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All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

MIRaGE-Lite V.4.X

SAND2022-4254 O The goal of Multiscale Inverse Rapid Group-theory for Engineered-metamaterials (MIRaGE), funded under the DARPA EXTREME program, is to create a group theory-based multiscale simulation tool that enables the inverse design of metamaterials exhibiting exotic electromagnetic behaviors beyond the limits of conventional optics. Sandia National Laboratories is a multimission laboratory managed and operated by National Technology & Engineering Solutions of Sandia, LLC, a wholly owned subsidiary of Honeywell International Inc., for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-NA0003525.

El-Kady, Ihab↗
DOE OSTI2026

Inverse problem in the large momentum effective theory framework

One proposal to compute parton distributions from first principles is the large momentum effective theory (LaMET), which requires the Fourier transform of matrix elements computed nonperturbatively. Lattice quantum chromodynamics (QCD) provides calculations of these matrix elements over a finite range of Fourier harmonics that are often noisy or unreliable in the largest computed harmonics. It has been suggested that enforcing an exponential decay of the missing harmonics helps alleviate this issue. Using nonperturbative data, we show that the uncertainty introduced by this inverse problem in a realistic setup remains significant without very restrictive assumptions, and that the importance of the exact asymptotic behavior is minimal for values of 𝑥 where the framework is currently applicable. We show that the crux of the inverse problem lies in harmonics of the order of 𝜆 = 𝑧⁢𝑃 𝑧 ∼ 5–15, where the signal in the lattice data is often barely existent in current studies, and the asymptotic behavior is not firmly established. We stress the need for more sophisticated techniques to account for this inverse problem, whether in the LaMET or related frameworks like the short-distance factorization. We also address a misconception that, with available lattice methods, the LaMET framework allows a “direct” computation of the 𝑥-dependence, whereas the alternative short-distance factorization only gives access to moments or fits of the 𝑥-dependence.

Dutrieux, Hervé [Aix-Marseille Université, Marseil↗
DOE OSTI2021

A Comparison of Exact and Model Exchange–Correlation Potentials for Molecules

Accurate exchange–correlation (XC) potentials for three-dimensional systems–via solution of the inverse density functional theory (DFT) problem–are now available to test the quality of DFT approximations. Herein, the exact XC potential for seven molecules–dihydrogen at four different bond-lengths, lithium hydride, water, and ortho-benzyne–are computed from full configuration interaction reference densities. These are compared to model XC potentials from nonlocal (B3LYP, HSE06, SCAN0, and M08-HX) and semilocal/local (SCAN, PBE, and PW92) XC functionals. Whereas for most systems, relative errors in the ground-state densities are O(10 –3 –10 –2 ) , the model XC potentials have much higher errors of O(10 –1 –10 0 ) . Among the model XC functionals, SCAN0 offers the best agreement with the exact XC potential, underlining the significance of satisfying exact conditions as well as including nonlocal effects in XC functionals. This work indicates that tests against the exact XC potential will provide a promising new direction for building more accurate XC functionals for DFT.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Geometry of conformal manifolds and the inversion formula

Families of conformal field theories are naturally endowed with a Riemannian geometry which is locally encoded by correlation functions of exactly marginal operators. We show that the curvature of such conformal manifolds can be computed using Euclidean and Lorentzian inversion formulae, which combine the operator content of the conformal field theory into an analytic function. Analogously, operators of fixed dimension define bundles over the conformal manifold whose curvatures can also be computed using inversion formulae. These results relate curvatures to integrated four-point correlation functions which are sensitive only to the behavior of the theory at separated points. We apply these inversion formulae to derive convergent sum rules expressing the curvature in terms of the spectrum of local operators and their three-point function coefficients. We further show that the curvature can smoothly diverge only if a conserved current appears in the spectrum, or if the theory develops a continuum. We verify our results explicitly in 2d examples. In particular, for 2d (2,2) superconformal field theories we derive a lower bound on the scalar curvature, which is saturated by free theories when the central charge is a multiple of three.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2024

The development of Gibbs's dyadic and implications for the gradient of a vector field

