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.

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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 interfacial­ segregation, pre-melting​ 61 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 2D materials39.40 2016 either on the bottom by a substrate through adhesion QSH effect observed in and friction forces or at the ends, preventing thermal monolayer WTe (refs34,35) 2017 Discovery of correlated phases and 2 unconventional superconductivity fluctuations from destroying the flatness of the mate- 27,30 Electrostatic-gating-induced in twisted bilayer graphene rial. Nonetheless, out-​of-​plane flexural vulnerabilities structural phase transition realized 2018 51 are intrinsic to any 2D material and, when coupled with in monolayer MoTe2 (ref. ) Ferroelectricity in bilayer 70 external stimuli locally or globally, they can give rise to and trilayer WTe2 (ref. ) a variety of interesting behaviours. The effect of dimensionality can be understood in terms of short-​range and long-​range interactions. Short-​range effects mainly occur in the form of coor- Prior to the emergence of free-​standing 2D mate- dination number and symmetry of chemical bonding, rials, extended defects in 3D material hosts, such as whereas long-​range interactions can be much longer stacking faults, surfaces, grain boundaries and phase than the interatomic distance and include electrostatic, boundaries, have been considered 2D ‘phases’ in con- magnetostatic and elastic interactions. Both short-​range tact with 3D phase(s), on either side or both sides of the and long-​range interactions can undergo substantial

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changes going from D = 3 to D = 2. In addition, the 2D short-​range coordination and symmetry can still be nature of these materials facilitates coupling between affected. In this case, electron–phonon interactions can the system and the environment, leading to higher change through confinement-​induced modifications in susceptibility of phase stability to external stimuli. the electronic structure63,64, vibrational spectrum65 or dielectric environment66. Owing to the small thickness Short-​range interactions of 2D materials, dielectric screening normal to the layer Dimensionality reduction gives rise to the loss of coor- is limited; a 2D material in the out-​of-​plane direction dination number, causing rehybridization of valence resembles a molecule surrounded by vacuum. Therefore, electrons (for example, competition between sp3 and sp2 the electrostatic potential generated by lattice vibrations hybridization in carbonaceous materials) that can shift in 2D materials is less screened than in 3D bulk mate- the energetic order of phases and cause the emergence of rials, which increases the strength of electron–phonon new symmetries. In 2D surfaces, which we have argued interactions. Consequently, 2D materials are more sus- to be analogous to 2D materials, cutting off one half of ceptible to charge density wave and Peierls distortions67, the bulk necessitates the breaking of strong bonding lattice instabilities (Fig. 2a) that can considerably alter interactions, such as metallic, covalent or ionic bonds the short-range​ coordination and bonding symmetry. in the vertical direction, which can lead to the surface reconstruction of certain inorganic materials, such as Long-​range interactions the 7 × 7 reconstruction on the (111) surface of silicon20. Long-range​ interactions in 2D materials, such as electro­ Indeed, surface reconstruction can be considered a 2D static and elastic interactions, are also fundamentally phase transition. different from their counterparts in 3D bulk materi- If a 2D material is exfoliated from the bulk through als (Fig. 2b). The dielectric property of a suspended, the removal of weak interactions, for example, in isolated 2D material is analogous to that of a layer many-​layered 3D crystals, in which interlayer inter- of molecules, owing to weak dielectric screening in action is predominantly of the van der Waals type, the out-​of-​plane direction. In the in-​plane directions, a Short-range interactions b Long-range interactions c Spatial control + S D hν

Uniform charge density Electrostatic doping

Surface reconstruction Charge density wave Reduced mechanical constraints d Thermodynamics e Kinetics f Defects g Corrosion and passivation

2H Epoxy O2 H O O 2 β 2 Same-sign ripplocations: attract

IPCM 1T γ O2 SiO 2 Ge Si Te α 10 nm Sb Same-sign dislocations: repel

Fig. 2 | Distinct features of phase transitions in 2D materials. are shown81. Confined atomic motion results in low volume and small a | Short-range​ interactions. Dimensionality reduction causes the breaking entropy loss per volume, and, thus, low switching energy. e | Phase of chemical bonds, which can lead to 2D structural transformations, such transformation kinetics are illustrated by the 2H-to-1T​ phase transition of 76 as surface reconstruction of inorganic materials. Dimensionality monolayer MoS2 (ref. ). Intermediate phases (α, β and γ) are formed prior confinement can also cause an increase in charge density wave instability to the transformation from the 2H to the 1T phase. f | Defects, such as and Peierls distortion, which are short-range​ lattice instabilities owing to ripplocations, can form in 2D materials during phase transition73, which electron–phonon interactions. b | Long-range​ interactions. Weak dielectric attract each other when close in distance; by contrast, same-​sign screening in the out-​of-​plane direction enables electrostatic doping of dislocations in 3D repel each other. g | The atomic thickness and poor 2D materials to achieve high carrier densities. In addition, mechanical environmental stability of 2D materials require new passivation strategies constraints are reduced in 2D materials, owing to the volumetric nature of against corrosion, for example, coating with waterproof monolayers to the strain energy and the low energy cost of forming ripples. c | Spatial prevent the oxidation–dissolution cycle in corrosion. Panel d reprinted addressability allows coupling with external stimuli and the precise local from ref.81, Springer Nature Limited. Panel e adapted from ref.76, Springer control of phase transitions. d | The thermodynamics of 2D phase Nature Limited. Panel f adapted with permission from ref.73, American transitions are illustrated in interfacial phase-​change materials (IPCM). Chemical Society. Panel g reprinted with permission from ref.97, National

A transmission electron micrograph and atomistic model of (GeTe)2(Sb2Te 3)4 Academy of Sciences.

