836–837, 1–74 (2019).

    Article  Google Scholar 

  193. Carr, S., Fang, S. & Kaxiras, E. Electronic-structure methods for twisted moiré layers. Nat. Rev. Mater. 5, 748–763 (2020).

    Article  CAS  Google Scholar 

  194. Andrei, E. Y. & MacDonald, A. H. Graphene bilayers with a twist. Nat. Mater. 19, 1265–1275 (2020).

    Article  CAS  Google Scholar 

  195. Kennes, D. M. et al. Moiré heterostructures as a condensed-matter quantum simulator. Nat. Phys. 17, 155–163 (2021).

    Article  CAS  Google Scholar 

  196. IEEE. International Roadmap for Devices and Systems: 2020 Edition (IEEE, 2020).

  197. Baxter, R. J. Eight-vertex model in lattice statistics. Phys. Rev. Lett. 26, 832–833 (1971).

    Article  CAS  Google Scholar 

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

    Article  CAS  Google Scholar 

  199. Young, A. P. Melting and the vector Coulomb gas in two dimensions. Phys. Rev. B 19, 1855–1866 (1979).

    Article  CAS  Google Scholar 

  200. Nelson, D. R. & Halperin, B. I. Dislocation-mediated melting in two dimensions. Phys. Rev. B 19, 2457–2484 (1979).

    Article  CAS  Google Scholar 

  201. Thouless, D. J., Kohmoto, M., Nightingale, M. P. & den Nijs M. Quantized Hall conductance in a two-dimensional periodic potential. Phys. Rev. Lett. 49, 405–408 (1982).

    Article  CAS  Google Scholar 

  202. Laughlin, R. B. Anomalous quantum Hall effect: An incompressible quantum fluid with fractionally charged excitations. Phys. Rev. Lett. 50, 1395–1398 (1983).

    Article  Google Scholar 

  203. Bednorz, J. G. & Müller, K. A. Possible high Tc superconductivity in the Ba–La–Cu–O system. Z. Phys. B Condens. Matter 64, 189–193 (1986).

    Article  CAS  Google Scholar 

  204. Kantor, Y. & Nelson, D. R. Crumpling transition in polymerized membranes. Phys. Rev. Lett. 58, 2774–2777 (1987).

    Article  CAS  Google Scholar 

  205. Kane, C. L. & Mele, E. J. Z(2) topological order and the quantum spin Hall effect. Phys. Rev. Lett. 95, 146802 (2005).

    Article  CAS  Google Scholar 

  206. Mayorov, A. S. et al. Micrometer-scale ballistic transport in encapsulated graphene at room temperature. Nano Lett. 11, 2396–2399 (2011).

    Article  CAS  Google Scholar 

  207. Rehn, D. A. & Reed, E. J. Memristors with distorted structures. Nat. Mater. 18, 8–9 (2019).

    Article  CAS  Google Scholar 

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Acknowledgements

J.L. acknowledges support by NSF DMR-1923976. X.Q. acknowledges support by NSF DMR-1753054. W.L. is grateful for the support by NSFC under project no. 62004172, Westlake Multidisciplinary Research Initiative Center (MRIC) under award no. 20200101 and Westlake University HPC Center. We thank the anonymous reviewers for their valuable comments and suggestions.

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Authors and Affiliations

  1. School of Engineering and Key Laboratory of 3D Micro/Nano Fabrication and Characterization of Zhejiang Province, Westlake University, Hangzhou, China

    Wenbin Li

  2. Department of Materials Science and Engineering, Texas A&M University, College Station, TX, USA

    Xiaofeng Qian

  3. Department of Nuclear Science and Engineering and Department of Materials Science and Engineering, Massachusetts Institute of Technology, Cambridge, MA, USA

    Ju Li

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J.L. conceived the framework of the Review. All authors researched data for the article, discussed the content and contributed to the writing and revising of the manuscript.

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Li, W., Qian, X. & Li, J. Phase transitions in 2D materials. Nat Rev Mater 6, 829–846 (2021). https://doi.org/10.1038/s41578-021-00304-0

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