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At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Scattering Matrix Determination in Crystalline Materials from 4D Scanning Transmission Electron Microscopy at a Single Defocus Value

Recent work has revived interest in the scattering matrix formulation of electron scattering in transmission electron microscopy as a stepping stone toward atomic-resolution structure determination in the presence of multiple scattering. Here, we discuss ways of visualizing the scattering matrix that make its properties clear. Through a simulation-based case study incorporating shot noise, we shown how regularizing on this continuity enables the scattering matrix to be reconstructed from 4D scanning transmission electron microscopy (STEM) measurements from a single defocus value. Intriguingly, for crystalline samples, this process also yields the sample thickness to nanometer accuracy with no a priori knowledge about the sample structure. The reconstruction quality is gauged by using the reconstructed scattering matrix to simulate STEM images at defocus values different from that of the data from which it was reconstructed.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Scattering matrix pole expansions for complex wave numbers in R -matrix theory

In this followup article to Ducru et al., we establish new results on scattering matrix pole expansions for complex wave numbers in R-matrix theory. In the past, two branches of theoretical formalisms emerged to describe the scattering matrix in nuclear physics: R-matrix theory and pole expansions. The two have been quite isolated from one another. Recently, our study of Brune's alternative parametrization of R-matrix theory has shown the need to extend the scattering matrix (and the underlying R-matrix operators) to complex wave numbers. Two competing ways of doing so have emerged from a historical ambiguity in the definitions of the shift S and penetration P functions: the legacy Lane and Thomas's “force closure” approach versus analytic continuation (which is the standard in mathematical physics). The R-matrix community has not yet come to a consensus as to which to adopt for evaluations in standard nuclear data libraries, such as ENDF. Here, in this article, we argue in favor of analytic continuation of R-matrix operators. We bridge R-matrix theory with the Humblet-Rosenfeld pole expansions, and discover new properties of the Siegert-Humblet radioactive poles and widths, including their invariance properties to changes in channel radii a c . We then show that analytic continuation of R-matrix operators preserves important physical and mathematical properties of the scattering matrix—canceling spurious poles and guaranteeing generalized unitarity—while still being able to close channels below thresholds.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2025

Quantitative Structure Determination from Experimental Four-Dimensional Scanning Transmission Electron Microscopy via the Scattering Matrix

Considerable inroads have recently been made on algorithms to determine the sample potential from four-dimensional scanning transmission electron microscopy data from thick samples where multiple scattering cannot be neglected. This paper further develops the scattering matrix approach to such structure determination. Through simulation, we demonstrate how this approach can be modified to better handle partial spatial coherence, unknown probe defocus, and information from the dark field region. By combining these developments we reconstruct the electrostatic potential of a monolithic SrTiO 3 crystal showing good quantitative agreement with the expected structure.

4D STEM↗
DOE OSTI2021

Geometry and entanglement in the scattering matrix

A formulation of nucleon–nucleon scattering is developed in which the S-matrix, rather than an effective-field theory (EFT) action, is the fundamental object. Spacetime plays no role in this description: the S-matrix is a trajectory that moves between RG fixed points in a compact theory space defined by unitarity. This theory space has a natural operator definition, and a geometric embedding of the unitarity constraints in four-dimensional Euclidean space yields a flat torus, which serves as the stage on which the S-matrix propagates. Trajectories with vanishing entanglement are special geodesics between RG fixed points on the flat torus, while entanglement is driven by an external potential. The system of equations describing S-matrix trajectories is in general complicated, however the very-low-energy S-matrix –that appears at leading-order in the EFT description– possesses a UV/IR conformal invariance which renders the system of equations integrable, and completely determines the potential. In this geometric viewpoint, inelasticity is in correspondence with the radius of a three-dimensional hyperbolic space whose two-dimensional boundary is the flat torus. This space has a singularity at vanishing radius, corresponding to maximal violation of unitarity. The trajectory on the flat torus boundary can be explicitly constructed from a bulk trajectory with a quantifiable error, providing a simple example of a holographic quantum error correcting code.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Phenomenological R -Matrix parameterization of direct, doorway, and compound nuclear reactions [Abstract]

