Scattering Wave Vector Research Articles

Dipolar Spin Ice Regime Proximate to an All-In-All-Out Néel Ground State in the Dipolar-Octupolar Pyrochlore Ce2Sn2O7

The dipolar-octupolar (DO) pyrochlores, R2M2O7 (R=Ce,Sm,Nd), are key players in the search for realizable novel quantum spin liquid (QSL) states as a large parameter space within the DO pyrochlore phase diagram is theorized to host QSL states of both dipolar and octupolar nature. New single crystals and powders of Ce2Sn2O7, synthesized by hydrothermal techniques, present an opportunity for a new characterization of the exchange parameters in Ce2Sn2O7 using the near-neighbor XYZ model Hamiltonian associated with DO pyrochlores. Utilizing quantum numerical linked cluster expansion fits to heat capacity and magnetic susceptibility measurements, and classical Monte Carlo calculations to the diffuse neutron diffraction of the new hydrothermally grown Ce2Sn2O7 samples, we place Ce2Sn2O7’s ground state within the ordered dipolar all-in-all-out (AIAO) Néel phase, with quantum Monte Carlo calculations showing a transition to long-range order at temperatures below those accessed experimentally. Indeed, our new neutron diffraction measurements on the hydrothermally grown Ce2Sn2O7 powders show a broad signal at low scattering wave vectors, reminiscent of a spin ice, in striking contrast from previous powder neutron diffraction on samples grown from solid-state synthesis, which found diffuse scattering at high scattering wave vectors associated with magnetic and suggested an octupolar quantum spin ice state. We conclude that new hydrothermally grown Ce2Sn2O7 samples host a finite-temperature proximate dipolar spin ice phase, above the expected transition to AIAO Néel order. Published by the American Physical Society 2024

Engineering Ultrasoft Interactions in Stiff All-DNA Dendrimers by Site-Specific Control of Scaffold Flexibility.

A combined experimental and theoretical study of the structural correlations in moderately concentrated suspensions of all-DNA dendrimers of the second generation (G2) with controlled scaffold rigidity is reported here. Small-angle X-ray scattering experiments in concentrated aqueous saline solutions of stiff all-DNA G2 dendritic constructs reveal a novel anomalous liquid-like phase behavior which is reflected in the calculated structure factors as a two-step increase at low scattering wave vectors. By developing a new design strategy for adjusting the particle's internal flexibility based on site-selective incorporation of single-stranded DNA linkers into the dendritic scaffold, it is shown that this unconventional type of self-organization is strongly contingent on the dendrimer's stiffness. A comprehensive computer simulation study employing dendritic models with different levels of coarse-graining, and two theoretical approaches based on effective, pair-potential interactions, remarkably confirmed the origin of this unusual liquid-like behavior. The results demonstrate that the precise control of the internal structure of the dendritic scaffold conferred by the DNA can be potentially used to engineer a rich palette of novel ultrasoft interaction potentials that could offer a route for directed self-assembly of intriguing soft matter phases and experimental realizations of a host of unusual phenomena theoretically predicted for ultrasoft interactingsystems.

Hydrogen-bond network in an equimolar acetic acid–water mixture as studied by neutron scattering and density functional theory

The present study explores the hydrogen-bond network in an equimolar mixture of acetic acid and water (AA–W). The investigation was conducted using a combination of neutron scattering and Density Functional Theory (DFT). New neutron scattering data at large scattering wave vectors were analyzed to determine the total structure factor SM(q) and the molecular form factor F1(q) of the system. DFT calculations using the 6-311++G(d, p) basis set were performed to optimize the monomers and various AA–W H-bonded clusters, including one acetic acid (AA) molecule connected to one, two, and three water molecules. Consequently, three dimers, three trimers, and one tetramer have been considered in order to describe the local order in the mixture. In addition, this study focused on the H-bond interactions in the most probable clusters in the solution, using the natural bond orbital and the atoms in molecules analyses. Our analysis particularly shows that stronger H-bond interactions occur in the ring structures.

On the Problem of Observing the Maximum of a Superposition Wave Field A.

