2D Phase Transition Research Articles

Non-parametric learning critical behavior in Ising partition functions: PCA entropy and intrinsic dimension

We provide and critically analyze a framework to learn critical behavior in classical partition functions through the application of non-parametric methods to data sets of thermal configurations. We illustrate our approach in phase transitions in 2D and 3D Ising models. First, we extend previous studies on the intrinsic dimension of 2D partition function data sets, by exploring the effect of volume in 3D Ising data. We find that as opposed to 2D systems for which this quantity has been successfully used in unsupervised characterizations of critical phenomena, in the 3D case its estimation is far more challenging. To circumvent this limitation, we then use the principal component analysis (PCA) entropy, a “Shannon entropy” of the normalized spectrum of the covariance matrix. We find a striking qualitative similarity to the thermodynamic entropy, which the PCA entropy approaches asymptotically. The latter allows us to extract-through a conventional finite-size scaling analysis with modest lattice sizes-the critical temperature with less than 1% error for both 2D and 3D models while being computationally efficient. The PCA entropy can readily be applied to characterize correlations and critical phenomena in a huge variety of many-body problems and suggests a (direct) link between easy-to-compute quantities and entropies.

Thermal Hysteresis and Ordering Behavior of Magnetic Skyrmion Lattices.

The physics of phase transitions in two-dimensional (2D) systems underpins research in diverse fields including statistical mechanics, nanomagnetism, and soft condensed matter. However, many aspects of 2D phase transitions are still not well understood, including the effects of interparticle potential, polydispersity, and particle shape. Magnetic skyrmions are chiral spin-structure quasi-particles that form two-dimensional lattices. Here, we show, by real-space imaging using in situ cryo-Lorentz transmission electron microscopy coupled with machine learning image analysis, the ordering behavior of Néel skyrmion lattices in van der Waals Fe3GeTe2. We demonstrate a distinct change in the skyrmion size distribution during field-cooling, which leads to a loss of lattice order and an evolution of the skyrmion liquid phase. Remarkably, the lattice order is restored during field heating and demonstrates a thermal hysteresis. This behavior is explained by the skyrmion energy landscape and demonstrates the potential to control the lattice order in 2D phase transitions.

Observation of a phase transition within the domain walls of ferromagnetic Co3Sn2S2

The ferromagnetic phase of Co3Sn2S2 is widely considered to be a topological Weyl semimetal, with evidence for momentum-space monopoles of Berry curvature from transport and spectroscopic probes. As the bandstructure is highly sensitive to the magnetic order, attention has focused on anomalies in magnetization, susceptibility and transport measurements that are seen well below the Curie temperature, leading to speculation that a “hidden” phase coexists with ferromagnetism. Here we report spatially-resolved measurements by Kerr effect microscopy that identify this phase. We find that the anomalies coincide with a deep minimum in domain wall (DW) mobility, indicating a crossover between two regimes of DW propagation. We demonstrate that this crossover is a manifestation of a 2D phase transition that occurs within the DW, in which the magnetization texture changes from continuous rotation to unidirectional variation. We propose that the existence of this 2D transition deep within the ferromagnetic state of the bulk is a consequence of a giant quality factor for magnetocrystalline anisotropy unique to this compound. This work broadens the horizon of the conventional binary classification of DWs into Bloch and Néel walls, and suggests new strategies for manipulation of domain walls and their role in electron and spin transport.

Electronic and Lattice Thermal Conductivity Switching by 3D−2D Crystal Structure Transition in Nonequilibrium (Pb1−xSnx)Se

AbstractDynamic control of thermal transport in solid materials is highly desired for thermal management technology. However, the development of a material exhibiting large modulation of thermal conductivity (κ) by external stimuli remains a major challenge. Here, the large κ modulation is reported by the reversible 3D to 2D crystal structure transition in a nonequilibrium solid solution of (Pb1−xSnx)Se, where Pb2+ stabilizes a 3D cubic structure while Sn2+ does a 2D layered structure. The phase boundary of these phases is induced in (Pb0.5Sn0.5)Se bulk polycrystals by thermally quenching the high‐temperature solid solution phase. Through the 3D–2D phase transition, the 1/2.9‐times decrease of lattice κ (κlat.) is achieved by strong phonon scattering in the 2D layered structure, and the electronic κ (κele.) is also decreased by 5 orders of magnitude due to the electronic phase transition from a 3D high conductivity state to a 2D semiconducting state. The total κ (=κlat. + κele.) modulation ratio κ3D phase/κ2D phase = 3.6 is attained at 373 K. The present strategy will lead to a novel concept for designing thermal management materials through crystal‐structure dimensionality switch using nonequilibrium phase boundaries.

