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Optimum state variable selection to determine constraints for nonlinear system stability, using Liapunov second method
π-Conjugated covalent organic frameworks provide a versatile molecular scaffold for the realization of designer quantum nanomaterials. Strong electron–electron correlation within these artificial lattices can give rise to exotic phases of matter. Their experimental realization, however, requires precise control over orbital symmetry, charge localization and band dispersion, all arising from the effective hybridization between molecular linkers and nodes. Here we present a modular strategy for constructing diatomic kagome lattices from aza-[3]triangulene nodes, in which a D 3h -symmetric ground state is stabilized through resonance contributions from a cumulenic linker. First-principles density functional theory and scanning tunnelling spectroscopy reveal that the hybridization of a sixfold-degenerate set of edge-localized Wannier functions in the unit cell gives rise to orbital-phase-frustration-induced non-trivial flat bands. These results establish a general design principle for engineering orbital interactions in organic lattices and open a pathway towards programmable covalent-organic-framework-based quantum materials with correlated electronic ground states.
Seismic tomography studies have revealed a high-velocity anomaly at depths between 100 km and 300 km in the Farallon plate. However, the reasons for the high-velocity anomaly continue to be debated. An analysis of the mineral proportions of eclogites exhumed from the Farallon plate shows that the average amount of zoisite in eclogite is ∼16.0 vol%. Therefore, the presence of zoisite eclogite needs to be considered to explain the high-velocity anomaly of the Farallon plate. However, the thermal equation of state and stability of zoisite have not been fully investigated under high pressure−temperature (P-T) conditions. We investigated the high-pressure and high-temperature behavior of natural zoisite utilizing synchrotron single crystal-X-ray diffraction (XRD). The results indicate that zoisite is metastable up to 24.8 GPa and 700 K. We obtained the ambient unit-cell volume V0 = 901.26(3) Å3 by synchrotron single crystal-XRD measurement. We also fitted the pressure-volume-temperature data to a high-temperature Birch-Murnaghan equation of state and obtained the zero-pressure bulk modulus K0 = 134.7(8) GPa, the temperature derivative of the bulk modulus (∂K/∂T)P = −0.011(4) GPa/K, and the thermal expansion coefficients α0V = 1.9(7) × 10−5 K−1 and α1V = 3(2) × 10−8 K−2 when the pressure derivative of bulk modulus (K′0) is fixed at 4. By incorporating the results from previous studies, we calculated the density and bulk sound velocity profiles of zoisite eclogite along the Farallon plate geotherm. Finally, we infer that zoisite could carry water to depths of ∼300 km within cold subducting slabs and that the bulk sound velocity of typical zoisite eclogite with ∼61.0 vol% omphacite, ∼23.0 vol% garnet, and ∼16.0 vol% zoisite could cause the high-velocity anomalies at depths of 100−300 km in the Farallon plate.
Here, this paper studies the topological and magnetic properties of a noncollinear spin state on a honeycomb lattice that evolves from coplanar to ferromagnetic with a magnetic field applied along the z axis. The coplanar state is stabilized by nearest-neighbor ferromagnetic interactions, single-ion anisotropy along z, and DzyaloshinskiiMoriya interactions between next-nearest-neighbor sites. Below the critical field H$_c$ that aligns the spins, the magnetic unit cell contains six sites and the spin dynamics contains six magnon modes. Although the classical energy is degenerate with respect to the twist angle φ between nearest-neighbor spins, the dependence of the free energy on φ at low temperatures is dominated by the magnon zero-point energy, which contains extremum at φ = πl/3 for integer l. The only unique ground states GS(φ) have l = 0 or 1. For H < H$'_c$, the zero-point energy has minima at even l and the ground state is GS(0); for H$'_c$ < H < H$'_c$, the zero-point energy has minima at odd l and the ground state is GS(π/3). In GS(0), the magnon density of states exhibits five distinct topological phases with increasing field associated with the opening and closing of energy gaps between two or three magnonic bands. While the Berry curvature vanishes for the coplanar φ = 0 phase in zero field, the Berry curvature and Chern numbers exhibit signatures of the five topological phases below H$'_c$. Whereas the Berry curvature and Chern number are sensitive to changes in the magnon density of states within GS(π/3), the inelastic spectrum S(k,ω) is sensitive to changes in the intensity of the magnon modes in the different magnetic phases GS(0) and GS(π/3) rather than the five topological phases within GS(π/3).
