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Phase-change random-access memory (PCRAM) is one of the leading candidates for next-generation data-storage devices, but the trade-off between crystallization (writing) speed and amorphous-phase stability (data retention) presents a key challenge. We control the crystallization kinetics of a phase-change material by applying a constant low voltage via prestructural ordering (incubation) effects. A crystallization speed of 500 picoseconds was achieved, as well as high-speed reversible switching using 500-picosecond pulses. Ab initio molecular dynamics simulations reveal the phase-change kinetics in PCRAM devices and the structural origin of the incubation-assisted increase in crystallization speed. This paves the way for achieving a broadly applicable memory device, capable of nonvolatile operations beyond gigahertz data-transfer rates.

The Dicke model with a weak dissipation channel is realized by coupling a Bose–Einstein condensate to an optical cavity with ultranarrow bandwidth. We explore the dynamical critical properties of the Hepp–Lieb–Dicke phase transition by performing quenches across the phase boundary. We observe hysteresis in the transition between a homogeneous phase and a self-organized collective phase with an enclosed loop area showing power-law scaling with respect to the quench time, which suggests an interpretation within a general framework introduced by Kibble and Zurek. The observed hysteretic dynamics is well reproduced by numerically solving the mean-field equation derived from a generalized Dicke Hamiltonian. Our work promotes the understanding of nonequilibrium physics in open many-body systems with infinite range interactions. Significance Nonequilibrium phenomena in quantum many-body systems are not well understood to date. This applies in particular for open systems, coupled to an external bath. We use a Bose–Einstein condensate in a high-finesse optical resonator with ultralow bandwidth to emulate the open Dicke model. In well-controlled sweeps across the Hepp–Lieb–Dicke phase transition, we observe hysteretic dynamics showing power-law scaling with respect to the transition time, which suggests an interpretation in terms of a Kibble–Zurek mechanism. Our observations indicate the possibility of universal behavior in the presence of dissipation.

Complex crystallization pathways are common in protein crystallization, tetrahedrally coordinated systems, and biomineralization, where single or multiple precursors temporarily appear before the formation of the crystal. The emergence of precursors is often explained by a unique property of the system, such as short-range attraction, directional bonding, or ion association. But, structural characteristics of the prenucleation phases found in multistep crystallization remain unclear, and models are needed for testing and expanding the understanding of fluid-to-solid ordering pathways. Here, we report 3 instances of 2-step crystallization of hardparticle fluids. Crystallization in these systems proceeds via a highdensity precursor fluid phase with prenucleation motifs in the form of clusters, fibers and layers, and networks, respectively. The density and diffusivity change across the fluid–fluid phase transition increases with motif dimension. We observe crystal nucleation to be catalyzed by the interface between the 2 fluid phases. The crystals that formare complex, including, notably, a crystalwith 432 particles in the cubic unit cell. Our results establish the existence of complex crystallization pathways in entropic systems and reveal prenucleation motifs of various dimensions.

The study of first-order structural transformations has been of great interest to scientists in many disciplines. Expectations from phase-transition theory are that the system fluctuates between two equilibrium structures near the transition point and that the region of transition broadens in small crystals. We report the direct observation of structural fluctuations within a single nanocrystal using transmission electron microscopy. We observed trajectories of structural transformations in individual nanocrystals with atomic resolution, which reveal details of the fluctuation dynamics, including nucleation, phase propagation, and pinning of structural domains by defects. Such observations provide crucial insight for the understanding of microscopic pathways of phase transitions.

Materials are described here that can change their crystalline phase in response to the electrically controlled insertion or extraction of oxygen and hydrogen ions, giving rise to three distinct phases with different optical, electrical and magnetic properties. Changing to the next phase Materials that change their phase in response to the electrical injection or extraction of an ionic species are harnessed in a wide range of applications, including batteries that can operate in a range of climates and smart windows that can control the amount of light or heat that passes through them. As Nianpeng Lu et al . report, increasing the number of transferrable ionic species can greatly enhance the functionality of the system. Specifically, they report a material system in which the electrical insertion and extraction of oxygen (O 2− ) and hydrogen (H + ) ions can be independently controlled, giving reversible access to three distinct material phases that have very different optical, electrical and magnetic properties. This finding could further broaden the range of potential applications for phase-changing materials. Materials can be transformed from one crystalline phase to another by using an electric field to control ion transfer, in a process that can be harnessed in applications such as batteries 1 , smart windows 2 and fuel cells 3 . Increasing the number of transferrable ion species and of accessible crystalline phases could in principle greatly enrich material functionality. However, studies have so far focused mainly on the evolution and control of single ionic species (for example, oxygen, hydrogen or lithium ions 4 , 5 , 6 , 7 , 8 , 9 , 10 ). Here we describe the reversible and non-volatile electric-field control of dual-ion (oxygen and hydrogen) phase transformations, with associated electrochromic 2 and magnetoelectric 11 effects. We show that controlling the insertion and extraction of oxygen and hydrogen ions independently of each other can direct reversible phase transformations among three different material phases: the perovskite SrCoO 3− δ (ref. 12 ), the brownmillerite SrCoO 2.5 (ref. 13 ), and a hitherto-unexplored phase, HSrCoO 2.5 . By analysing the distinct optical absorption properties of these phases, we demonstrate selective manipulation of spectral transparency in the visible-light and infrared regions, revealing a dual-band electrochromic effect that could see application in smart windows 2 , 9 . Moreover, the starkly different magnetic and electric properties of the three phases—HSrCoO 2.5 is a weakly ferromagnetic insulator, SrCoO 3− δ is a ferromagnetic metal 12 , and SrCoO 2.5 is an antiferromagnetic insulator 13 —enable an unusual form of magnetoelectric coupling, allowing electric-field control of three different magnetic ground states. These findings open up opportunities for the electric-field control of multistate phase transformations with rich functionalities.