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the Coulomb potential cannot be effectively screened steel. The replacement of long-​range elastic energy by at the long-​wavelength limit either, given that most of shorter-range​ elastic bending energy73 and van der Waals the electric field lines associated with spatially separated adhesion energy fundamentally alters the energy land- charges would reside in the vacuum region and not pass scape of phase transitions in 2D crystals, as compared through the 2D material65. Therefore, the macroscopic with bulk 3D crystals, leading to faster transitions59,60 with dielectric screening in a 2D insulator is not characterized a lower nucleation energy barrier. by a simple dielectric constant tensor as in the 3D crys- tal but is intrinsically dependent on the wavevector q. Spatial control At the long-​wavelength limit, the in-​plane dielectric An important feature of 2D materials is that all atoms function of an isotropic 2D dielectric can be written as are either located on the surface or a few Ångstroms ε()qq=1+2πα ∥∥2D∣∣, where q is the in-plane​ wavevector away from the surface. Thus, the atoms in 2D materi- ∥ 66 and α2D is the polarizability of the 2D dielectric sheet . als are more exposed to the environment than in 3D At the limit of q approaching zero, the value of the die- materials. This, in conjunction with internal electronic ∥ lectric function reaches the vacuum value of unity, which structure properties, such as van Hove singularities means that the Coulomb potential becomes essentially in the electronic density of states74, leads to enhanced unscreened. coupling with external fields, such as electromagnetic The weakened dielectric screening in 2D materials waves of a certain frequency (Fig. 2c). Electric fields can has a range of consequences for phase transitions. In penetrate through 2D semiconductors and insulators, addition to the aforementioned charge density wave owing to their atomic thickness and restricted dielectric and Peierls instabilities, which can arise from enhanced screening52. Based on this, electrostatic doping can uni- electron–phonon interactions, because the thickness of formly or heterogeneously (‘charge puddles’) control the 2D materials is typically smaller than the Debye screen- carrier density of the material68, and laser and focused ing length, 2D materials can be electrostatically doped. electron beams can induce phase transitions at distinct A high carrier density of up to 1014 e cm−2 can be achieved locations50. Moreover, adsorbates can cover the surface by applying a gate voltage in the out-​of-plane​ direction68. and induce phase transformations75. The possibility of Such electrostatic doping is not possible in 3D materials, spatially controlled induction of phase transitions by because a net positive charge density ρ (e cm−3) in 3D external stimuli also allows atomic-​level visualization bulk must lead to the divergence of the cohesive energy of the phase transformation process by transmission per atom, also called 3D Coulomb explosion. In contrast, electron microscopy (TEM)76. electrostatic doping of a 2D sheet (e cm−2) in contact with Optical or electrical readouts are often sensitive a 3D electrode is energetically feasible and provides a ver- enough to locate 2D materials or to detect monolayer-​ satile tool to control carrier density and phase transitions scale changes: consider, for example, Benjamin in 2D, as long as there are compensating charges outside Franklin’s famed experiment at Clapham Common of the plane (electrical double layer). Indeed, electrostatic pond that described the swift spread of oil on water77. doping has been employed to study 2D phase transitions, Lord Rayleigh carried out a similar experiment about a including classical51 and quantum27,68,69 phase transitions. century later and calculated, for the first time, the thick- Remarkably, owing to restricted dielectric screening in ness of an oleic acid monolayer78. Monolayer graphene the out-of-​ plane​ direction, 2D metals, such as few-layer​ can also be visually detected by the naked eye because it 70,71 79 WTe 2 and graphene, can also exhibit ferroelectricity absorbs 2.3% of light — the physical basis of the Scotch or flexoelectricity72. Here, the out-​of-​plane polarity tape method of 2D sample preparation6,23. can be switched by an electric field (ferroelectricity) or generated by a strain gradient or a bending curvature72 Thermodynamics (flexoelectricity). Such macroscopic polarization is not The free energy needed to drive a phase transition is a possible in a 3D metal, because electric polarization will crucial factor for the application of phase-​change mate- be fully screened by free electrons. rials. A first-​order phase transition involves latent heat Elastic interaction, which is an important long-range​ that originates from a discontinuity in entropy. The interaction in classical phase transition theory, is funda- latent heat L is given by L = TΔS, where T is the transition mentally altered when going from D = 3 to D = 2 (ref.73). temperature and ΔS is the difference in entropy between 2D materials, such as graphene and transition-​metal higher-entropy​ and lower-entropy​ phases. For a classical dichalcogenides, exist in a 3D space and, thus, can bend solid-to-​ solid​ diffusionless phase transition, the entropy out-​of-​plane. In-​plane compression triggers buckling difference ΔS mainly arises from a variation in the vibra- instability and, therefore, only positive in-​plane stress tional, electronic and/or magnetic entropy between two (tension) can exist along any of the two principal axes phases, whereas for a phase transition that involves a of a homogeneous stress field. In addition, owing to a liquid or gas phase, a change in configurational entropy lack of constraint in the z-​direction, the elastic energy often dominates. Entropy is an extensive quantity and, penalty along a phase transformation pathway is less thus, the volume reduction associated with a dimen- significant than in 3D, in particular, if the membrane sionality change from 3D to 2D can lead to a substantial is slightly pre-​compressed59. It is known from physical decrease in latent heat. Therefore, in most cases, much metallurgy that long-range​ elastic energy often competes less energy is required to induce a readable phase change with short-​range interfacial energy in determining the in 2D materials compared with 3D materials. dominant length scale in microstructures, for example, Latent heat can be supplied either through contact the characteristic twin thickness of lath martensites in with a heat bath or by dissipative processes, such as

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Joule heating. In the general case that external work distinct defect population dynamics and inelastic relaxa- is also involved in driving a first-​order phase transi- tion mechanisms; namely, while the mechanical strength tion, the total external energy supply can be deter- of large-​volume 3D bulk materials is mainly controlled mined by the fundamental thermodynamic relation by the propagation of existing glissile defects, such as

d=UTd+SY∑i iidX , where Yi represents a generalized dis­locations and cracks, the plastic flow or fracture force and Xi represents the corresponding general- strength of 2D materials are often controlled by defect ized displacement. For example, for a 2D structural phase nucleation. For example, while there are glissile disloca- 80 transition induced by electrostatic gating , Yi and Xi take tions in 2D materials, such as the pentagon–­heptagon the form of voltage V and total charge Q, respectively. defect in graphene85, there is no equivalence of the

Both Xi and S are extensive quantities and, therefore, Frank–Read dislocation source in 3D materials. These dimensionality reduction can result in a considerable factors enable 2D materials to withstand higher elastic reduction in the external energy input. strain before irreversible strain-​energy relaxation pro- In addition to the volumetric effect, dimensional con- cesses occur, such as fracture and plasticity, as com- finement can also decrease the entropy difference per pared with 3D materials84. For example, experimentally volume. For a phase transition that involves substantial confirmed tensile elastic strain limits of graphene

configurational entropy variation, for example, a melting and MoS2 mono­layers can be as high as 20% and 10%, transition or order-​to-​disorder solid-​state transforma- respectively86,87. In contrast, the elastic strain limit of tion, such a reduction of entropy difference per volume many bulk inorganic materials is typically only ~0.2%, occurs if the 2D material is confined in a heterostructure indicating that a substantially larger strain space setup, spatially restricting out-​of-​plane atomic motion. becomes available for controlling the physical proper- Confined atomic movement reduces the phase space ties and phase transitions of 2D materials. Thus, elastic available for thermal excitation, causing entropy loss. strain engineering88 and inelastic strain engineering of Therefore, interfacial phase-​change materials81, such 2D materials are experimentally more feasible than in 3D

as GeTe/Sb2Te 3 superlattices, require considerably less bulk materials, owing to the higher tolerance of 2D mate-

switching energy than bulk Ge2Sb2Te 5 alloys, owing rials to residual tensile and shear stresses before inelas- to melting-​free switching in the confined GeTe layers, tic deformation occurs, such as plasticity, creep, damage which occurs through the local atomic displacements of or fracture. Large-​tensile-​strain-​induced phase transi- only the Ge atoms (Fig. 2d). tions have been theoretically48 and experimentally89,90 demonstrated in 2D materials. Transformation kinetics and defects 2D materials placed on curved surfaces of 3D mate- A first-​order classical phase transition that entails a dis- rials also show defect mechanics distinct from 3D continuous change in the order parameter necessarily materials. For example, in 2D crystals self-​assembled involves the nucleation and growth of a new phase. The on the surface of liquid droplets, the spatial curvature kinetics of nucleation and growth are both substantially of the droplets can lead to the free termination of grain affected by D. For example, given that a first-order​ phase boundaries in the crystal, resulting in a disclination transition involves latent heat, the thermal conductivity monopole91. The disclination monopole is energetically of 2D materials, which depends on the dimensionality82, too expensive to form in 3D bulk crystals and, there- affects the growth kinetics. Whether the 2D material is fore, grain boundaries in 3D bulk must terminate at on a 3D substrate or not can also matter. In addition, triple junctions connected to other grain boundaries, the atomic vibrational frequency, the reaction coordi- which is not necessarily the case in 2D materials with nate of unit processes and the energy barrier for atomic 3D curvature. rearrangements control the transformation kinetics and depend on dimensionality. Phase boundaries and domain Corrosion and passivation walls in 2D materials are quasi-1D objects, in contrast Environmental stability is crucial for the practical usage with the 2D nature of phase and domain boundaries in of 2D materials. Chemical complexity and thermochem- bulk materials. In particular, the great reduction of elastic ical stability issues are already well known for grain energy constraints in 2D materials facilitates displacive boundaries and surfaces, as reflected by the Langmuir– phase transitions with glissile transformation interfaces. McLean and Fowler–Guggenheim isotherms92. Generally For example, an in situ TEM study of the phase transition speaking, if one regards surfaces and grain boundaries as

between two structural polymorphs of monolayer MoS2 2D phases (embedded in a 3D phase), they have differ- showed that the transformation between the semicon- ent equilibrium chemistries, as exemplified by interfacial ducting (2H) and metallic (1T) phases involves the ini- segregation and the Gibbs adsorption isotherm, and, also, tial formation of an intermediate phase and subsequent thermochemical or electrochemical stability windows gliding of atomic planes of sulfur and molybdenum different from the 3D host phase; thus, they can undergo within a single layer76 (Fig. 2e), which has very little elastic phase transitions even when the 3D host does not, when energy penalty, especially if the 2D membrane is slightly an intensive thermodynamic variable (for example, pre-​compressed59, that is, given some ‘slack’. temperature T, stress σ, voltage U) is varied. Corrosion, Defects are the essential facilitators and by-​products which is the degradation of materials in a chemical of phase transitions, and can also serve as preferred environment, could be considered a phase transition. nucleation sites for new phases. In 2D materials, the Many 2D crystals corrode in air, and, with the excep­ physics and mechanics of defect nucleation and propa­ tion of graphene, almost all metallic 2D materials gation are different than in 3D systems83,84, leading to have air stability problems93, even at room temperature.