Hydrogen bonding accelerates many catalytic reactions by orienting intermediates, stabilizing transition states, and even opening reaction pathways. However, most mechanistic studies regarding the decomposition of formic acid (FA), a promising hydrogen storage material, neglect hydrogen-bonding interactions even though FA is a strong hydrogen-bond donor and acceptor. Here, we probe the formation of bimolecular hydrogen-bonded complexes between FA and formate (FA–HCOO complexes) adsorbed on metal surfaces and how these complexes affect HCOO* decomposition. Using first-principles density functional theory (DFT) calculations on 12 close-packed (111)/(0001) and 8 open (100) surfaces of 12 transition metals—Ag, Au, Co, Cu, Ir, Ni, Os, Re, Pd, Pt, Rh, and Ru, we—show that FA–HCOO complexes are generally thermodynamically stable, even at elevated temperatures and pressures. We then illustrate that these complexes produce infrared spectroscopic signatures consistent with as yet unassigned experimental peaks. We last demonstrate that by stabilizing the dangling bond of monodentate HCOO*, these complexes significantly lower the barriers for rotation of HCOO* from a bidentate to a monodentate configuration, the rate-limiting step for HCOO* decomposition on many surfaces. FA thus acts as a cocatalyst for HCOO* decomposition. Our results may guide the community toward improved catalysts for reactions involving HCOO* such as FA decomposition, methanol steam reforming, and the water gas shift reaction. More broadly, our work highlights the ability of hydrogen bonding to modify the adsorbed structures of intermediates and lower the barriers for their reaction on heterogeneous catalysts. Lastly, this phenomenon can be relevant for other reactions involving ammonia, alcohols, and carboxylic acids.
Radical–radical association reactions are challenging to address theoretically due to difficulties finding the bottleneck that variationally minimizes the reactive flux. For this purpose, the variable reaction coordinate (VRC) formulation of the variational transition state theory (VTST) represents an appropriate tool. Here, we revisited the kinetics of two radical–radical association reactions of importance in combustion modelling and poly-aromatic hydrocarbon (PAH) chemistry by performing VRC calculations: benzyl + HO 2 and benzoxyl + OH, both forming the adduct benzyl hydroperoxide. Our calculated rate constants are significantly lower than those previously reported based on VTST calculations, which results from a more efficient minimization of the reactive flux through the bottleneck achieved by the VRC formulation. Both reactions show different trends in the variation of their rate constants with temperature. We observed that if the pair of single occupied molecular orbitals (SOMOs) of the associating radicals show a similar nature, i.e. similar character, and thereby a small energy gap, a highly stabilized transition state structure is formed as the result of a very efficient SOMO–SOMO overlap, which may cancel out the free energy bottleneck for the formation of the adduct and result in large rate constants with a negative temperature dependence. This is the case of the benzoxyl and OH radical pair, whose SOMOs show O 2p nature with an energy gap of 20.2 kcal mol –1 . On the other hand, the benzyl and HO 2 radical pair shows lower rate constants with a positive temperature dependence due to the larger difference between both SOMOs (a 28.9 kcal mol –1 energy gap) as a consequence of the contribution of the multiple resonance structures of the benzyl radical. The reverse dissociation rate constants were also calculated using multi-structural torsional anharmonicity partition functions, which were not included in previous work, and the results show a much slower dissociation of benzyl hydroperoxide. Our work may help to improve kinetic models of interest in combustion and PAH formation, as well as to gain further understanding of radical–radical association reactions, which are ubiquitous in different environments.
Ferroelectric tunnel junctions (FTJs) utilizing hafnium zirconium oxide (HZO) have emerged as promising non-volatile memory elements for microelectronics, compatible with back end of line (BEOL) complementary–metal–oxide semiconductor fabrication. This study investigates asymmetric electrode TaN/HZO/Ta devices with a 6 nm thick HZO layer as FTJs for multistate resistive memory applications. The individual FTJs exhibit a resistance ratio exceeding 10× when utilized as a binary state device, with pulsing between −1.7 and +1.4 V to set the high resistance state (HRS) and low resistance state (LRS), respectively. Following with reduced write voltage pulses allows the ferroelectric device to operate with a selection of over 32 distinct resistance states (2 5 bits) between the LRS and HRS. This work then explores the stability of the resistance states during write/read pulse cycling, along with the stability of the state after multiple read pulses. Accessing the multibit state shows stability within 50 reads with the binary state remaining stable for more than 4000 reads pulses. With their multistate tunability and versatility, FTJs hold promise as BEOL memory elements for compute-in-memory (CiM) arrays, binary digital memory, or weighted vector matrix multiplication applications with low power consumption during computations.