Although formal expressions for scattering matrix accounting for direct, doorway, and compound nuclear (CN) resonant reactions have been derived several decades ago in both the transition ( T -)matrix formalism and the reactance ( K -)matrix formalism, the absence of corresponding expressions in phenomenological R -matrix formalism has limited the application of the latter to CN resonant reactions only. We remove this limitation by parameterizing direct, doorway, and CN resonant reactions in a phenomenological R -matrix scattering matrix, and provide a parameterization for a corresponding Reich-Moore approximation of eliminated capture channels. Direct reactions induce (previously neglected) mixing among the incoming or outgoing R -matrix channel wave functions, parameterized by real and orthonormal channel-rotation matrix, M , whereby the original scattering matrix U is transformed into M T UM . Any real and orthonormal matrix, M , can be equivalently expressed as e η , where η is a real and skew-symmetric 2 rotation-generating matrix that subsequently yields a more intuitive parameterization of eliminated direct capture reactions in Reich-Moore approximation. A phenomenological R -matrix parameterization of doorway reactions is inferred by equating the expression for reactance ( K -)matrix, given in terms of Brune’s alternative R -matrix parameterization, to a corresponding expression derived using Feshbach’s projection operator formalism. Assuming that all doorway states, just like CN states, are confined within spheres defined by R -matrix channel radii, a new R -matrix-like term induced by doorway states is gleaned, wherein each doorway state is parameterized by its energy, width, and the strength of its coupling to each CN state. Since a Reich-Moore approximation for retained-channel scattering matrix ought to approximate the effect of eliminated capture channels taking place via direct, doorway, or CN reactions, each of the three kinds of reactions contributing to the capture entails a corresponding Reich-Moore parameterization in a first-order approximation: direct contribution is parameterized by introducing finite diagonal elements of a retained-channel rotation-generating matrix, doorway contribution is parameterized by doorway capture widths, while CN contribution is parameterized by conventional Reich-Moore capture widths. We will present evidence of direct and doorway reactions observed in recent measurements of resolved resonance cross sections at the Gaerttner LINAC Center at Rensselaer Polytechnic Institute, and will outline a path for implementing this new R -matrix parameterization into the SAMMY nuclear data evaluation code.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2025

Competing ionization and dissociation: Extension of the energy-dependent frame transformation to the gerade symmetry of H 2

This article solves two major tasks that frequently arise in the theory of electron collisions with a target molecular cation. First, it extends the energy-dependent frame transformation (EDFT) treatment, which is needed to map fixed-nuclei electron-molecule scattering matrices into an energy-dependent laboratory-frame scattering matrix with vibrational channel indices. The EDFT mapping can now be carried out even when the target molecule possesses multiple low-energy potential curves, significantly transcending previous applications. Second, it implements a method to extract the rest of the full laboratory-frame scattering matrix, i.e., the columns and rows describing input and/or output dissociation channels. The treatment is benchmarked in this article against the essentially exact solution of a refined two-dimensional model of the singlet gerade Σ symmetry of H 2 . Our tests demonstrate that the theory accurately maps fixed-nuclei scattering information, of the type provided by existing electron-molecule computer codes, into a laboratory-frame scattering matrix that includes both ionization and dissociation. Furthermore, this treatment can provide a general framework applicable to a broad class of electron collision processes involving diatomic target ions, suitable for an accurate description of challenging processes such as dissociative recombination.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2024

A 2D chiral microcavity based on apparent circular dichroism

Abstract Engineering asymmetric transmission between left-handed and right-handed circularly polarized light in planar Fabry–Pérot (FP) microcavities would enable a variety of chiral light-matter phenomena, with applications in spintronics, polaritonics, and chiral lasing. Such symmetry breaking, however, generally requires Faraday rotators or nanofabricated polarization-preserving mirrors. We present a simple solution requiring no nanofabrication to induce asymmetric transmission in FP microcavities, preserving low mode volumes by embedding organic thin films exhibiting apparent circular dichroism (ACD); an optical phenomenon based on 2D chirality. Importantly, ACD interactions are opposite for counter-propagating light. Consequently, we demonstrated asymmetric transmission of cavity modes over an order of magnitude larger than that of the isolated thin film. Through circular dichroism spectroscopy, Mueller matrix ellipsometry, and simulation using theoretical scattering matrix methods, we characterize the spatial, spectral, and angular chiroptical responses of this 2D chiral microcavity.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

