REVIEWS Phase transitions in 2D materials Wenbin Li 1 ✉ , Xiaofeng Qian 2 and Ju Li 3 ✉ 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 transi- tions. 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. Self- organization of a large number of nuclides and discovery of the quantum Hall effect (QHE)16 and the electrons leads to the emergence of different phases of fractional quantum Hall effect (FQHE)17. The invention matter. A phase represents a certain style of organiza- of the scanning tunnelling microscope (STM)18 and the tion that can be spatially replicated ad infinitum, with atomic force microscope (AFM)19 in the 1980s enabled properties that change continuously in response to real- space imaging of surface reconstruction20,21 and of external fields, that are distinct from the other phases. the phase transformation of Langmuir monolayers22. Therefore, certain system properties are altered as the Techniques for isolating planar sheets of crystals from material undergoes a phase transition. A general charac- their bulk counterparts only became available in the teristic of a phase transition is that it either involves early 2000s6,23, paving the way for experimental stud- a discontinuity in an order parameter according to the ies of phase transitions in free- standing 2D materials. Landau paradigm of phase transitions1–3 or a change in A wide range of phase transitions have been explored in a topological invariant4,5. 2D materials, including quantum electronic phase tran- The discovery, characterization and control of dif- sitions, such as QHE24, FQHE25,26, metal–insulator ferent phases of matter is a central task in condensed transitions27, superconductivity28–30, the quantum spin matter physics and materials science. In particular, the Hall (QSH) effect31–35, the quantum anomalous Hall study of phase transitions in 2D systems has played a (QAH) effect36–38, magnetic phase transitions39–45 and crucial role in advancing our understanding of phase classical phase transitions, such as polymorphic phase transitions (Fig. 1). 2D materials6–10 are matter that can transitions46–54 and ferroic phase transitions55–59 (Fig. 1). infinitely replicate in two directions but have thickness The reduction in dimensionality from 3D to 2D leads 1 School of Engineering at the atomic level in the third direction. For example, to peculiar statistical physics (for example, melting and and Key Laboratory of 3D Micro/Nano Fabrication monolayer MoS2 has a thickness of 6.7 Å and is typically critical point behaviours), quantum physics (for exam- and Characterization of micrometres in- plane in laboratory samples produced ple, quantum confinement) and mechanics (for example, Zhejiang Province, Westlake by mechanical exfoliation6, thus, possessing an aspect out- of- plane bending and buckling), and makes University, Hangzhou, China. ratio of ~103 or more. For comparison, a typical piece of 2D systems more sensitive to the ambient chemical 2Department of Materials A4-sized paper (~100 μm × 29.7 cm × 21 cm) would have environment (for example, adsorption and corrosion), Science and Engineering, a similar aspect ratio of ~103. Although 2D↔3D/1D external fields and physical contacts. Indeed, investi- Texas A&M University, College Station, TX, USA. phase transitions are certainly interesting subjects of gating 2D materials could be regarded as the ultimate 3Department of Nuclear discussion, here, we focus on 2D→2D transitions. ‘surface science’, because all effects are happening on Science and Engineering The earliest studies of 2D phase transitions were or near the surface. From an engineering perspective, and Department of Materials mostly theoretical; for example, the exact solution this creates both opportunities and challenges for con- Science and Engineering, of the 2D Ising spin model11, the proposition of the trolling and using phase change in 2D. For example, an Massachusetts Institute Hohenberg–Mermin–Wagner theorem12,13 and the dis- optomechanical phase change59,60 is easier to induce in of Technology, Cambridge, 14,15 (Fig. 1) MA, USA. covery of the Kosterlitz–Thouless transition . In free-standing 2D materials, owing to less elastic confine- ✉e- mail: liwenbin@ the early 1980s, progress in semiconductor technology ment and strong light–matter interactions in 2D com- westlake.edu.cn; [email protected] allowed the experimental study of 2D electron systems pared with 3D bulk. However, air