We report state estimation is a fundamental task in power systems. Although distribution systems are increasingly equipped with sensing devices and smart meters, measurements are typically reported at different rates and asynchronously; these aspects pose severe strains on workhorse state estimation algorithms, which are designed to process batches of data collected in a synchronous manner from all the measurement units. In this paper, we develop a novel state estimation algorithm to continuously update the estimate of the state based on measurements received in an asynchronous manner from measurement units. The synthesis of the algorithm hinges on a proximal-point type method, implemented in an online fashion, and capable of processing measurements received sequentially from sensors. A performance analysis is presented by providing bounds on the estimation error in terms of the mean and variance that hold at each iteration and asymptotically. The scheme is also compared with a more traditional Weighted Least Squares estimator that compensates for the lack of measurement data by using, as pseudo measurements, the measurement retrieved during a certain time window. Numerical simulations on the IEEE 37-bus feeder corroborate the analytical findings.
Following on our previous work studying the orbits of quantum states under Clifford circuits via reachability graphs, we introduce contracted graphs whose vertices represent classes of quantum states with the same entropy vector. These contracted graphs represent the double cosets of the Clifford group, where the left cosets are built from the stabilizer subgroup of the starting state and the right cosets are built from the entropy-preserving operators. We study contracted graphs for stabilizer states, as well as 𝑊 states and Dicke states, discussing how the diameter of a state's contracted graph constrains the entropic diversity of its two-qubit Clifford orbit. We derive an upper bound on the number of entropy vectors that can be generated using any 𝑛-qubit Clifford circuit, for any quantum state. Here, we speculate on the holographic implications for the relative proximity of gravitational duals of states within the same Clifford orbit. Although we concentrate on how entropy evolves under the Clifford group, our double-coset formalism, and thus the contracted graph picture, is extendable to generic gate sets and generic state properties.
We use the topological heavy fermion (THF) model and its Kondo lattice (KL) formulation to study the possibility of a symmetric Kondo (SK) state in twisted bilayer graphene. Via a large-N approximation, we find a SK state in the KL model at fillings v = 0,±1,±2 where a KL model can be constructed. In the SK state, all symmetries are preserved and the local moments are Kondo screened by the conduction electrons. At the mean-field level of the THF model at v = 0,±1,±2,±3 we also find a similar symmetric state that is adiabatically connected to the symmetric Kondo state. We study the stability of the symmetric state by comparing its energy with the ordered (symmetry-breaking) states found in [H. Hu et al., Phys. Rev. Lett. 131, 026502 (2023)., Z.-D. Song and B. A. Bernevig, Phys. Rev. Lett. 129, 047601 (2022).] and find the ordered states to have lower energy at v = 0,±1,±2. However, moving away from integer fillings by doping the light bands, our mean-field calculations find the energy difference between the ordered state and the symmetric state to be reduced, which suggests the loss of ordering and a tendency toward Kondo screening. In order to include many-body effects beyond the mean-field approximation, we also performed dynamical mean-field theory calculations on the THF model in the nonordered phase. The spin susceptibility follows a Curie behavior at v = 0,±1,±2 down to ~2 K where the onset of screening of the local moment becomes visible. This hints to very low Kondo temperatures at these fillings, in agreement with the outcome of our mean-field calculations. At noninteger filling v = ±0.5,±0.8,±1.2 dynamical mean-field theory shows deviations from a 1/T susceptibility at much higher temperatures, suggesting a more effective screening of local moments with doping. Lastly, we study the effect of a C 3z -rotational-symmetry-breaking strain via mean-field approaches and find that a symmetric phase (that only breaks C 3z symmetry) can be stabilized at sufficiently large strain at v = 0,±1,±2. Our results suggest that a symmetric Kondo phase is strongly suppressed at integer fillings, but could be stabilized either at noninteger fillings or by applying strain.