Topographic Control of Order in Quasi-2D Granular Phase Transitions.

We experimentally investigate the nature of 2D phase transitions in a quasi-2D granular fluid. Using a surface decorated with periodically spaced dimples we observe interfacial tension between coexisting granular liquid and crystal phases. Measurements of the orientational and translational order parameters and associated susceptibilities indicate that the surface topography alters the order of the phase transition from a two-step continuous one to a first-order liquid-solid one. The interplay of boundary inelasticity and geometry, either order promoting or inhibiting, controls whether it is the granular crystal or the granular fluid which makes contact with the edge. This order induced wetting has important consequences, determining how coexisting phases separate spatially.

Temperature dependence of chemisorbed carbon critical cover in graphene formation due to 2D phase transition on Rh(111).

Temperature dependence of chemisorbed atomic carbon critical cover, θcr = f(T) has been measured for a metal able to dissolve carbon in the bulk, Rh(111); this is the cover when graphene islands start to form on the surface. It has been shown that value of θcr varies from 0.11 at 1000 K to 0.22 at 1800 K, where θcr = 1 corresponds to the carbon surface concentration NСm = 3.86•1015 cm−2. Relationship and differences between surface phase transition parameters and bulk solubility limit has been discussed. The activation energy Eatt = 2.6 eV has been determined for atomic carbon attachment to the graphene island from the chemisorbed phase.

Three-dimensional network model for strong topological insulator transitions

We construct a three-dimensional (3D), time-reversal symmetric generalization of the Chalker-Coddington network model for the integer quantum Hall transition. The novel feature of our network model is that in addition to a weak topological insulator phase already accommodated by the network model framework in the pre-existing literature, it hosts strong topological insulator phases as well. We unambiguously demonstrate that strong topological insulator phases emerge as intermediate phases between a trivial insulator phase and a weak topological phase. Additionally, we found a non-local transformation that relates a trivial insulator phase and a weak topological phase in our network model. Remarkably, strong topological phases are mapped to themselves under this transformation. We show that upon adding sufficiently strong disorder the strong topological insulator phases undergo phase transitions into a metallic phase. We numerically determine the critical exponent of the insulator-metal transition. Our network model explicitly shows how a semi-classical percolation picture of topological phase transitions in 2D can be generalized to 3D and opens up a new venue for studying 3D topological phase transitions.

Phase transitions in 2D materials

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. Phase transformations in 2D materials have distinct kinetic and thermodynamic features, resulting from their reduced dimensionality and unique interactions. This Review discusses the properties of phase transitions and defects in 2D materials, and examines technological applications and challenges in the study of 2D phase transitions.

Reliable 2D Phase Transitions for Low-Noise and Long-Life Memory Programming

Extending cycling endurance and suppressing programming noise of phase-change random-access memory (PCRAM) are the key challenges with respect to the development of nonvolatile working memory and high-accuracy neuromorphic computing devices. However, the large-scale atomic migration along electrical pulse direction in the unconstrained three-dimensional phase transitions of the phase-change materials (PCMs) induces big resistance fluctuations upon repeated programming and renders the classic PCRAM devices into premature failure with limited cycling endurance. Previous efforts of superlattice-like and superlattice PCM schemes cannot effectively resolve such issues. In this work, we demonstrated that, through fine-tuning the sputtering techniques, a phase-change heterostructure (PCH) of Sb2Te3/TiTe2 can be successfully constructed. In contrast to its superlattice-like counterpart with inferior crystal quality, the well-textured PCH architecture ensures the reliable (well-confined) two-dimensional phase transitions, promoting an ultralow-noise and long-life operation of the PCRAM devices. Our study thus provides a useful reference for better manufacturing the PCH architecture and further exploring the excellent device performances and other new physics.

Phase Transitions and Water Splitting Applications of 2D Transition Metal Dichalcogenides and Metal Phosphorous Trichalcogenides.