The well-known Laue condition determining the intensity maximums of diffracted on an ideal crystal structure plane wave is discussed. It is proved that the Laue conditions, which are restrictions imposed on the values of the scattering wave vector, is more correctly to be considered as a pair of two conditions. The first conditions relate to the wave vector of an incident wave and the second conditions relate to the wave vector of an observation direction. In other words, to observe the maximums, it is not enough that only the difference (the scattering wave vector) of these two vectors satisfies the Laue condition. To observe the maximums, it is necessary that each of these vectors separately, i.e. the wave vector of the incident wave and the wave vector of the observation direction, satisfy the Laue condition. It is shown that such a doubling of the maximums conditions leads to a decrease in the number of observed maximums compared to the condition imposed only on the scattering wave vector.

Fluctuations, structure, and size inside coacervates.

Aqueous solutions of oppositely charged macromolecules exhibit the ubiquitous phenomenon of coacervation. This subject is of considerable current interest due to numerous biotechnological applications of coacervates and the general premise of biomolecular condensates. Towards a theoretical foundation of structural features of coacervates, we present a field-theoretic treatment of coacervates formed by uniformly charged flexible polycations and polyanions in an electrolyte solution. We delineate different regimes of polymer concentration fluctuations and structural features of coacervates based on the concentrations of polycation and polyanion, salt concentration, and experimentally observable length scales. We present closed-form formulas for correlation length of polymer concentration fluctuations, scattering structure factor, and radius of gyration of a labelled polyelectrolyte chain inside a concentrated coacervate. Using random phase approximation suitable for concentrated polymer systems, we show that the inter-monomer electrostatic interaction is screened by interpenetration of all charged polymer chains and that the screening length depends on the individual concentrations of the polycation and the polyanion, as well as the salt concentration. Our calculations show that the scattering intensity decreases monotonically with scattering wave vector at higher salt concentrations, while it exhibits a peak at intermediate scattering wave vector at lower salt concentrations. Furthermore, we predict that the dependence of the radius of gyration of a labelled chain on its degree of polymerization generally obeys the Gaussian chain statistics. However, the chain is modestly swollen, the extent of which depending on polyelectrolyte composition, salt concentration, and the electrostatic features of the polycation and polyanion such as the degree of ionization.

THE PROBLEM OF OBSERVING THE MAXIMUM OF A SUPERPOSITION WAVE FIELD

The well-known Laue condition determining the intensity maximums of diffracted on an ideal crystal structure plane wave is discussed. Initially the consideration is performed for the near observation region and after that by means of applying the corresponding approximation the expression of superposition field is presented as a sum of plane waves. So, the description of the superposition field for the far observation region is made. It is proved that the Laue conditions, which are restrictions imposed on the values of the scattering wave vector, is more correctly to be considered as a pair of two conditions. The first condition relates to the wave vector of an incident wave and the second condition relates to the wave vector of an observation direction. In other words, to observe the maximums, it is not enough when only the difference (the scattering wave vector) of these two vectors satisfies the Laue condition. To observe the maximums, it is necessary that each of these vectors separately, i.e. the wave vector of the incident wave and the wave vector of the observation direction satisfy the Laue condition. It is shown that such a doubling of the maximum conditions leads to a decrease in the number of the observed maximums compared to the condition imposed only on the scattering wave vector. Within the framework of the previously developed method, a number of formerly known results related to the kinematic theory of diffraction of a plane wave by an ideal crystal structure were reproduced. It is assumed that the generation of secondary waves of each atom of the crystal is provoked by the presence in the volume of the crystal of a primary field, which in Fraunhofer formulation is considered in the form of a plane and time-harmonic wave. The intensity distribution, as well as the positions of the maxima of the diffraction pattern, was studied depending on the spatial parameters of the crystal lattice.

Scattering signatures of invasion percolation.