Quantum phase transitions (QPTs) involve transformations between different states of matter that are driven by quantum fluctuations 1 . These fluctuations play a dominant part in the quantum critical region surrounding the transition point, where the dynamics is governed by the universal properties associated with the QPT. Although time-dependent phenomena associated with classical, thermally driven phase transitions have been extensively studied in systems ranging from the early Universe to Bose–Einstein condensates 2 – 5 , understanding critical real-time dynamics in isolated, non-equilibrium quantum systems remains a challenge 6 . Here we use a Rydberg atom quantum simulator with programmable interactions to study the quantum critical dynamics associated with several distinct QPTs. By studying the growth of spatial correlations when crossing the QPT, we experimentally verify the quantum Kibble–Zurek mechanism (QKZM) 7 – 9 for an Ising-type QPT, explore scaling universality and observe corrections beyond QKZM predictions. This approach is subsequently used to measure the critical exponents associated with chiral clock models 10 , 11 , providing new insights into exotic systems that were not previously understood and opening the door to precision studies of critical phenomena, simulations of lattice gauge theories 12 , 13 and applications to quantum optimization 14 , 15 . A Rydberg atom quantum simulator with programmable interactions is used to experimentally verify the quantum Kibble–Zurek mechanism through the growth of spatial correlations during quantum phase transitions.

Machine-learning driven models have proven to be powerful tools for the identification of phases of matter. In particular, unsupervised methods hold the promise to help discover new phases of matter without the need for any prior theoretical knowledge. While for phases characterized by a broken symmetry, the use of unsupervised methods has proven to be successful, topological phases without a local order parameter seem to be much harder to identify without supervision. Here, we use an unsupervised approach to identify boundaries of the topological phases. We train artificial neural nets to relate configurational data or measurement outcomes to quantities like temperature or tuning parameters in the Hamiltonian. The accuracy of these predictive models can then serve as an indicator for phase transitions. We successfully illustrate this approach on both the classical Ising gauge theory as well as on the quantum ground state of a generalized toric code.

The problem of optimizing over random structures emerges in many areas of science and engineering, ranging from statistical physics to machine learning and artificial intelligence. For many such structures, finding optimal solutions by means of fast algorithms is not known and often is believed not to be possible. At the same time, the formal hardness of these problems in the form of the complexity-theoretic NP-hardness is lacking. A new approach for algorithmic intractability in random structures is described in this article, which is based on the topological disconnectivity property of the set of pairwise distances of near-optimal solutions, called the Overlap Gap Property. The article demonstrates how this property 1) emerges in most models known to exhibit an apparent algorithmic hardness; 2) is consistent with the hardness/tractability phase transition for many models analyzed to the day; and, importantly, 3) allows to mathematically rigorously rule out a large class of algorithms as potential contenders, specifically the algorithms that exhibit the input stability (insensitivity).

The motion of atoms on interatomic potential energy surfaces is fundamental to the dynamics of liquids and solids. An accelerator-based source of femtosecond x-ray pulses allowed us to follow directly atomic displacements on an optically modified energy landscape, leading eventually to the transition from crystalline solid to disordered liquid. We show that, to first order in time, the dynamics are inertial, and we place constraints on the shape and curvature of the transition-state potential energy surface. Our measurements point toward analogies between this nonequilibrium phase transition and the short-time dynamics intrinsic to equilibrium liquids.

The lattice dynamics and high-temperature structural transition in SnS and SnSe are investigated via inelastic neutron scattering, high-resolution Raman spectroscopy and anharmonic first-principles simulations. We uncover a spectacular, extreme softening and reconstruction of an entire manifold of low-energy acoustic and optic branches across a structural transition, reflecting strong directionality in bonding strength and anharmonicity. Further, our results solve a prior controversy by revealing the soft-mode mechanism of the phase transition that impacts thermal transport and thermoelectric efficiency. Our simulations of anharmonic phonon renormalization go beyond low-order perturbation theory and capture these striking effects, showing that the large phonon shifts directly affect the thermal conductivity by altering both the phonon scattering phase space and the group velocities. These results provide a detailed microscopic understanding of phase stability and thermal transport in technologically important materials, providing further insights on ways to control phonon propagation in thermoelectrics, photovoltaics, and other materials requiring thermal management. Thermoelectric efficiency of SnS and SnSe is reported to peak around the phase transition temperature around 800 K; however, the transition mechanism and origin of ultralow thermal conductivity remain unclear. Here, the authors reveal the soft-mode mechanism of the phase transition that impacts thermal transport and thermoelectric efficiency.