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For many 3D materials, the air stability problem is cir- with layered structures10,101–106. Compared with oxygen cumvented by the formation of a surface passivation layer; and most halogens (F, Cl, Br), chalcogen elements for example, a 2–5-​nm stable layer of alumina that pro- (S, Se and Te) have a relatively small electronegativity tects the material is formed if aluminium is exposed to the and, thus, in many chalcogenides, ionic and covalent air. Here, passivation layers would only make up a small bonding compete, which leads to the generation of fraction of the otherwise unreacted bulk material. By con- structural polymorphs with different bonding configu- trast, the thickness of 2D materials is comparable or even rations that are close in energy. Therefore, perturbations smaller than that of passivation layers, making their pas- induced by weak external stimuli can drive polymorphic sivation challenging. The corrosion of materials depends transitions in these materials. The most widely studied

on the availability of oxygen (O2) and water (H2O) or 2D materials exhibiting structural phase transitions are

hydrogen (H2). By changing the partial pressure of O2 group 6 transition-​metal dichalcogenide monolayers

or H2, the redox potential and chemical transformation with the chemical formula MX2, where M stands for Mo 94 can be controlled, illustrated in the Pourbaix diagram , or W and X stands for S, Se or Te. Monolayer MX2 mate- which is a chemical or electrochemical phase diagram. rials have three well-​known structural polymorphs46,107, A boundary line in the Pourbaix diagram corresponds that is, 2H, 1T and 1T′ (Fig. 3a). The 2H phase has a to a chemical transformation induced by the environment trigonal prismatic coordination pattern, whereas the and the redox potential. Most 2D materials cannot form coordination patterns in the 1T and 1T′ phases are octa- a natural passivation layer from their own reaction prod- hedral and distorted octahedral, respectively. Monolayer

ucts and, therefore, strategies are required to restrict the MX2 in the semiconducting 2H phase has an optical (ref.108) contact of the material with O2 and H2O and to prevent bandgap in the range of 1.0–2.5 eV . The 1T the oxidation–dissolution cycle of corrosion. For exam- phase is metallic but unstable in isolation and subject ple, environmentally fragile 2D materials can be covered to Peierls distortion48,49. The 1T phase spontaneously with more robust materials, such as graphene or hexa­ transforms into the 1T′ phase through the distortion of gonal boron nitride95,96, or coated with water-​repelling octahedral coordination. The 1T′ phase of monolayer 97 33 molecular monolayers, such as linear alkylamines . MX2 was first theoretically predicted and then exper- imentally confirmed34,35,109 to be a QSH insulator with a New phase engineering concepts sizeable bandgap on the order of 0.1 eV (refs33,49,110). The The unique features of 2D phase transitions have led 1 × 2 Peierls reconstruction causes the metal-dominated​ to new concepts for engineering the phases and prop- d-band,​ which is typically the electron donor, to become erties of 2D materials. For example, the possibility of lower in energy than the chalcogen-dominated​ p-​band precise spatial addressability (as 2D locating is much around the Γ-point,​ causing a topological band inversion easier than 3D locating), strong coupling with light and and ‘tying the knot’ in the electronic band structure in the propensity for displacive phase transitions enable the Brillouin zone. This gives a perfect edge conduc­ 2 opto­mechanical switching. Here, a laser beam is used to tance of e /h = 1/25.813 kΩ at T < 100 K for 1T′-​WTe 2 induce ultrafast, diffusionless, order-to-​ order​ phase tran- monolayer35 with magnetic field dependence, and, com- sitions in 2D materials with degenerate ground states59. bined with the fact that it is also a 2D superconductor (ref.111) The large tensile elastic strain limit of 2D materials at Tc ≈ 0.7 K , gives rise to the prospect of using it allows the imposition of a large elastic strain tensor for topological quantum computing. for tuning the electrical98, optical99 and catalytic100 pro­ Theoretical calculations based on density func- perties of 2D materials, and for controlling their phase tional theory (DFT) indicate that the 2H phase is the 88 transitions . 2D materials cannot sustain compressive ground-​state phase of all monolayer MX2, except for 48 strain and they have less constraints for structural relax- WTe 2, for which the 1T′ phase has the lowest energy ation in the layer-​normal direction, as compared with (Fig. 3b). The energy differences between the 2H and

3D materials. Therefore, compressive strain can lead to 1T′ phases decrease in the order of MS2→MSe2→MTe 2. 73 (Fig. 2f) the formation of ripplocations , which are line For MoS2, the DFT-​computed energy of the 1T′ phase defects that play an important role in the deformation is ~0.5 eV per formula unit higher than that of the 2H

of layered materials. Furthermore, the atomic-​level phase, whereas for MoTe2, the DFT-​computed energy thickness of 2D materials and their weak environ­mental is only 43 meV per formula unit higher. Thus, chem- stability have led to the development of new protection ical processes are required for the transition between

strategies, such as coating with molecular layers on the 2H and 1T′ phases of MoS2. By contrast, for MoTe2, the 2D materials97 (Fig. 2g). H-​to-​T′ transition can be induced by non-​chemical factors, including temperature49,112, tensile strain48,89,90, 2D phase transitions laser irradiation50, electrostatic doping51,113 and electric A variety of 2D phase transitions have been investigated fields52. thus far. Here, we discuss notable examples, illustrat-

ing the richness of phase transformation behaviour in Chemically induced transition. The transition of MoS2 2D materials. from the 2H phase to the 1T or 1T′ phase occurs through the intercalation of alkali metals107,114,115 by Polymorphic phase transitions charge transfer from the s orbitals of alkali metals to the The most prominent examples of 2D materials discov- d orbitals of the transition-​metal atoms. The increase ered so far that exhibit polymorphic phase transitions in in d-​orbital filling causes the stability of the 1T or 1T′ near-ambient​ conditions are derived from chalcogenides phase to be higher than that of the 2H phase beyond

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a b 2H-MX2 1T-MX2 1T′-MX2 X1 )

2 0.5 M

X2

(eV per MX 0.25 H U

–

T ′ U y WTe 0 2 MoS2 WS2 MoSe2 WSe2 MoTe2 x c Chemical d Thermal e Strain T (K) T (K)

MoS2 1,100 1,000 1T 2H 1T 1T′-MoTe2 900

750 MoTe Mixed 2 650

500 2H-MoTe2

1 μm 10 μm SiO2 Te deficient 66.7 Te excessive Te (%) f Laser irradiation g Electrostatic gating h Electric field Ionic liquid (DEME-TFSI) Top gate