Motivated by recent experiments, we investigate the scattering properties of percolation clusters generated by numerical simulations on a three-dimensional cubic lattice. Individual clusters of given size are shown to present a fractal structure up to a scale of order of their extent, even far away from the percolation threshold p_{c}. The influence of intercluster correlations on the structure factor of assemblies of clusters selected by an invasion phenomenon is studied in detail. For invasion from bulk germs, we show that the scattering properties are determined by three length scales, the correlation length ξ, the average distance between germs d_{g}, and the spatial scale probed by scattering, set by the inverse of the scattering wave vector Q. At small scales, we find that the fractal structure of individual clusters is retained, the structure factor decaying as Q^{-d_{f}}. At large scales, the structure factor tends to a limit, set by the smaller of ξ and d_{g}, both below and above p_{c}. We propose approximate expressions reproducing the simulated structure factor for arbitrary ξ, d_{g}, and Q, and illustrate how they can be used to avoid to resort to costly numerical simulations. For invasion from surfaces, we find that, at p_{c}, the structure factor behaves as Q^{-d_{f}} at all Q, i.e., the fractal structure is retained at arbitrarily large scales. Results away from p_{c} are compared to the case of bulk germs. Our results can be applied to discuss light or neutrons scattering experiments on percolating systems. This is illustrated in the context of evaporation from porous materials.

Electronic nature of the pseudogap in electron-doped Sr2IrO4

In high-temperature (Tc) cuprate superconductors, many exotic phenomena are rooted in the enigmatic pseudogap state, which has been interpreted as consisting of preformed Cooper pairs or competing orders or a combination thereof. Observation of pseudogap phenomenologically in electron-doped Sr2IrO4—the 5d electron counterpart of the cuprates, has spurred intense interest in the strontium iridates as a testbed for exploring the exotic physics of the cuprates. Here, we examine the pseudogap state of electron-doped Sr2IrO4 by angle-resolved photoemission spectroscopy (ARPES) and parallel theoretical modeling. Our analysis demonstrates that the pseudogap state of Sr2IrO4 appears without breaking the particle–hole symmetry or inducing spectral broadening which are telltale signatures of competing orders in the cuprates. We find quasiparticle dispersion and its temperature dependence in the pseudogap state of Sr2IrO4 to point to an electronic order with a zero scattering wave vector and limited correlation length. Particle–hole symmetric preformed Cooper pairs are discussed as a viable mechanism for such an electronic order. The potential roles of incommensurate density waves are also discussed.

Oxygen vacancy-rich ultrafine CoP/Co3O4 nanoparticles as high-efficiency trifunctional electrocatalyst

Exploring highly stable and active electrocatalyst for hydrogen evolution, oxygen evolution and oxygen reduction reactions is an unremitting target for the supply and storage of sustainable energies. Here, we report a type of oxygen vacancy-rich nanostructure in which uniform CoP/Co3O4 nanoparticles (NPs) are coated and dispersed on an amorphous carbon network (pPVP). This hybrid nanostructure labeled as ‘CoP/Co3O4-fC-pPVP’ is synthesized by a pyrolysis-oxidation-phosphatization strategy, which can accelerate charge transfer and improve carrier separation owing to introducing copious oxygen vacancy. Benefiting from the modulated electronic structure and advantage of interfacial and synergistic effect among active CoP, Co3O4 and pPVP layer, the CoP/Co3O4-fC-pPVP hybrid structure exhibits excellent trifunctional electrocatalytic performance. The scattering wave vector (q) of the samples before and after catalytic reactions remains unchanged from small angle X-ray scattering (SAXS) tests, indicating the stable phase structure. As for CoP/Co3O4-fC-pPVP, only a very low potential of 1.585 V is needed to reach 10 mA cm−2 in the overall water splitting process. Furthermore, the peak power density of CoP/Co3O4-fC-pPVP-based Zn-air batteries reaches 154 mW cm−2 and the charge-discharge voltage gap almost maintains the initial overpotential after 727 h cycle test.

Enhancement of superconductivity by electronic nematicity in cuprate superconductors