stability and chemical https://doi.org/10.1038/ confined at semiconductor interfaces and under intense purity become bigger issues in 2D and influence the s41578-021-00304-0 magnetic fields, which led to the ground- breaking phase- change behaviour. NATURE REVIEWS | MATERIALS VOLUME 6 | SEPTEMBER 2021 | 829 0123456789();: REVIEWS Fig. 1 | Timeline of key developments in the study of Exact solution of the 2D Theory Experiment Ising model by Onsager11 1944 2D phase transitions. AFM, atomic force microscope; FQHE, fractional quantum Hall effect; hBN, hexagonal Proof of the Hohenberg–Mermin– boron nitride; MOSFET, metal–oxide–semiconductor 1966 Wagner theorem12,13 field-effect transistor; QHE, quantum Hall effect; QSH, Proof of the absence of quantum spin Hall; STM, scanning tunnelling microscope; translational long-range order in 1968 infinite, free-standing 2D crystals62 TMD, transition- metal dichalcogenide. Exact solution of the square 1971 lattice eight-vertex model197 2D plane. Thermodynamic and kinetic features, such as inter facial segregation, pre- melting61 and glissile versus Discovery of topological 1972 phase transitions in 2D diffusive reconstruction, are analogous to phase transi- 14,15 XY spin model 1973 tions in free- standing 2D materials. Therefore, surface and interfacial science shares many features with 2D materials science and, aside from different long- range 1978 Theory of 2D elastic and electrostatic energy expressions, many melting198-200 surface/interfacial phase transitions are similar to phase 1979 transitions in 2D materials. Experimental discovery of the Experimental discovery of the In this Review, we outline unique features of phase FQHE in the 2D electron gas of a 1980 QHE in a 2D electron gas inside transitions that emerge in 2D materials and highlight semiconductor heterojunction17 16 the inversion layer of a MOSFET recent key studies of 2D material phase transitions and Invention of the STM18 1982 technological implications of 2D phase changes. We will Theory of the FQHE202 also provide an outlook to future opportunities of phase Interpretation of the QHE 201 transformations in 2D materials. using topological concepts 1983 Real-space imaging of surface reconstruction by STM20 Invention of Unique features of 2D phase transitions the AFM19 1986 Discovery of high-temperature superconductivity in cuprates203 Dimensionality (D) reduction can strongly affect inter- nal interactions and statistical physics, and, thus, the Theory of the crumpling 1987 transition of tethered surfaces204 behaviour of phase transitions. In 1968, Mermin showed that thermal fluctuations destroy the long- range dif- Experimental isolation of 2004 fraction order of infinite, free- standing 2D crystals62. graphene and other Experimental observation of the 24 Similarly, in 1D polymers, the preferred stress- free monolayer 2D materials6,23 half-integer QHE in graphene 2005 configuration at finite temperature is a ‘globule of yarn’ Theory of the 1/2 QSH effect31,205 with an end- to- end distance of ∝ N , where N is the QSH effect experimentally contour length, caused by conformational entropy. observed in HgTe quantum well32 2007 A completely unconstrained 2D material cannot main- FQHE observed in tain its flatness in a 3D space and would prefer to adopt 2009 25,26 suspended graphene the configuration of a ‘paper ball’. In contrast with 3D crystals or liquids, which can sustain static compression, hBN encapsulation for protecting 2010 properties of 2D materials and free-standing 2D crystals cannot sustain static compres- for observing unique condensed Prediction of flat-band correlation phases of matter95,206 physics in magic-angle twisted sion even at zero temperature, owing to long- wavelength 2011 bilayer graphene188 Euler-buckling- like instability, which occurs at arbitrar- Prediction of structural phase Prediction of the QSH ily small compressive stress for infinite crystals. Thus, transitions in monolayer TMDs48 2014 effect in monolayer TMDs33 1D and 2D crystals are more fragile than 3D crystals in the statistical physics sense, shown by the Hohenberg– 12,13 2015 Experimental observation of Mermin–Wagner theorem for systems with suffi- Discovery of intrinsic superconductivity in the exact 2D ciently short-range interactions in D ≤ 2. In reality, most ferromagnetism in limit in monolayer NbSe (refs28,67) 2 2D crystals are not completely free and are constrained