MoTe2 MoTe2 2H 2H 2H V d 1T′ 10 nm

1T′ 2H 2Hd

2H Ground

5 Å 5 Å

2 μm MoTe2 Before forming Afer forming

Fig. 3 | Polymorphic transitions in 2D transition-metal dichalcogenides. inverse piezoelectric effect. f | Laser-​induced patterning of MoTe2 few a | Atomistic structures of MX2 monolayers. M represents (Mo, W) and X layers from the 2H into the 1T′ phase. g | Schematic of an ionic liquid represents (S, Se, Te). Three structural polymorphs, that is, 2H, 1T and 1T′ field-​effect transistor, showing the electrostatic-​doping-​driven phase phases, are shown. The red rectangles outline the unit cells. b | Energy transition of a 2H MoTe2 monolayer to the 1T′ phase. DEME-​TFSI, differences (eV per MX ) between the 1T and 2H phases (U U ) are shown diethylmethyl(2-​methoxyethyl)ammonium bis(trifluoromethylsulfonyl) 2 ′ T′ − H for different MX2 monolayers, computed by density functional theory. imide. h | Vertical-electric-​ field-​ induced​ formation of a conducting filament 33 c | Chemically driven polymorphic transition of MoS2. The electrostatic force with 2Hd phase in 2H-​MoTe2. Panel a reprinted with permission from ref. , microscopy phase image shows the local conversion of a MoS2 nanosheet American Association for the Advancement of Science. Panel b reprinted from the 2H phase into the 1T phase through chemical patterning using with permission from ref.112, American Chemical Society. Panel c adapted 47 49 organolithium. d | Thermally driven polymorphic transition of MoTe2. from ref. , Springer Nature Limited. Panel d adapted from ref. , Springer Tellurium deficiency decreases the thermal transition temperature of Nature Limited. Panel e adapted from ref.90, Springer Nature Limited. 50 MoTe2 from the 2H to the 1T′ phase. e | Strain-driven​ transition of MoTe2. The Panel f reprinted with permission from ref. , American Association for the 51 optical micrograph shows a MoTe2 flake on a ferroelectric substrate, which Advancement of Science. Panel g reprinted from ref. , Springer Nature 52,207 can impose electric-​field-​induced strain on MoTe2 flakes, owing to the Limited. Panel h reprinted from ref. , Springer Nature Limited.

a certain doping threshold. This phenomenon can be and semiconducting regions on monolayer MoS2 by understood in terms of crystal field theory10,101,116. An area-​selective phase transformation47 (Fig. 3c). The incomplete doping-​induced phase transition in mono­ metallic 1T region can serve as the low-​resistance con-

layer MoS2 can give rise to the coexistence of 2H, 1T tact for MoS2 transistors, leading to improved device and 1T′ phases with coherent phase boundaries46. The performance, including high drive currents, high elec-

2H phase of MoS2 is semiconducting, whereas the 1T tron mobility, low subthreshold swing values and large phase is metallic, motivating the patterning of metallic on/off ratios47.

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Thermally driven transition. Compared with MoS2, is sandwiched between a MX2 monolayer and a metal

the 2H and 1T′ phases of MoTe2 have a smaller energy plate, a gate voltage of several volts can drive a 2H-to-1T​ ′

difference, enabling a wider range of external stimuli phase transition of monolayer MoTe2, as shown by DFT-​ to induce the 2H-​to-1T′ phase transition. Temperature based theoretical analysis80,113. Electrostatic-​doping-​

alone can drive the phase transition of MoTe2 from the induced phase transition was further experimentally

2H phase to the 1T′ phase, owing to the higher vibra- demonstrated in monolayer MoTe2 using ionic liquid as tional and electronic entropy of the 1T′ phase as com- the dielectric in a field-​effect-​transistor configuration51 pared with the 2H phase49,112. The transition temperature (Fig. 3g); a gate voltage of ~4 V fully converted the 2H

in bulk MoTe2, which depends on the deficiency or phase into the 1T′ phase. excess of Te, is 500–820 °C, with Te deficiencies caus- ing lower transition temperatures49 (Fig. 3d). Theoretical Electric-field-​ driven​ transition. In vertical devices based

calculations indicate that the transition temperature dif- on MoTe2 and Mo1−xWxTe 2 thin films, an electric field

ference between bulk and monolayer MoTe2 is modest applied across the film thickness direction can induce

(<20%), owing to weak phonon dispersion along the the transition of MX2 from the 2H phase into a dis- 112 out-of-​ plane​ direction . By alloying MoTe2 with WTe 2, torted transient structure, 2Hd, in which the monolayer the 2H-to-1T​ ′ phase transition temperature can be sub- structure is distinct from the three known phases of 112 (ref.52) (Fig. 3h) stantially decreased , because the 1T′ phase is the stable MX2 . The exact atomic configuration

phase of WTe2 at ambient conditions. of monolayers in the 2Hd phase has not yet been fully resolved; however, experimental evidence52 suggests that

Strain-​driven transition. Tensile-​strain-​induced tran- 2Hd monolayers have a transitional structure, between

sitions between the 2H and 1T′ phases of MoTe2 and 2H and 1T′. As a side remark, a strong enough verti- 48 other MX2 monolayers have been theoretically cal electric field can also cause topological-​insulator to and experimentally investigated89,90. The driving force normal-​insulator transition within the same structural for strain-induced​ phase transitions originates from the polymorph33, an extremely rapid (femtosecond level)

different unit-cell​ dimensions of the 2H and 1T′ phases, transition in the quantum Z2 invariant for the electronic allowing the system to minimize the thermodynamic structure. potential by transforming into a phase that reduces the elastic strain energy. The critical strain value needed Ferroic phase transitions to drive the 2H-​to-1T′ phase transition is expected to Ferroics possess two or more orientation states (domain depend on the mechanical boundary conditions48. variants), which are degenerate in free energy and can be 117 Experimentally, a phase transition in MoTe2 thin films switched by an external field . Ferroics can be catego- has been demonstrated at room temperature with a rized into four types, based on the properties associated 0.2% in-plane​ biaxial strain89. This level of strain can be with the orientation states, that is, ferroelectrics, ferro- generated by mechanical deformation of a suspended magnets, ferroelastics and ferrotoroidics. Ferroics have 2D material using an AFM tip89 or through the inverse been extensively studied in bulk form. Ferroelectrics piezoelectric effect of a ferroelectric, to which the 2D show spontaneous electric polarization, which can be material is clamped90 (Fig. 3e). switched by an electric field; ferromagnets show spon- taneous magnetization, which is switchable by a mag- Laser-​driven transition. Laser irradiation can cause the netic field; ferroelastics possess domain variants with

irreversible transition of a multilayer MoTe2 in the 2H spontaneous stress-​free strain, which can be switched phase to the 1T′ phase (Fig. 3f), owing to the generation by applying stress; and ferrotoroidics possess inter- of Te vacancies50. DFT calculations showed that the nal chiral order. Ferroic materials are typically formed formation of 3% Te vacancies alters the relative stabi­ through ferroic phase transitions characterized by the lity between the 2H and 1T′ phases. This mechanism is loss of point-​group symmetry operations, for exam- consistent with the reduced 2H-​to-1T′ thermal phase ple, by spatial inversion in the case of ferroelectricity, 49 transition temperature in MoTe2 with a Te deficiency . rotational symmetry in the case of ferroelasticity or Laser-​induced phase transition enables the local pat- time-reversal​ symmetry in the case of ferromagnetism117.

terning of metallic 1T′ regions in 2H-​MoTe2 multilay- A material is multiferroic if more than one ferroic order ers, akin to phase patterning using chemical methods is present. (ref.47) in MoS2 . The metallic 1T′ phase forms an ohmic homojunction with the semiconducting 2H phase, Ferroelastic transition. The high elastic strain limit

substantially increasing the carrier mobility of MoTe2 and the abundance of structures with low symmetry transistors. render 2D materials promising candidates for dis- tinct mechanical responses related to ferroelasticity. Electrostatic-​doping-​driven transition. Electrostatic In group 6 transition-​metal dichalcogenide monolay- doping through the application of a gate voltage can ers, the 1T-​to-1T′ phase transition was theoretically generate­ a carrier density of up to 1014 e cm−2 in mon- predicted to be a ferroelastic phase transition accom- (ref.68) 57 olayer MX2 , corresponding to ~0.1 e per for- panied by spontaneous hydrostatic and shear strains , mula unit. This feature has motivated the study of which has been supported experimentally118. The three electrostatic-​doping-​induced structural phase tran- symmetry-equivalent​ directions of structural distortion

sitions in MX2 monolayers. In an electrostatic gating lead to three orientation variants with distinct unit-​cell device configuration, in which an appropriate dielectric dimensions. Thus, transformation strains (also called