OLEDs on planarized light outcoupling-enhancing structures in plastic

Light extraction from OLEDs remains a challenge. While consumer demand for OLEDs in display technology continues to grow as prices decline, commercial use of OLEDs in solid state lighting (SSL) applications is lagging due to low light extraction, which results in low efficiency. Previous studies have been directed toward increasing the light extraction factor η out , but cost effective approaches that will enable high throughput and potential upscaling, as well as elucidation of the extraction process, are still lagging. One promising approach is the use of buried light extraction enhancing patterns that are planarized with a high refractive index (RI) layer. When adding substrate mode extracting means, the highest external quantum efficiencies (EQEs) were achieved using a complex approach of planarized vacuum nano holes. Here we present η out -enhancing planarized extraction structures (PES) in plastic. While plastic substrates currently present long-term stability issues and other drawbacks, as we show, they provide a tool for simple, inexpensive, and rapid generation of various enhancing structures that importantly can be transferred to the preferred rigid and flexible glass substrates. Moreover, plastic substrates are attractive for biomedical applications. The successful structures we present are easily scalable periodic corrugations, e.g., with pitch a ~ 4.25 µm and pitch/depth ratio a/h ~2.4 planarized by a layer of RI ~1.9, resulting in maximal EQEs exceeding 60% for a green OLED and 48.5% for a white OLED. Comparable increased EQEs were achieved for structures with a ~ 15 and 16 µm, and a/h ~ 2.1 and 4, respectively. Enhanced extraction was also observed with a very simply fabricated quasiperiodic nanohole array, and surprisingly, with a random shallow design. The latter is at variance with simulations based on diffraction only. Results are discussed in terms of a, h, and structural parameters together with scattering matrix simulations to assess the effect of various PES parameters and the nanoparticle-embedded planarizing layer on η out . The experiments and simulations indicate contributions of diffraction, reflection, and scattering to EQE enhancement.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Resolution of Virtual Depth Sectioning from Four-Dimensional Scanning Transmission Electron Microscopy

Abstract One approach to three-dimensional structure determination using the wealth of scattering data in four-dimensional (4D) scanning transmission electron microscopy (STEM) is the parallax method proposed by Ophus et al. (2019. Advanced phase reconstruction methods enabled by 4D scanning transmission electron microscopy, Microsc Microanal25, 10–11), which determines the scattering matrix and uses it to synthesize a virtual depth-sectioning reconstruction of the sample structure. Drawing on an equivalence with a hypothetical confocal imaging mode, we derive contrast transfer and point spread functions for this parallax method applied to weakly scattering objects, showing them identical to earlier depth-sectioning STEM modes when only bright field signal is used, but that improved depth resolution is possible if dark field signal can be used. Through a simulation-based study of doped Si, we show that this depth resolution is preserved for thicker samples, explore the impact of shot noise on the parallax reconstructions, discuss challenges to making use of dark field signal, and identify cases where the interpretation of the parallax reconstruction breaks down.

3D imaging↗
DOE OSTI2020

Probing exciton/exciton interactions with entangled photons: Theory

Quantum entangled photons provide a sensitive probe of many-body interactions and offer a unique experimental portal for quantifying many-body correlations in a material system. In this paper, we present a theoretical demonstration of how photon–photon entanglement can be generated via interactions between coupled qubits. Here, we develop a model for the scattering of an entangled pair of photons from a molecular dimer. We develop a diagrammatic theory for the scattering matrix and show that one can correlate the von Neumann entropy of the outgoing bi-photon wave function with exciton exchange and repulsion interactions. Finally, we conclude by discussing possible experimental scenarios for realizing these ideas.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

Causality and dimensionality in geometric scattering

We report the scattering matrix which describes low-energy, non-relativistic scattering of spin-1/2 fermions interacting via finite-range potentials can be obtained from a geometric action principle in which space and time do not appear explicitly. In the case of zero-range forces, causality leads to constraints on scattering trajectories in the geometric picture. The effect of spatial dimensionality is also investigated by considering scattering in two and three dimensions. In the geometric formulation it is found that dimensionality is encoded in the phase of the harmonic potential that appears in the geometric action.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Substrate effects on spin relaxation in two-dimensional Dirac materials with strong spin-orbit coupling