ABSTRACT The cuprate superconductors are characterised by numerous ordering tendencies, with the electronically nematic order being the most distinct form of order. Here the intertwinement of the electronic nematicity with superconductivity in cuprate superconductors is studied based on the kinetic-energy-driven superconductivity. It is shown that the optimised takes a dome-like shape with the weak and strong strength regions on each side of the optimal strength of the electronic nematicity, where the optimised reaches its maximum. This dome-like shape nematic-order strength dependence of thus indicates that the electronic nematicity enhances superconductivity. Moreover, this nematic order induces the anisotropy of the electron Fermi surface, where although the original electron Fermi surface contour with the four-fold rotation symmetry is broken up into that with a residual twofold rotation symmetry, this electron Fermi surface contour with the twofold rotation symmetry still is truncated to form the disconnected Fermi arcs with the most spectral weight that locates at around the tips of the Fermi arcs. Concomitantly, these tips of the Fermi arcs connected by the scattering wave vectors construct an octet scattering model, however, the partial scattering wave vectors and their respective symmetry-corresponding partners occur with unequal amplitudes, leading to these electronically ordered states being broken both rotation and translation symmetries. As a natural consequence, the electronic structure is inequivalent between the and directions in momentum space. These anisotropic features of the electronic structure are also confirmed via the result of the autocorrelation of the single-particle excitation spectra, where the breaking of the rotation symmetry is verified by the inequivalence on the average of the electronic structure at the two Bragg scattering sites. The theory also indicates that the order parameter of the electronic nematicity achieves its maximum in the characteristic energy and then decreases rapidly as the energy moves away from the characteristic energy.

Intermolecular interactions in an equimolar methanol-water mixture: Neutron scattering, DFT, NBO, AIM, and MD investigations

A detailed analysis of equimolar methanol–water (MeW) liquid structure at 298 K and atmospheric pressure is performed using neutron scattering, Density Functional Theory (DFT) calculation and Molecular Dynamics (MD) simulations. New neutron scattering data at large scattering wave vectors were explored to determine the structure factor SMq , the molecular form factor F1q and the intermolecular pair correlation function gLr . To describe the local order of the mixture, a large variety of H-bonded clusters has been optimized using DFT calculation with the 6–311++ G(d, p) basis. Experimental data were interpreted in terms of two cyclic trimers involving respectively 2Me-1W and 2W-1Me molecules. A detailed study of the H-bond interactions in the most probable clusters in the mixture was performed using Natural Bond orbital (NBO) and Atomsin Molecules (AIM) analyses. To have more structural information about the mixture at medium and large distances as well as the dynamic of molecules in solution, MD simulations were performed using three force fields. Our results show that several H-bonds between water molecules and between methanol ones are broken in favor of the formation of water-methanol H-bonded clusters. The self-diffusion coefficients of monomers decrease when going from the pure to the mixed states.

Three-dimensional transfer function of optical microscopes in reflection mode.

Three-dimensional (3D) transfer functions build the basis for a comprehensive characterization of optical imaging systems in the spatial frequency domain. Utilizing the projection-slice theorem, the 2D modulation transfer function of an incoherent imaging system can be derived from a 3D transfer function by integration with respect to the axial spatial frequency. For a diffraction limited microscope with homogeneous incoherent pupil illumination, the modulation transfer function equals the 2D autocorrelation function of a circular disc. However, until now to the best of our knowledge no 3D transfer function has been published, which exactly leads to the 2D modulation transfer function of a diffraction limited microscope in reflection mode. In this article, we derive a formula, which after integration with respect to the axial spatial frequency coordinate perfectly fits to the diffraction limited 2D modulation transfer function. The inverse three-dimensional Fourier transform of the 3D transfer function results in a complex-valued 3D point spread function, from which the depth of field, the lateral resolution and, in addition, the corresponding 3D point spread function of both, a conventional and an interference microscope, can beobtained.

The fractal characteristics of atmospheric coated soot: Implication for morphological analysis

In this work, we have numerically investigated the variation of fractal characteristics of soot particles as soot is coated. We found that the ideal fractal law can fit the morphologies of coated soot only when the radius of gyration (Rg) of coated soot is identical to that of the soot core. In that case, the fractal dimension (Df) of coated soot is close to that of the soot core, which can explain why the unchanged fractal dimension was observed by the previous study as soot was evenly coated. As the voids among monomers is commonly filled firstly, the Rg of coated soot obtained from the two-dimensional (2D) method would be close to that of the soot core, so the measured fractal dimension would be close to that of the soot core. Our results also show that the fractal parameters of coated soot at different size scales can be varied, so the ideal fractal law is difficult to fit the structures of unevenly coated soot universally. Besides, we also found that the effective fractal dimension can increase as soot is unevenly coated. The results of the Q-space analysis show that as soot particles are unevenly coated, the power-law exponent of the structure factor (S(q)) versus the scattering wave vector (q) tends to -4 for heavily coated soot. This means that heavily, unevenly coated soot exhibits the characteristics of nearly spherical particles.