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stress-​free strains) of a variant can couple to the ener- material is at the monolayer level121. The low-temperature​ getics of the system, causing the transformation from ferroelastic phase of α-​SnO has an orthorhombic sym- one orientation variant to another. DFT calculations metry with two equivalent orientation states. The degen- suggested that a tensile strain of a few percent is suffi- erate structural ground states can be energetically biased 59 cient to switch monolayer 1T′-​WTe 2 from one orienta- when illuminated with a linearly polarized laser pulse . tion domain to another. Strain energy minimization can For example, when the system is subjected to an alternat- also lead to the coexistence of different domains and the ing electric field with a particular polarization direction, stable formation of domain or phase boundaries (Fig. 4a). the anisotropic dielectric response of the low-symmetry​ 33 Monolayer 1T′-MX​ 2 are QSH insulators and, therefore, ferroelastic phase will lead to a non-​degenerate free their phase boundaries possess distinct electronic trans- energy landscape along the reaction coordinate of the port properties, owing to the bulk-edge​ correspondence phase transformation, which is similar to optical tweez- in topologically non-trivial​ systems119,120. ing of dielectric microbeads, but along the generalized First-​principles calculations have also shown that reaction coordinate of the phase transformation instead α-​SnO becomes ferroelastic if the thickness of the of the x–y position of a bead. Phase-​change materials

a Ferroelasticity (WTe2) b Ferroelectricity (SnTe)

[001] 1 UC SnTe Sn Graphene Te [100] [010] 0 8 Height (Å) 2 nm

aL2 a a a R1 R2 L1 P 0 [010] 0 1 UC SnTe [100]

50 nm Graphene 1 nm Δα Δα Domain wall

c Ferromagnetism (Cr2Ge2Te6) d Ferromagnetism (CrI3)

75 10 B = 0.075 T I 0 60 Cr –10 –H +H

ad) 1L 45 * (K) (mr c K T

θ 50 a 30 Cr b 0 Experiment Ge Theory –50 Te 15 2L 1 2 3 4 5 Bulk –1.0 –0.5 0.0 0.5 1.0

Number of layers μ0H (T)

Fig. 4 | Ferroic phase transitions in 2D materials. a | Symmetry-equivalent​ Cr2Ge2Te 6 and the layer-​dependent ferromagnetic transition temperature orientation states and ferroelasticity in monolayer 1T′-​WTe2. The under a perpendicular magnetic field of 0.075 T are shown, obtained from three orientation variants have slightly different spontaneous strains with experimental measurements (blue squares) and theoretical calculations respect to the parental 1T phase, which allows strain-​induced switching (orange spheres). d | Ferromagnetism in atomically thin CrI3. The crystal from one orientation to another. The atomistic model shows domain structure of a monolayer CrI3 and the Kerr rotation angles (θK) of monolayer boundaries formed between two orientation variants. b | Ferroelectricity in (1L) and bilayer (2L) CrI3 as a function of the perpendicular magnetic atomically thin SnTe. Schematic of the crystal structure of SnTe and SnTe field (μ0H) are shown, providing evidence of magnetic ordering. Insets thin films is shown with a thickness of one unit cell (UC). Lattice distortion schematically show the magnetic ground states of the systems under and atomic displacements are illustrated in the ferroelectric phase. Two symmetry-​ different field strengths. Panel a reprinted from ref.57, CC BY 4.0 (https:// equivalent distortion directions lead to two variants of ferroelectric creativecommons.org/licenses/by/4.0/). Panel b reprinted with permission domains separated by domain walls, as shown in the scanning tunnelling from ref.55, American Association for the Advancement of Science. Panel c microscope image of atomically thin SnTe, coloured in purple. reprinted from ref.40, Springer Nature Limited. Panel d adapted from ref.39, c | Ferromagnetism in Cr2Ge2Te 6 atomic layers. The crystal structure of Springer Nature Limited.

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have been proposed to operate on the basis of such the system141–143. Furthermore, finite size effects can sta- optomechanically driven 2D martensitic transitions59,60, bilize phase transitions in 2D, including a ferromagnetic which have multiple advantages compared with tradi- transition, because the divergence of fluctuations in 2D tional, thermally driven phase-​change systems (such is only logarithmic with sample size and, thus, a slow as Ge-​Sb-​Te alloys), including faster transformation divergence62. Ferromagnetism has been experimentally kinetics, reduced energy dissipation and more robust observed in a range of 2D materials41–45, including semi- (ref.40) (ref.39) resistance against functional fatigue. conducting Cr2Ge2Te 6 , CrI3 , CrXBr (X = S, 144–147 (refs70,148,149) (Fig. 4c,d) Se) and metallic Fe3GeTe 2 . Ferroelectric transition. Ferroelectricity in thin-​film perovskite materials has been intensively studied122; High-​temperature diffusive phase changes however, in ferroelectrics with out-​of-​plane polariza- In diffusive transformations, changes in labelled atomic tion, the ferroelectric order disappears if the film thick- registries are non-​deterministic, and the macroscopic ness is below a critical value, owing to the effects of the order parameters of the new phase or domain do not depolarization field and surface reconstruction122,123. By reveal detailed atom-to-​ atom​ correspondences between contrast, in-​plane polarization is less susceptible to the the old and new phases, because changes in the regis- thickness-​dependent depolarization effect, and, thus, try are caused by multiple randomized atomic hops. ferroelectric order may remain stable in 2D. Indeed, By contrast, in an ideal displacive transformation, the robust in-​plane ferroelectricity has been experimentally nearest-​neighbour relation of an atom either remains realized in atomic-​thick SnTe, with a ferroelectric tran- unchanged or changes in a deterministic way within a sition temperature of 270 K (ref.55) (Fig. 4b). Ferroic phase domain variant. Displacive transformations are often transitions have also been theoretically investigated in driven by a strong directional field, for example, stress, group IV monochalcogenide MX (M = Ge, Sn; X = S, Se), an electric field or a magnetic field. Most ferroelastic which are closely related to SnTe (refs58,124–128). MX and ferroelectric transitions, which involve the loss of mono­layers can further be ferroelectric and ferroelastic rotational symmetry or spatial inversion symmetry, are at the same time, making them multiferroic58,124. displacive transformations. The kinetics of displacive Ferroelectricity has also been experimentally transformations are characterized by a threshold-​type

demonstrated in other 2D systems, including In2Se3 behaviour of the domain-​growth speed v with respect to (refs56,129–132) (refs133,134) , CuInP2S6 , monolayer MoTe2 the thermodynamic driving force F; the nonlinear v(F) is with distorted 1T phase135,136, as well as bilayers and nearly zero below a certain threshold, but substantially (ref.70) trilayers of WTe2 . Notably, 2D α-In2Se3 pos- increases above a threshold Fthresh, and then saturates at sesses both out-of-plane and in-plane ferroelectric the phonon group velocity. The growth speed of a dis- orders, and the out-of-plane polarization is resistant to placive phase-​change domain thus has to be fitted by a n the depolarization field owing to the locking between highly nonlinear function v ∝ (F/Fthresh) , where n can be out-of-plane dipoles and in-plane lattice asymme- as large as 20. In comparison, diffusive transformations try56,131. Furthermore, out-​of-​plane ferroelectricity can have a more linear-​response-​type growth velocity law be present in 2D semimetals, for example, in few-​layer v(F), where n is 1 or close to 1, but is often much more

WTe 2, because dielectric screening in the layer-​normal temperature-sensitive.​ direction is suppressed in a 2D system. Remarkably, Diffusive motion is usually thermally activated ultrafast symmetry switching behaviour was observed and, therefore, more prevalent at high temperatures, at (ref.53) 137 in 3D bulk WTe2 , a type II Weyl semimetal . In which atomic defects have higher concentration and also

contrast with monolayer 1T′-WTe​ 2, which is centrosym- become more labile, allowing the system to fully sample

metric, multilayer and bulk WTe2 have an orthorhom- the configurational space (entropy), which results in bic structure with distorted octahedral coordination and an optimal organization (phase) and, thus, approach-

broken inversion symmetry (the Td phase, space group ing the equilibrium phase diagram. By changing the 138 Pmn21) . Upon electric gating along the layer-​normal chemical precursors during chemical vapour deposi-

direction, multilayer WTe2 shows ferroelectric switch- tion, 2D [Mo,W]S2 forms either a two-phase​ MoS2/WS2 ing with a butterfly-​shaped conductance curve54,70. heterostructure with sharp phase boundaries at 650 °C