Understanding substrate effects on spin dynamics and relaxation is of key importance for spin-based information technologies. However, the key factors that determine such effects, in particular for materials with strong spin-orbit coupling (SOC), have not been well understood. Here we performed first-principles real-time density-matrix dynamics simulations with SOC and the electron phonon and electron-impurity scattering for spin lifetimes (τ s ) of supported/free-standing germanene, a prototypical strong SOC 2D Dirac material. We show that the effects of different substrates on τ s can surprisingly differ by two orders of magnitude. We find that substrate effects on τ s are closely related to substrate-induced modifications of the SOC-field anisotropy, which changes the spin flip scattering matrix elements. We propose a new electronic quantity, named spin-flip angle θ ↑↓ , to characterize spin relaxation through intervalley spin-flip scattering. We find that $τ^{-1}_s$ is approximately proportional to the averaged value of sin 2 (θ ↑↓ /2), which serves as a guiding parameter of controlling spin relaxation.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Shadow poles in the alternative parametrization of R-matrix theory

In this work, we discover new, hitherto unknown, shadow poles in Brune’s alternative parametrization of R-matrix theory [C. R. Brune, Phys. Rev. C 66, 044611 (2002)]. Where these poles are, and how many, depends on how one continues R-matrix operators to complex wavenumbers (specially the shift S and penetration P functions). This has little consequence for the exact R-matrix formalism (past the last energy threshold), as we show one can still always fully reconstruct the scattering matrix with only the previously known alternative parameters (poles and corresponding resonance widths), for which there were as many poles as the number of levels Nλ. However, we generalize the alternative parametrization to the Reich-Moore formalism, and show that the choice of continuation is now critical as it changes the alternative parameters values (poles and residue widths are now complex). In order to establish nuclear libraries with alternative parameters, the nuclear community will thus have to decide what convention to adopt. We argue in favor of analytical continuation (against the legacy Lane and Thomas approach) in a follow-up article [P. Ducru, Phys. Rev. C, submitted (2020)]. We observe the first evidence of shadow poles in the alternative parametrization of R-matrix theory in isotope xenon 134 Xe spin-parity group J π = 1=2 (–) , and show how they indeed depend on the choice of continuation to complex wavenumbers.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2023

Using angular two-point correlations to self-calibrate the photometric redshift distributions of DECaLS DR9

Calibrating the redshift distributions of photometric galaxy samples is essential in weak lensing studies. The self-calibration method combines angular auto- and cross-correlations between galaxies in multiple photometric redshift (photo-z) bins to reconstruct the scattering rates matrix between redshift bins. In this paper, we test a recently proposed self-calibration algorithm using the DECaLS Data Release 9 and investigate to what extent the scattering rates are determined. We first mitigate the spurious angular correlations due to imaging systematics by a machine learning based method. We then improve the algorithm for χ 2 minimization and error estimation. Finally, we solve for the scattering matrices, carry out a series of consistency tests, and find reasonable agreements: (1) finer photo-z bins return a high-resolution scattering matrix, and it is broadly consistent with the low-resolution matrix from wider bins; (2) the scattering matrix from the Northern Galactic Cap is almost identical to that from Southern Galactic Cap; (3) the scattering matrices are in reasonable agreement with those constructed from the power spectrum and the weighted spectroscopic subsample. We also evaluate the impact of cosmic magnification. Although it changes little the diagonal elements of the scattering matrix, it affects the off-diagonals significantly. The scattering matrix also shows some dependence on scale cut of input correlations, which may be related to a known numerical degeneracy between certain scattering pairs. In conclusion, this work demonstrates the feasibility of the self-calibration method in real data and provides a practical alternative to calibrate the redshift distributions of photometric samples.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2021