Abstract Sulfide‐based solid‐state electrolytes (SSEs) exhibit many tantalizing properties including high ionic conductivity and favorable mechanical properties for next‐generation solid‐state batteries. Widespread adoption of these materials is hindered by their intrinsic instability under ambient conditions, which makes them difficult to process at scale, and instability at the Li||SSE and cathode||SSE interfaces, which limits cell performance and lifetime. Atomic layer deposition is leveraged to grow thin Al 2 O 3 coatings on Li 6 PS 5 Cl powders to address both issues simultaneously. These coatings can be directly grown onto Li 6 PS 5 Cl particles with negligible chemical modification of the underlying material and enable exposure of powders to pure and H 2 O‐saturated oxygen environments for ≥4 h with minimal reactivity, compared with significant degradation of the uncoated powder. Pellets fabricated from coated powders exhibit ionic conductivities up to 2× higher than those made from uncoated material, with a simultaneous decrease in electronic conductivity and significant suppression of chemical reactivity at the Li‐SSE interface. These benefits result in significantly improved room temperature cycle life at high capacity and current density. It is hypothesized that this enhanced performance derives from improved intergranular properties and improved Li metal adhesion. This work points to a completely new framework for designing active, stable, and scalable materials for next‐generation solid‐state batteries.
The conversion of CO2 into high-value chemicals through a photoreduction reaction in water is a promising route to reduce the dependence on fossil fuels. Enhancing selectivity toward hydrocarbons or alcohols can be achieved by Ag-Cu alloys. However, the stabilized surface state created by Ag-Cu interactions is still poorly understood. In this work, multi-modal in situ X-ray experiments reveals underlying mechanisms and the evolution of Ag-Cu nanoparticles under CO2 reduction reaction (CO2RR) conditions. Both morphological and chemical changes of Ag and Cu species induced by diffusion mechanics are tracked during nanocatalyst operation. The initial spheroid Ag-Cu nanoparticles are composed of a Cu-rich shell and Ag-rich core. The reduction treatment promotes Ag migration toward the surface. During photocatalytic CO2 reduction reaction, Cu atoms migrate back to the surface, forming Ag-Cu-O species. The study observes the surface oxidation of Cu(0) to Cu+ and the presence of Ag at the sub-surface region. Furthermore, nanoparticles change their shape, decreasing their specific surface area, driven by Cu diffusion during the CO2 photoreduction reaction. The results provide invaluable insights into the dynamic restructuring of the catalyst under reaction conditions and into the active species responsible for CO2 conversion.
Atomic‐scale phase transformations profoundly influence the functional properties of Ga₂O₃ polymorphs. By combining irradiation experiments with microstructure characterization and theoretical approaches, phase‐specific energy‐dissipation pathways in α‐, β‐, and ε‐Ga₂O₃ are uncovered and strategies for targeted property design are outlined. Competing antiphase boundaries (APBs) and twin domain boundaries (TDBs) promote irreversible α→ε interconversion through domain fragmentation. In β‐Ga₂O₃, defect‐induced stress gradients drive two distinct local transformations: surface Ga‐aggregated β→δ that stabilizes transient states, and latent‐track‐confined β→κ phase transition with recoverable distortions via cation reordering. Under electronic excitation, β‐Ga₂O₃ forms nanohillocks via robust GaO₆ octahedra (high density/strong Ga─O bonds), while α/ε‐Ga₂O₃ generates nanopores from tetrahedral Ga looseness (low bonding energy), highlighting phase‐dependent surface dynamics shaped by atomic packing and bonding anisotropy. Defect‐regulated recombination suppresses visible photoluminescence in α/β‐Ga₂O₃, whereas in ε‐Ga₂O₃ bandgap narrowing of ΔE: 0.30 eV is observed, enhancing emission. Linking phase‐dependent defect‐carrier interactions and metastable‐phase engineering in Ga₂O₃ enables property optimization for power‐electronics and optoelectronics devices.