Different from local atomic-​movement-​induced ferro­ or a single-​phase random solid-​solution MoxW1−xS2 at electric transition139 (for example, through breaking and ≥680 °C (ref.150) (Fig. 5a). Compared with lattice diffusion switching of local W–W bonds or by local distortion in 3D crystals, diffusion in 2D crystals is easier because and rotation of W–Te bonds), low-energy​ interlayer glid- surface diffusivity is commonly acknowledged to be ing is likely responsible for the switching behaviour in much faster than bulk diffusivity. The phase-​separated (refs71,140) multilayer and bulk WTe2 . MoS2/WS2 heterostructure can be applied in optoelec-

tronics and the solid-​solution MoxW1−xS2 alloy phase Ferromagnetic transition. A consequence of the can be used to tune the relative phase stabilities of dif- Hohenberg–Mermin–Wagner theorem12,13 is that long-​ ferent polymorphs (2H, 1T and 1T′) by changing the range ferromagnetism cannot exist at finite temperature Mo/W ratio. Generally speaking, at high temperatures, in 2D, if the spin Hamiltonian has a continuous symmetry it is important to probe and precisely navigate the with sufficient short-​range interactions13, as ample equilibrium temperature-composition​ phase diagram. gapless spin waves will destroy the ferromagnetic The size, morphology and defect content of 2D mate- state. However, ferromagnetism can be stabilized at rials not only depend on the composition but also on finite temperature if magnetic anisotropy is present in the growth conditions (Fig. 5b). For example, large-​area

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a Phase mixing and separation c Phase-selective growth Pure 2H 800 Stage III-L 1T′ 1T′/2H bilayer MoS2 /WS2

W S Mo S 650°C 750 1T′ and 2H mixture

Stage III-H 1T′ Mo W S 1-x x 2 700 Temperature (°C) Temperature Stage I Stage II ≥680 °C 2H

WS2 WS2 /MoS2 1,100 °C 650 b Synthesis of 2D chalcogenides using CVD 0 2 4 6 8 10 12 14

H2 concentration (%) d 2D-templated phase change Metal precursor Chalcogen precursor TiN TiN Evaporate Te Sb Te High mass flux Low mass flux PCM PCH Void Sb SiO Oxygen Metal Chalcogen SiO 2 2 W W SiO2 SiO2 Route I Route II Route III Route IV

Low growth rate High growth rate Low growth rate High growth rate Sb Te 30 2 3

20 TiTe 2 10

Vertical direction (Å) direction Vertical Sb Te 0 2 3 0 15 30 45 1,300 K 30 ps 1,300 K 65 ps 1,300 K 100 ps D (×10–10 m2 s–1) Grain v boundary 40 μm 0.2 mm 10 μm 50 μm

Fig. 5 | 2D or 2D-templated diffusive phase transitions. a | Chemical H2 concentration. d | 2D-​templated diffusive phase transition in a TiTe2/ vapour deposition (CVD) growth of a phase-​separated MoS2/WS2 Sb2Te 3 phase-change​ heterostructure (PCH). The 2D TiTe2 layers, which have heterostructure and solid-solution​ MoxW1−xS2 alloy. Compositional mixing a lower diffusion coefficient (Dv) than the Sb2Te 3 layers, block the and segregation are favoured at high and low growth temperatures, electrical-field-​ assisted​ transport of charged species in the Sb2Te 3 diffusive respectively. b | Synthesis of 2D transition-metal​ chalcogenides by CVD. The switching layers, leading to less noise and drift for memory operation than morphology and defect content of 2D transition-​metal chalcogenides traditional phase-​change memory (PCM) materials. Panel a adapted with depend on the growth kinetics, including mass flux of metal precursors and permission from ref.150, American Chemical Society. Panel b adapted from growth rate. c | Phase diagram for the growth of the 1T′ and 2H phases of a ref.151, Springer Nature Limited. Panel c reprinted from ref.155, Springer 159 MoS2 monolayer using K2MoS4 as the growth precursor. Controlled growth Nature Limited. Panel d reprinted with permission from ref. , American of 1T′ and 2H phases can be realized by varying the growth temperature and Association for the Advancement of Science.

growth of 2D metal chalcogenides can be achieved by the basis for information storage in CDs and DVDs, using molten salt as a growth medium151, which reduces as well as for the newest generation of non-​volatile the melting point of metal-​ion-​bearing precursors solid-​state drives. For example, sub-​nanosecond writ- 152 and allows passivation of different growth edges . ing has been achieved with Sc0.2Sb2Te 3 as the active Moreover, under out-​of-​thermal-​equilibrium condi- crystalline-​to-​amorphous phase-​change material156. tions, for example, under external irradiation (photons, However, several challenges remain to be addressed, electrons), electrical current or plasma treatment, phase including high-​temperature-​induced volatility and changes can occur in a manner that does not abide by the resistance-level​ drifting157, which will require a thorough equilibrium phase diagram153. In addition, conditions understanding and fine control of the ionic motion dur- can be designed to directly grow thermodynamically ing device operation. Owing to their atomic thickness, metastable phases105,154,155 (Fig. 5c). 2D active materials have distinct thermal conduction 2D and 2D-​templated diffusive phase transfor- characteristics and phase transformation kinetics, fea- mations have played a key role in the development of turing less elastic energy constraints, facile diffusion phase-change​ memory (PCM) materials. PCM provided kinetics and sensitive coupling to external conditions, as

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a +/– – Au (A) Au (B) 1T′ 1T′ 2H Li Mo S

SiO2 + Si b c 2 Wi-Fi band I Pd Au radiation Antenna t Wi-Fi band 1 μm

I 1T/1T ′ MoS radiation I Flexible rectifier – – t t e e – 2H-to-1T e 2 G MoS G Antenna Pd Au Load phase junction (anode) (cathode) Load

2H MoS2 1T/1T′ MoS2 I

Self-aligned MoS2 phase junction t

2 Ωc (Å ) d Ferroelectric transition in trilayer WTe e Trilayer 2 2,400 π/4b 200 D Td,↓ –iFE (Cs) PE (C ) +iFE (Cs) ky 2h 2,100 Γ G ( μ S) 1,800 –π/4b

2 0 ) ) 30 –1 II, ω π/4b T V 0 d,↑ / ( V –3 k I y Γ ⊥ ,2 ω

(10 –30 D V – /4b –200 –0.4 –0.2 0 0.2 0.4 π –π/2a kx –π/2a –1 E⊥ (Vnm ) WTe 2 V –d –P d = 0 P = 0 +d +P t x z x z x z Graphite hBN L V j Pz d x j C Pt y z x C L jy j hBN x y Graphite Pz –iFE Ferroelectric transition +iFE

Odd-layer WTe2 f g

AA′ AB′ P Laser FE pulse 1

P Ferroelastic SP membrane

P

FE2

compared with 3D bulk materials. These characteristics of Ge and Te atoms within 5-​Å-​thick GeTe 2D crystal can be exploited to improve the temperature-driven​ read, layers can be modulated by the immobile and strained 158 write and storage performance of PCM devices, increas- Sb2Te 3 2D crystal layer . The strained Sb2Te 3 layer ing speed, reducing energy consumption and increasing affects the quenching-​to-​amorphous and crystallization storage density. For example, in a PCM device con- kinetics of the GeTe layer in the van der Waals hetero-

structed from a 2D Sb2Te 3-GeTe​ superlattice, the diffusion structure, leading to increased atomic diffusivity in the