2D layered materials turn out to be the most attractive hotspot in materials for their unique physical and chemical properties. A special class of 2D layered material refers to materials exhibiting phase transition based on environment variables. Among these materials, transition metal dichalcogenides (TMDs) act as a promising alternative for their unique combination of atomic‐scale thickness, direct bandgap, significant spin–orbit coupling and prominent electronic and mechanical properties, enabling them to be applied for fundamental studies as catalyst materials. Metal phosphorous trichalcogenides (MPTs), as another potential catalytic 2D phase transition material, have been employed for their unusual intercalation behavior and electrochemical properties, which act as a secondary electrode in lithium batteries. The preparation of 2D TMD and MPT materials has been extensively conducted by engineering their intrinsic structures at the atomic scale. In this study, advanced synthesis methods of preparing 2D TMD and MPT materials are tested, and their properties are investigated, with stress placed on their phase transition. The surge of this type of report is associated with water‐splitting catalysis and other catalytic purposes. This study aims to be a guideline to explore the mentioned 2D TMD and MPT materials for their catalytic applications.

First principles and molecular dynamics study of Li wetting and diffusion on W surfaces

Surface diffusion is an interesting and practically important phenomenon in many areas of chemistry and physics. One emerging problem is that of Li wetting on high-Z plasma-facing metals, especially tungsten, for application in tokamak reactors. We report construction of a Li-W binary force field to describe the interface between liquid Li and solid W. We show that this force field can simulate well the atomic processes of liquid Li diffusing across the W surface, as compared with results from first-principles calculations. We find that Li atoms have different wetting behaviors on different surfaces of W. Diffusion is the fastest on the (110) surface and the slowest on the (100) surface. Diffusion of second Li layer on the (110) surface is activated at relatively low temperatures above 262 K. In addition, the diffusion rate of single-layer Li changes with the coverage rate of Li on (110) surface. High diffusion coefficients at coverage rate of θ = 1/6, 1/3 and 1 are found to be related to the 2D phase transition of Li on the (110) surface.

Atomic Carbon Transport between the Rh Surface and Bulk in Graphene Formation and Destruction

The equilibrium transport of atomic carbon between the Rh surface and bulk, which controls the kinetics of the phase transition resulting in graphene growth or destruction, is investigated. The difference between the activation energy Es1 of atomic-carbon dissolution and the energy E1s of its segregation from the bulk to the surface is found to be ΔE = 0.7 eV. The temperature dependence of the critical coating Neq = Neq(T) in the chemisorbed carbon layer is measured. It is a 2D phase transition that takes place at this coating, and graphene islands start to grow: for example, Neq = 7.7 × 1014 cm–2 at T = 1800 K, and Neq = 3.1 × 1014 cm–2 at T = 1000 K.

Транспортные процессы с участием атомов углерода между поверхностью и объемом родия при образовании и разрушении графена

Equilibrium transport of atomic carbon between Rh surface and bulk has been studied. This transport controls the kinetics of the phase transition resulting in graphene growth or destruction. The difference ΔE=0.7 eV has been measured between the activation energy of atomic carbon dissolution E1s and that of its segregation from the bulk to the surface E1s. The temperature dependence of chemisorbed carbon critical cover Neq = Neq(T) has been measured, that is the cover when 2D phase transition takes place and graphene islands start to grow. E.g., Neq = 7.7•1014 cm-2 at T = 1800 K, and Neq = 3.1•1014 cm-2 at T = 1000 K.

Influence of quenched non-magnetic impurities on phase transitions in the two-dimensional Potts model with q = 5

Abstract Thermodynamic properties and phase transitions in 2d weakly diluted Potts model on a square lattice are investigated by the Monte Carlo method. We consider the systems with linear sizes L × L = N, L = 10–160. Using the fourth order Binder cumulant method, it was shown that the introduction of non-magnetic impurities into the spin system described by the two-dimensional Potts model with q = 5 leads to a change in the first-order phase transition to the second-order phase transition.

Melting and re-entrant melting of polydisperse hard disks

Because of long-wavelength fluctuations, the nature of solids and phase transitions in 2D are different from those in 3D systems, and have been heavily debated in past decades, in which the focus was on the existence of hexatic phase. Here, by using large scale computer simulations, we investigate the melting transition in 2D systems of polydisperse hard disks. We find that, with increasing the particle size polydispersity, the melting transition can be qualitatively changed from the recently proposed two-stage process to the Kosterlitz-Thouless-Halperin-Nelson-Young scenario with significantly enlarged stability range for hexatic phase. Moreover, re-entrant melting transitions are found in high density systems of polydisperse hard disks, which were proven impossible in 3D polydisperse hard-sphere systems. These suggest a new fundamental difference between phase transitions in polydisperse systems in 2D and 3D.

Atomically Thin CrCl3: An In-Plane Layered Antiferromagnetic Insulator.