A mathematical and numerical framework for gradient meta-surfaces built upon periodically repeating arrays of Helmholtz resonators

In this paper a mathematical model is given for the scattering of an incident wave from a surface covered with microscopic small Helmholtz resonators, which are cavities with small openings. More precisely, the surface is built upon a finite number of Helmholtz resonators in a unit cell and that unit cell is repeated periodically. To solve the scattering problem, the mathematical framework elaborated in Ammari et al. (2019) is used. The main result is an approximate formula for the scattered wave in terms of the lengths of the openings. Our framework provides analytic expressions for the scattering wave vector and angle and the phase-shift. It justifies the apparent absorption. Moreover, it shows that at specific lengths for the openings and a specific frequency there is an abrupt shift of the phase of the scattered wave due to the subwavelength resonances of the Helmholtz resonators. A numerically fast implementation is given to identify a region of those specific values of the openings and the frequencies.

Phase-sensitive determination of nodal d -wave order parameter in single-band and multiband superconductors

Determining the exact pairing symmetry of the superconducting order parameter in candidate unconventional superconductors remains an important challenge. Recently, a new method, based on phase sensitive quasiparticle interference measurements, was developed to identify gap sign changes in isotropic multiband systems. Here we extend this approach to the single-band and multiband nodal $d$-wave superconducting cases relevant, respectively, for the cuprates and likely for the infinite-layer nickelate superconductors. Combining analytical and numerical calculations, we show that the antisymmetrized correction to the tunneling density of states due to nonmagnetic impurities in the Born limit and at intermediate-scattering strength shows characteristic features for sign-changing and sign-preserving scattering wave vectors, as well as for the momentum-integrated quantity. Furthermore, using a realistic approach accounting for the Wannier orbitals, we model scanning tunneling microscopy data of ${\text{Bi}}_{2}{\text{Sr}}_{2}{\text{CaCu}}_{2}{\text{O}}_{8+\ensuremath{\delta}}$, which should allow the comparison of our theory with experimental data.

Renormalization of electrons in bilayer cuprate superconductors

Cuprate superconductors have a layered structure, and then the physical properties are significantly enriched when two or more two copper-oxide layers are contained in a unit cell. Here the characteristic features of the renormalization of the electrons in the bilayer cuprate superconductors are investigated within the framework of the kinetic-energy driven superconducting mechanism. It is shown that the electron quasiparticle excitation spectrum is split into its bonding and antibonding components due to the presence of the bilayer coupling, with each component that is independent. However, in the underdoped and optimally doped regimes, although the bonding and antibonding electron Fermi surface contours deriving from the bonding and antibonding layers are truncated to form the disconnected bonding and antibonding Fermi arcs, almost all spectral weights in the bonding and antibonding Fermi arcs are reduced to the tips of the bonding and antibonding Fermi arcs, which in this case coincide with the bonding and antibonding hot spots. These hot spots connected by the scattering wave vectors qi construct an octet scattering model, and then the enhancement of the quasiparticle scattering processes with the scattering wave vectors qi is confirmed via the result of the autocorrelation of the electron quasiparticle excitation spectral intensities. Moreover, the peak-dip-hump structure developed in each component of the electron quasiparticle excitation spectrum along the corresponding electron Fermi surface is directly related with the peak structure in the quasiparticle scattering rate except for at around the hot spots, where the peak-dip-hump structure is caused mainly by the pure bilayer coupling. Although the kink in the electron quasiparticle dispersion is present all around the electron Fermi surface, when the momentum moves away from the node to the antinode, the kink energy smoothly decreases, while the dispersion kink becomes more pronounced, and in particular, near the cut close to the antinode, develops into a break separating of the fasting dispersing high-energy part of the electron quasiparticle excitation spectrum from the slower dispersing low-energy part. By comparing with the corresponding results in the single-layer case, the theory also indicates that the characteristic features of the renormalization of the electrons are particularly obvious due to the presence of the bilayer coupling.