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Fig. 6 | New device applications of 2D phase-change materials. a | Schematic of the ◀ metallic 1T′ phases of MoTe2 can also be fabricated reversible 2H-​to-1T′ phase transition of LixMoS2 films through electric-field-​ controlled​ by laser-​induced phase transition, which causes the migration of Li+ ions. An increase in Li+ ion concentration causes the transformation of 2H-to-1T​ ′ transition of MoTe as a result of the creation the 2H phase into the 1T phase, and vice versa. Such reversible local phase transitions 2 ′ of Te vacancies50. impart electronic devices with excellent memristive properties162. b | Schematic of a MoS lateral Schottky diode, with the core component including a MoS semiconducting-​ The electrical and/or optical property changes asso- 2 2 ciated with 2D phase transitions are particularly inter- metallic (2H-​to-1T/1T′) phase junction. The resulting low resistance and ultralow junction capacitance allow fabrication of a flexible and ultrafast rectifier that can esting for the fabrication of non-volatile​ memories and generate D.C. electricity from A.C. signals at a frequency up to 10 GHz. c | Combining transport devices. For example, resistive random access the high-speed​ rectifier with a flexible antenna results in a flexible rectenna that can memories and ferroelectric phase-​change transistors harvest wireless radio-​frequency energy at the Wi-Fi-​ ​band. d | The ferroelectric nonlinear have been designed based on electric-​field-​induced52 anomalous Hall effect in time-​reversal invariant systems provides the theoretical basis and strain-​induced90 2H-​to-1T′ phase transitions of for nonlinear memory. Nonlinear anomalous Hall current switches in odd-layer​ WTe2 transition-​metal dichalcogenides, respectively. Since but remains invariant in even-​layer WTe upon ferroelectric transition. P is the electric 2 z the 1T′ phase of group 6 monolayer transition-​metal polarization along the z direction and d indicates the offset of the inversion centres x dichalcogenides is a QSH insulator33, controlling their between the middle and top/bottom layers along the x direction. Two ferroelectric states topological electronic properties based on the above are related to each other by an inversion operator, denoted as +iFE and −iFE, respectively. L phase transition can potentially enable the design of new Upon the ferroelectric transition, a nonlinear anomalous Hall current jx switches between the −x and +x directions under an external field with in-plane​ linear polarization, owing quantum electronic devices. C to the linear photogalvanic effect, while a nonlinear anomalous Hall current jy switches 2D materials with ferroic phase transitions and prop- between the −y and +y directions under circularly polarized light with normal incidence, erties enable the design of a range of ultrathin and owing to the circular photogalvanic effect. e | Experimental demonstration of the flexible smart materials and functional devices, with ferroelectric nonlinear anomalous Hall effect and Berry curvature memory in trilayer potential usages in micro/nano systems and conformal WTe 2. Nonlinear Hall voltage can be easily detected, and its sign informs the memory devices; for example, 2D ferroelastics can be used for state directly. V ,2 and V , are the nonlinear transverse voltage at frequency 2ω and 57 ⊥ ω ∥ ω 2 nanoscale actuators and shape-​memory materials ; nonlinear longitudinal voltage at frequency ω, respectively. The ratio of V /(V ) 55 ⊥∥,,2ωω 2D ferroelectrics can be applied for memory devices is proportional to the Berry curvature dipole D. As the electric field E switches, the ⊥ and ferroelectric tunnel junctions160; and 2D ferro- longitudinal conductance G shows a butterfly-shape​ hysteresis, while V /(V )2 ⊥∥,,2ωω 42,44 switches the sign, indicating the flipping of Berry curvature dipole D. This is reflected magnets can be used for spintronics . Certain 2D multiferroics, such as group IV monochalcogenides, in the Berry curvature Ωc distribution in the two-​dimensional kx–ky Brillouin zone. f | Optomechanical martensitic transition induced by a linearly polarized laser pulse can exhibit strong coupling between ferroelectric and in ferroelastic monolayer SnO (left) and SnSe (right). SnSe is multiferroic, showing both ferroelastic orders, as well as strong and anisotropic ferroelastic and ferroelectric order. Displacive domain switching associated with the excitonic absorption161, making them attractive for the optomechanical martensitic transition is accompanied by the switching of polarization development of 2D ferroelectric memory, 2D ferroelas- directions (FE1 and FE2). SP is the saddle point of ferroelastic and ferroelectric switching. tic memory, 2D nonvolatile photonic memory and 2D g | Scrollable optical disk drive based on the optomechanically driven transition in bilayer ferroelectric excitonic photovoltaics58. hexagonal boron nitride. Upon illumination by a laser pulse, the layer stacking pattern Several novel device prototypes that take advantage of each bilayer hexagonal boron nitride domain can switch from AA to AB . The size of ′ ′ of phase transitions in 2D materials have been exper- each domain is comparable to the spot size of the laser. The optical disk drive contains a lattice of domains, which can be scrolled to increase data density. Panel a adapted from imentally demonstrated. For example, excellent mem- ref.162, Springer Nature Limited. Panels b and c adapted from ref.163, Springer Nature ristive behaviour can be achieved by exploiting the 140 Limited. Panel d adapted from ref. , CC BY 4.0 (https://creativecommons.org/licenses/ reversible 2H-​to-1T′ phase transition of layered MoS2 + by/4.0/). Panel e adapted from ref.54, Springer Nature Limited. Panel f adapted with films, driven by electric-​field-​induced Li ion redistri- permission from ref.59, American Chemical Society. Panel g reprinted from ref.60, bution, for example, for the implementation of artificial Springer Nature Limited. neural networks in neuromorphic computing162 (Fig. 6a). Metallic-semiconducting​ (1T/1T′-to-2H)​ phase hetero­

active layer and higher energy efficiency of the device. junctions of MoS2 layers have been used to fabricate

Similarly, 2D TiTe2/3D Sb2Te 3 phase-​change hetero­ atomically thin and flexible lateral Schottky diodes with structures also show ultralow noise and drift159. The 2D ultralow junction capacitance and low series resistance.

TiTe 2 layers in the heterostructure suppress damage in the These Schottky diodes enable the design of flexible and

3D Sb2Te 3 structure by blocking the electrical-field-assisted ultrafast rectifiers, which can convert A.C. electrical transport of charged species (Fig. 5d). signals’ waves into D.C. electricity at a frequency of up to 10 GHz. Such flexible rectennas can harvest wireless Technological applications radio-frequency​ energy at the Wi-Fi​ band163 (Fig. 6b,c). The possibility to change material properties by 2D phase In addition, ferroelectricity-driven​ nonlinear photo- transitions, which can be coupled to external stimuli, current switching and a ferroelectric nonlinear anom- enables a broad range of potential device applications. alous Hall effect have been theoretically predicted140,164 For example, the 2H-​to-1T or 2H-​to-1T′ phase change and experimentally demonstrated54 in time-​reversal

of transition-​metal dichalcogenides can be induced invariant few-​layer WTe2. Upon ferroelectric transition

by alkali metal intercalation, which can be exploited in few-​layer WTe2, nonlinear anomalous Hall voltage

to improve the electrocatalytical performance of these switches the sign in odd-layer​ WTe2 (except monolayer 100 materials for electrochemical hydrogen gas evolution 1T′-​WTe 2) but remains invariant in even-​layer WTe2 or to fabricate lateral heterostructures of semiconducting (Fig. 6d,e). This oscillation originates from the absence and metallic phases for 2D electronic devices with low and presence of Berry curvature dipole reversal and shift contact resistance47,101. Such ohmic lateral heterophase dipole reversal, owing to distinct ferroelectric transfor- (ref.140) junctions formed between the semiconducting­ 2H and mations in even-​layered and odd-layered​ WTe2 .