Permanent magnets with strong anisotropy and high coercivity underpin modern information and energy technologies, yet rare-earth-free alternatives remain limited. Here, we show that thickness engineering via mechanical exfoliation induces hard magnetic behavior in the van der Waals ferromagnet Fe 3 GaTe 2 . Bulk crystals exhibit Curie temperatures above 350 K but negligible room-temperature coercivity. When thinned below ∼100 nm, the coercive field is dramatically enhanced, reaching nearly 1 T at room temperature for in-plane fields—comparable to conventional hard magnets. Micromagnetic analysis reveals a crossover in magnetization reversal from domain-mediated processes in bulk samples to quasi-coherent rotation in thin flakes, driven by increased effective anisotropy and suppressed domain formation. This thickness-dependent transition enables tuning of magnetic hardness without chemical modification. Combined with high saturation magnetization and robust room-temperature performance, Fe 3 GaTe 2 emerges as a promising rare-earth-free material for spintronic applications. Its layered structure further allows integration into van der Waals heterostructures, where large in-plane coercivity can stabilize magnetic states against perturbations and interlayer coupling, offering potential for high-density nonvolatile memory and domain-wall-based devices.
Understanding hydrogen evolution reaction (HER) behaviors over two-dimensional transition-metal dichalcogenides (2D-TMDs) is critical for the development of nonprecious HER electrocatalysts with better activity. Here, in this work, by combining density functional theory calculations with microkinetic modeling, we thoroughly investigated the HER mechanism on 2D-TMDs. We find an important dependence of simulated cell size on the calculated hydrogen adsorption energy and the activation barrier for MoS 2 . Distinct from previous “H migration” mechanisms proposed for the Heyrovsky reaction, the rate-determining step for MoS 2 , we propose that the Mo site only serves as the stabilized transition state rather than H adsorption. In comparison to transition-metal electrocatalysts, we find that the activation barrier of the Heyrovsky reaction on 2D-TMDs scales with the hydrogen adsorption energy exactly as for transition metals except that all activation energies are displaced upward by ca. 0.4 eV. This higher Heyrovsky activation barrier is responsible for the substantially lower activity of 2D-TMDs. We further show that this higher activation barrier stems from the more positively charged adsorbed hydrogen on the chalcogenides interacting repulsively with the incoming proton. Based on these insights, we discuss potential strategies for the design of nonprecious HER catalysts with activity comparable to Pt.
Ultrafast stimuli can stabilize metastable states of matter inaccessible by equilibrium means. Establishing the spatiotemporal link between ultrafast excitation and metastability is crucial to understand these phenomena. Here, in this work, we utilize single-shot optical pump–X-ray probe measurements to capture snapshots of the emergence of a persistent polar vortex supercrystal in a heterostructure that hosts a fine balance between built-in electrostatic and elastic frustrations by design. By perturbing this balance with photoinduced charges, an initially heterogeneous mixture of polar phase disorders within a few picoseconds, leading to a state composed of disordered ferroelectric and suppressed vortex orders. On the picosecond–nanosecond timescales, transient labyrinthine fluctuations develop, accompanied by the recovery of the vortex order. On longer timescales, these fluctuations are progressively quenched by dynamical strain modulations, which drive the collective emergence of a single vortex supercrystal phase. Our results, corroborated by dynamical phase-field modelling, reveal non-equilibrium pathways following the ultrafast excitation of designer systems to persistent metastability.
Metabotropic γ-aminobutyric acid receptors (GABA B ) are involved in the modulation of synaptic responses in the central nervous system and have been implicated in neuropsychological conditions that range from addiction to psychosis. GABA B belongs to class C of the G-protein-coupled receptors, and its functional entity comprises an obligate heterodimer that is composed of the GB1 and GB2 subunits. Each subunit possesses an extracellular Venus flytrap domain, which is connected to a canonical seven-transmembrane domain. In this paper we present four cryo-electron microscopy structures of the human full-length GB1–GB2 heterodimer: one structure of its inactive apo state, two intermediate agonist-bound forms and an active form in which the heterodimer is bound to an agonist and a positive allosteric modulator. The structures reveal substantial differences, which shed light on the complex motions that underlie the unique activation mechanism of GABA B . Our results show that agonist binding leads to the closure of the Venus flytrap domain of GB1, triggering a series of transitions, first rearranging and bringing the two transmembrane domains into close contact along transmembrane helix 6 and ultimately inducing conformational rearrangements in the GB2 transmembrane domain via a lever-like mechanism to initiate downstream signalling. This active state is stabilized by a positive allosteric modulator binding at the transmembrane dimerization interface.