ARPES Autocorrelation in Electron-Doped Cuprate Superconductors

The angle-resolved photoemission spectroscopy (ARPES) autocorrelation in the electron-doped cuprate superconductors is studied based on the kinetic-energy driven superconducting (SC) mechanism. It is shown that the strong electron correlation induces the electron Fermi surface (EFS) reconstruction, where the most of the quasiparticles locate at around the hot spots on EFS, and then these hot spots connected by the scattering wave vectors ${\bf q}_{i}$ construct an {\it octet} scattering model. In a striking analogy to the hole-doped case, the sharp ARPES autocorrelation peaks are directly correlated with the scattering wave vectors ${\bf q}_{i}$, and are weakly dispersive in momentum space. However, in a clear contrast to the hole-doped counterparts, the position of the ARPES autocorrelation peaks move toward to the opposite direction with the increase of doping. The theory also indicates that there is an intrinsic connection between the ARPES autocorrelation and quasiparticle scattering interference (QSI) in the electron-doped cuprate superconductors.

Short-Range Antiferromagnetic Correlation Effect on Conduction Electrons in Two-Dimensional Strongly Correlated Electron Systems

We investigate magnetic polarons in two-dimensional strongly correlated electron systems, where conduction electrons interact with antiferromagnetically interacting localized spins. Starting from a basic model, we derive a simplified model with the help of spin Green's function and a perturbation analysis. A strong coupling analysis is applied to the model, where the sum of the scattering wave vectors is approximated to be $(\pi,\pi)$ or zero, using the equation of motion for the conduction electron Green's function, and we discuss the pseudogap like behavior associated with the suppression of the quasiparticle weights and the transition from the large magnetic polaron to the small magnetic polaron. In the antiferromagnetic long-range ordered state, the spectral weight of the conduction electrons has a form of broad humps due to Franck-Condon broadening associated with the multi-magnon scattering. The band folding feature due to the $(\pi,\pi)$ scattering disappears as we increase the number of the magnons involved in the multi-magnon scattering. It is crucial to include long-range antiferromagnetic correlations as well as dumping of magnons.

Autocorrelation of quasiparticle spectral intensities and its connection with quasiparticle scattering interference in cuprate superconductors

ABSTRACTThe quasiparticle excitation is one of the most fundamental and ubiquitous physical observables in cuprate superconductors, carrying information about the bosonic glue forming electron pairs. Here the autocorrelation of the quasiparticle excitation spectral intensities in cuprate superconductors and its connection with the quasiparticle scattering interference are investigated based on the framework of the kinetic-energy driven superconducting mechanism by taking into account the pseudogap effect. It is shown that the octet scattering model of the quasiparticle scattering processes with the scattering wave vectors connecting the hot spots on the constant energy contours is intrinsically related to the emergence of the highly anisotropic momentum-dependence of the pseudogap. Concomitantly, the sharp peaks in the autocorrelation of the quasiparticle excitation spectral intensities with the wave vectors are directly correlated to the regions of the highest joint density of states. Moreover, the momentum-space structure of the autocorrelation patterns of the quasiparticle excitation spectral intensities is well consistent with the momentum-space structure of the quasiparticle scattering interference patterns observed from Fourier-transform scanning tunnelling spectroscopy experiments. The theory therefore confirms an intimate connection between the angle-resolved photoemission spectroscopy autocorrelation and quasiparticle scattering interference in cuprate superconductors.

Application of the scaling approach to particles having simple, fundamental shapes, in the Rayleigh–Debye–Gans diffraction limit

Presented is a scaling approach for understanding features, such as power laws and crossover points, of the light scattered in the m → 1, ρ = 2kRveq|m − 1| < 1, Rayleigh–Debye–Gans diffraction limit. The scaling approach is based on comparison of the length scale of the scattering, which is the inverse of the scattering wave vector, and the various length scales of the scattering entity. It will be shown that the scaling approach correctly predicts the exponents of the power law regions and the locations of the first and second Guinier regimes which define the boundaries of the power laws. Furthermore, the scaling approach yields a semi-quantitative prediction of the coefficients of the power laws. These Guinier boundaries and power law coefficients are described by a single parameter, the aspect ratio of the scattering object.