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These theoretical predictions and experimental demon- to the presence of soft phonon modes or strong lattice strations establish Berry curvature and shift dipole as anharmonicity)172, and remain stable or metastable at nonlinear order parameters, opening a route towards room temperature. These materials may not be accessible unconventional memory devices, such as a Berry cur- in traditional structural prediction algorithms167 or from vature memory based on nonlinear susceptibility. the mining of existing crystallographic databases173–177,

Weak interlayer gliding in WTe2 also offers a strategy because, at present, these approaches typically do not to engineering and controlling 2D ferroelectric patterns consider the entropy contribution to phase stabilization. by electric gating and optical switching, enabling high speed and low activation energy for electromechanical, Understanding the kinetics and controlling 2D phase optomechanical and neuromorphic applications. transitions Finally, optomechanical devices could benefit from The thermodynamics of 2D phase transitions have been the strong coupling between 2D phase-​change materials extensively studied; however, the kinetics of 2D phase and light, as well as from the extraordinary mechani- transitions remain less explored. In 2D materials, the cal properties of 2D materials. For example, a linearly transformation interfaces and pathways are expected polarized laser pulse can drive an ultrafast diffusionless to be substantially different than in bulk materials. martensitic phase transition of 2D ferroelastic mate- Understanding the kinetics is required to precisely con- rials, for example, of monolayer SnO and SnSe (ref.59). trol 2D phase transitions. In situ structural studies dur- Memory devices based on such optomechanical mar- ing phase transitions may be performed in real space (for tensitic transitions require an order of magnitude lower example, by in situ TEM178) or in reciprocal space energy input than traditional Ge-Sb-​ ​Te alloys59 (Fig. 6f). (for example, by in situ X-​ray diffraction179 or ultrafast In bilayer hexagonal boron nitride, a laser with selected electron diffraction180). In parallel with structural evo­ frequency can modify the energetics of different (meta-) lution, the accompanying changes in electronic structure, stable stacking patterns, and reversibly and controllably vibrational spectra or symmetry properties can be probed switch the stacking patterns without barriers, making by time-resolved​ angle-​resolved photoemission spectro­ this material attractive for data storage and optical phase scopy (tr-​ARPES)181, time-​resolved infrared and Raman masks60 (Fig. 6g). spectroscopy or time-​resolved second-​harmonic genera- tion (SHG) spectroscopy182, respectively. Recent advances Outlook in ultrafast dark-​field electron microscopy further allow To enable the industrial applications of 2D materials, the the real-​space imaging of order-​parameter dynamics realization of large-area​ growth of high-quality​ materials, during structural phase transitions in transition-​metal facile and robust material processing, high-performance​ dichalcogenides with nanometre spatial and femtosecond devices and systems, as well as long service lifetimes, all temporal resolution183. Combining in situ TEM experi- need to be achieved. The phase behaviour of 2D mate- ments, aberration-corrected​ TEM imaging of atomic-level​ rials is important in all these growth-processing-​ service​ structural evolution76, and dark-​field TEM imaging of steps. Furthermore, phase transitions have long been order-​parameter and microstructural dynamics183,184, explored to improve or enable distinct material func- allows a multiscale view of the kinetics of 2D structural tionalities. In particular, 2D phase transitions have a phase transitions driven by a variety of stimuli. variety of unique features, which can be exploited for electronic, optical, magnetic, electromechanical165, Flexural engineering of 2D phase transitions optomechanical59 and magnetomechanical166 systems. The flexural mode73,185 in 2D materials offers the pos- However, important challenges remain to be addressed sibility to control and configure 2D phase transitions, in the field of 2D phase transitions. which is difficult to achieve in bulk materials; for example, giant pseudomagnetic fields98 and exciton Discovery and characterization of new 2D funnelling99 in inhomogeneously strained 2D materials. phase-​change materials Flexoelectric, flexomagnetic and flexooptic couplings Most known 2D phase-​change materials are derived likely affect 2D phase transitions, which may allow pre- from chalcogenides that have a layered bulk struc- cise control of phase changes at a desired temperature ture. Expanding the portfolio of 2D phase-​change and spatial location, by configuring specific structural materials will open new application spaces. In princi- patterns (for example, ripples). Such periodic patterns ple, 2D phase-​change materials could exist in a range could be achieved by stacking 2D materials on a soft of materials systems, either in a free-​standing or in a substrate, followed by mechanical deformation (for substrate-​supported form, for example, oxides, pnic- example, tension and compression) or temperature tides and halides. First-​principles calculations can change (for example, by using substrates with different play a key role in the discovery of new phase-​change thermal expansion coefficient), to construct periodi- materials; for example, crystal structure prediction cally patterned ripples and wrinkles. Here, the combi- tools167 and machine learning168–170 could be applied nation of out-​of-​plane interfacial energy and in-​plane to explore the free energy landscape and discover new patterns may affect the phase transition. In addition, in 2D phase-​change materials, which may not even have a 2D materials stacked on a substrate with a large lattice bulk counterpart. Importantly, certain phase-change​ 2D mismatch or finite twisting angle, spatial inhomogeneity materials could be entropically stabilized at high temper- in the interlayer interaction and separation is naturally atures, as a result of large configurational entropy (com- induced, which leads to the creation of tunable periodic positional complexity)171 or vibrational entropy (owing structures with a strain gradient and flexoelectricity, as

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186 observed in Moiré superlattices . The flexoelectricity electrically driven interlayer sliding in few-​layer WTe2 could be exploited to control local deformation and, accompanied by ferroelectricity and the ferroelectric thus, phase transitions by external electric field. nonlinear anomalous Hall effect based on Berry cur- vature dipoles open up avenues for the development of Phase transitions in stacked 2D materials and 2D semimetal-​based memory devices54. This concept van der Waals heterostructures can be expanded to ferroelectric few-layer​ 2D semicon- Monolayer 2D materials have ultrathin thickness and ductors (for example, monolayer GeSe and SnTe)164 and

cover a wide variety of electronic structural types (met- topological quantum materials (for example, MnBi2Te 4, als, semiconductors, insulators, topological insulators which shows a quantum anomalous Hall effect)191. For and topological metals33). The absence of surface dan- example, a ferroelectric transition could be induced in gling bonds and the weak van der Waals interactions odd-​layer GeSe or SnTe, and the corresponding shift between layers enable the construction of stacked lay- current response could be measured. Demonstration ers and van der Waals heterostructures with infinite of shift current switching would provide the experi­ possibilities93. In such stacked materials, there is a hier­ mental foundation for realizing shift-dipole-​ based​ non- archy in the bonding energy scales between intralayer linear memory164. Furthermore, optomechanics could and interlayer interactions (covalent versus mostly play a key role in the phase engineering of stacked 2D van der Waals, with the former being much stronger71,187) materials by shifting interlayer stacking configurations in stacked layers, yet, the interlayer electronic inter­ through altering the energy landscape by a light field actions can still be strong and have a considerable influ- with a selected frequency60 or through the excitement of ence on the properties of the resulting materials. The coherent phonons by terahertz light192, driving the sys- emergence of flat bands and strong-​correlation physics tem into a metastable or more stable phase. This kind in stacked bilayer graphene with a twisting angle, includ- of strongly nonlinear light–matter interactions, driving ing superconductivity transitions27,30,188,189, as well as the phonon–polaritons to the nonlinear regime and even

transition of monolayer MoS2 from a direct-​bandgap beyond the convex part of the phonon energy land- semiconductor to an indirect-​bandgap semiconductor scape, could lead to a variety of nonlinear optical and in bilayers64, are eminent examples. stimulated emission effects that are quantum mechan- Phase transitions of 2D materials become richer in ical in nature. Optomechanics could also result in the stacked 2D materials and van der Waals heterostruc- change of the twist angles of stacked 2D materials, tures, as, in addition to monolayer structural degrees of either through the direct change of orientation degrees freedoms (polymorphs, domain variants and ripples), of freedom accompanying a light-​induced ferroelastic additional stacking degrees of freedom (stacking mate- transition59 or by the mechanical coupling to the strain rials and stacking order, including the relative shifts induced by optomechanical phase transitions, thus, con- and orientation angles between layers190) also come into tributing a useful set of tools in the emerging field of play. These stacking degrees of freedom are often eas- twistronics189,193–195. ier to manipulate, because the energy barriers between The rapid progress in semiconductor technology stacking orders are usually smaller than the monolayer has given us Moore’s law. Commercial transistors can structural degrees of freedom, owing to weak interlayer now be produced with a feature size of 5 nm, which may bonding interaction, thus, facilitating their control by soon be reduced to 3 nm and below196. Applying 2D external stimuli. The interplay between multiple external materials exhibiting phase transitions could address the fields (electrical, optical, magnetic, thermal, mechanical challenge of further miniaturization, resulting in more or chemical), monolayer phase transitions and stacking energy-​efficient and faster memory54,80, computing33, phase transitions can result in rich materials responses sensing and actuating57,59 devices. Therefore, research in by altering band structures and topologies53, electron– this area will not only produce fundamental new know­ phonon interactions and electron–electron correla- ledge but will also play a crucial role in the development tions27,30, to name a few, leading to new fundamental of new devices and technologies in the coming decades. discoveries and device concepts. As an example of a phase transition driven by a change in layer stacking geometry, Published online 9 April 2021

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