The recent discovery of magnetism in atomically thin layers of van der Waals (vdW) crystals has created new opportunities for exploring magnetic phenomena in the two-dimensional (2D) limit. In most 2D magnets studied to date, the c-axis is an easy axis, so that at zero applied field the polarization of each layer is perpendicular to the plane. Here, we demonstrate that atomically thin CrCl3 is a layered antiferromagnetic insulator with an easy-plane normal to the c-axis, that is, the polarization is in the plane of each layer and has no preferred direction within it. Ligand-field photoluminescence at 870 nm is observed down to the monolayer limit, demonstrating its insulating properties. We investigate the in-plane magnetic order using tunneling magnetoresistance in graphene/CrCl3/graphene tunnel junctions, establishing that the interlayer coupling is antiferromagnetic down to the bilayer. From the temperature dependence of the magnetoresistance, we obtain an effective magnetic phase diagram for the bilayer. Our result shows that CrCl3 should be useful for studying the physics of 2D phase transitions and for making new kinds of vdW spintronic devices.

Potential 2D Materials with Phase Transitions: Structure, Synthesis, and Device Applications.

Layered materials with phase transitions, such as charge density wave (CDW) and magnetic and dipole ordering, have potential to be exfoliated into monolayers and few-layers and then become a large and important subfamily of two-dimensional (2D) materials. Benefitting from enriched physical properties from the collective interactions, long-range ordering, and related phase transitions, as well as the atomic thickness yet having nondangling bonds on the surface, 2D phase-transition materials have vast potential for use in new-concept and functional devices. Here, potential 2D phase-transition materials with CDWs and magnetic and dipole ordering, including transition metal dichalcogenides, transition metal halides, metal thio/selenophosphates, chromium silicon/germanium tellurides, and more, are introduced. The structures and experimental phase-transition properties are summarized for the bulk materials and some of the obtained monolayers. In addition, recent experimental progress on the synthesis and measurement of monolayers, such as 1T-TaS2 , CrI3 , and Cr2 Ge2 Te6 , is reviewed.

Fluid–Solid Phase Transition in Molecular Layers Adsorbed on a Smooth Surface: A New Insight from Molecular Simulations

Two-dimensional (2D) phase transitions in molecular layers adsorbed on various surfaces have attracted much research attention over the past decades. Special attention is paid to the solidification...

A molecular dynamics study on the dependence of phase behaviors and structural properties of two-dimensional interfacial monolayer on surface area

The packing state and structure of monolayer at the air/water interface have important effect on its wide application. Using molecular dynamics (MD) simulation, phase transitions of sodium dodecyl sulfate (SDS) monolayer, dependent on the surface area per molecule, have been studied in the view of configuration entropy. With the reduction of surface area per molecule, three two-dimensional (2D) phases are defined, including gaseous, liquid expanded and liquid condensed phases. At small surface area per molecule, the 2D monolayer will collapse and 3D aggregates are formed in the bulk solution. We give a detailed description of the collapse mode from interfacial monolayer at the air/water interface to micelle in the solution at the molecular level. Using the quasi-harmonic (QH) approximation, the entropic change of SDS for 2D phase transition are first introduced, which is around −29.7 J mol−1 K−1 for the transition from 2D gaseous film to 2D liquid expanded film and −42.0 J mol−1 K−1 for the transition from 2D liquid expanded film to 2D liquid condensed film. The effect of different surface coverages on the dynamical and structural properties of SDS monolayer at the air/water interface is evaluated. Based on simulated results, a schematic diagram of 2D monolayer in different phases is proposed.

Tuning the ferroelectric-to-paraelectric transition temperature and dipole orientation of group-IV monochalcogenide monolayers

Coordination-related, two-dimensional (2D) structural phase transitions are a fascinating and novel facet of two-dimensional materials with structural degeneracies. Nevertheless, a unified theoretical account of these transitions remains absent, and the following points are established through {\em ab-initio} molecular dynamics and 2D discrete clock models here: Group-IV monochalcogenide (GeSe, SnSe, SnTe, ...) monolayers have four degenerate structural ground states, and a 2D phase transition from a three-fold coordinated onto a five-fold coordinated structure takes place at finite temperature. On unstrained samples, the 2D phase transition requires lattice parameters to freely evolve. A fundamental energy scale permits understanding this transition. The transition temperature $T_c$ and the orientation of the in-plane intrinsic electric dipole can be controlled by moderate uniaxial tensile strain, and a modified discrete clock model describes the transition on strained samples. These results establish a general underlying theoretical background to understand structural phase transitions in 2D materials and their effects on material properties.