Windowed multipole representation of R -matrix cross sections

Nuclear cross sections are basic inputs to any nuclear computation. Campaigns of experiments are fitted with the parametric R-matrix model of quantum nuclear interactions, and the resulting cross sections are documented—both pointwise and as resonance parameters (with uncertainties)—in standard evaluated nuclear data libraries (ENDF, JEFF, BROND, JENDL, CENDL, TENDL): these constitute our common knowledge of fundamental low-energy nuclear cross sections. In the past decade, a collaborative effort has been deployed to establish a new nuclear cross-section library format—the Windowed Multipole Library—with the goal of considerably reducing the computational cost of cross-section calculations in nuclear transport simulations. This work lays the theoretical foundations underpinning these efforts. From general R-matrix scattering theory, we derive the windowed multipole representation of nuclear cross sections. Though physically and mathematically equivalent to R-matrix cross sections, the windowed multipole representation is particularly well suited for subsequent temperature treatment of angle-integrated cross sections, in particular Doppler broadening, which is the averaging of cross sections over the thermal motion of the target atoms. Doppler broadening is of critical importance in neutron transport applications, as it ensures the stability of many nuclear reactors (negative thermal reactivity). Yet, Doppler broadening of nuclear cross sections has been a considerable bottleneck for nuclear transport computations, often requiring memory-costly pretabulations. We show that the windowed multipole representation can perform accurate Doppler broadening analytically (up to the first reaction threshold), from which we derive cross-section temperature derivatives to any order—all computable on the fly (without precalculations stored in memory). Furthermore, we here establish a way of converting the R-matrix resonance parameters uncertainty (covariance matrices) into windowed multipole parameters uncertainty. We show that generating stochastic nuclear cross sections by sampling from the resulting windowed multipole covariance matrix can reproduce the cross-section uncertainty in the original nuclear data file. The windowed multipole representation is therefore a novel nuclear physics formalism able to generate Doppler broadened stochastic nuclear cross sections on the fly, unlocking breakthrough computational gains for nuclear computations. Through this foundational paper, we hope to make the windowed multipole representation accessible, reproducible, and usable for the nuclear physics community, as well as provide the theoretical basis for future research on expanding its capabilities.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2021

S-matrix bootstrap in 3+1 dimensions: regularization and dual convex problem

The S-matrix bootstrap maps out the space of S-matrices allowed by analyticity, crossing, unitarity, and other constraints. For the 2 → 2 scattering matrix S 2→2 such space is an infinite dimensional convex space whose boundary can be determined by maximizing linear functionals. On the boundary interesting theories can be found, many times at vertices of the space. Here we consider 3 + 1 dimensional theories and focus on the equivalent dual convex minimization problem that provides strict upper bounds for the regularized primal problem and has interesting practical and physical advantages over the primal problem. Its variables are dual partial waves k ℓ (s) that are free variables, namely they do not have to obey any crossing, unitarity or other constraints. Nevertheless they are directly related to the partial waves f ℓ (s), for which all crossing, unitarity and symmetry properties result from the minimization. Numerically, it requires only a few dual partial waves, much as one wants to possibly match experimental results. We consider the case of scalar fields which is related to pion physics.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2023

Patterned OLEDs: effect of substrate corrugation pitch and height

Abstract An ongoing OLED challenge is cost-effective enhancement of light extraction, i.e., increasing the external quantum efficiency ( EQE ∼20% in conventional devices). OLEDs on corrugated substrates often show enhanced EQE s providing insight into light emission processes. In particular, patterned plastic substrates directly imprinted easily at room temperature and amenable to low-cost R2R production are ideal for studying/optimizing various structures, further elucidating the extraction process. We show new semi-quantitative data of the effect of the pitch ( a ) and height/depth ( h ) of plastic substrate patterns on the OLEDs’ stack and EQE , focusing on new designs, interestingly, some showing surprisingly enhanced EQE s that were neither reported nor discussed before. These includ e : ( i ) shallow ( h < 200 nm) convex polycarbonate with a ∼ 750 versus ∼400 nm, where the h gradually decreases as the OLED stack is built and ( ii ) concave PET/CAB with large a (∼2.8 and ∼7.8 μ m), where the EQE enhancement of conformal OLEDs may be due largely to scattering. EQE s of green, blue, and white phosphorescent OLEDs were measured. OLEDs on substrates with narrow a ∼ 400 nm and low h < 200 nm s h owed no enhancement, resembling flat devices. In contrast, OLEDs on substrates with comparable or smaller h , but larger a ∼ 750 nm show signific a nt EQE enhancement despite h reduction across the stack. Green OLEDs with a ∼ 750 nm and h ∼ 160 to ∼180 nm, showed EQE s ∼30%, reaching ∼58% with substrate mode extraction. Surprisingly, fully conformal OLEDs on a PET/CAB substrate with a ∼ 7.8 μ m showed blue a nd white EQE s reaching ∼33%, without substrate mode extraction. The enhancing patterns increase the OLEDs’ EQE by reducing surface plasmon excitation and internal waveguiding. The experimental results for OLEDs on substrates with a < 2 μ m are supported by scattering matrix simulations that assume conformal stacks, incorporating diffraction for internal losses reduction. EQE enhancement not predicted by simulations may be due additionally to scattering mostly for substrates with a signific a ntly larger than the emitting wavelength.

42 ENGINEERING↗