In this paper, we review the history of the dyadic as developed by Gibbs. This mathematical construct appeared in the second part of Gibbs's pamphlet on vector analysis (published in 1884), and it represented the first known development of a Cartesian theory of tensors. Gibbs made extensive use of the dyadic to express his theory of linear vector functions, that is, functions that acted on vectors and mapped them to new vectors. The dyadic proved to be a capable vehicle in Gibbs's hands, and his theory for dyadics (which we would now call second-order Cartesian tensors) was relatively advanced. The theory detailed notions such as the decomposition of vectors and conditions under which a tensor would have an inverse. While Gibbs's theory for linear operators expressed by dyadics was robust, it did not seem to garner the attention that the more conventional vector analysis (published in the first half of his pamphlet in 1881) did. Perhaps in part because of the general unfamiliarity with the dyadic, two distinct and conflicting definitions of the gradient of a vector field have arisen in the literature. The details of these differences in notation, possible reasons for the difference, and a potential resolution are proposed.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Inverse Volume Scaling of Finite-Size Error in Periodic Coupled Cluster Theory

Coupled cluster theory is one of the most popular post-Hartree-Fock methods for molecular quantum chemistry. The finite-size error of the correlation energy in periodic coupled cluster calculations for three-dimensional insulating systems has been observed to satisfy the inverse volume scaling, even in the absence of any correction schemes. This is surprising, as simpler theories that utilize only a subset of the coupled cluster diagrams exhibit much slower decay of the finite-size error, which scales inversely with the length of the system. In this study, we review the current understanding of finite-size error in quantum chemistry methods for periodic systems. We introduce new tools that elucidate the mechanisms behind this phenomenon in the context of coupled cluster doubles calculations. This reconciles some seemingly paradoxical statements related to finite-size scaling. Our findings also show that singularity subtraction can be a powerful method to effectively reduce finite-size errors in practical quantum chemistry calculations for periodic systems. Published by the American Physical Society 2024

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Ultrafast Carrier–Lattice Interactions and Interlayer Modulations of Bi 2 Se 3 by X-ray Free-Electron Laser Diffraction

We report as a 3D topological insulator, bismuth selenide (Bi 2 Se 3 ) has potential applications for electrically and optically controllable magnetic and optoelectronic devices. Understanding the coupling with its topological phase requires studying the interactions of carriers with the lattice on time scales down to the sub-picosecond regime. Here we investigate the ultrafast carrier-induced lattice contractions and interlayer modulations in Bi 2 Se 3 thin films by time-resolved diffraction using an X-ray free-electron laser. The lattice contraction depends on the carrier concentration and is followed by an interlayer expansion accompanied by oscillations. Using density functional theory (DFT) and the Lifshitz model, the initial contraction can be explained by van der Waals force modulation of the confined free carrier layers. Our theory suggests that band inversion, related to a topological phase transition, is modulated by the expansion of the interlayer distance. These results provide insights into the topological phase control by light-induced structural change on ultrafast timescales.

77 NANOSCIENCE AND NANOTECHNOLOGY↗
DOE OSTI2023

Valence transition and termination-dependent surface states in the topological Kondo semimetal YbPtBi

Here, the Yb-terminated and Bi-terminated (111) surface electronic structure of topological Kondo semimetal YbPtBi is investigated using both density-functional-theory (DFT) -based calculations and angle-resolved photoemission spectroscopy (ARPES). The cleavage plane is found to be between Yb-layers and Bi-layers in both experiment and theory, and the broken inversion symmetry ensures the Yb-terminated surface does not mix with the Bi-terminated surface. The ARPES results at the Bi-terminated surface are similar to those reported for YPtBi or LuPtBi, and they can be well explained using DFT calculations assuming trivalent Yb atoms. In contrast, at the Yb-terminated surface, a trivalent to divalent transition and reduced hybridization with conduction electrons for the topmost Yb atoms are observed, as a result of reduced bonding with Bi-atoms. In addition, the Fermi arc features induced by the triply degenerate-points, which are missing at the Bi-terminated surface, can be identified at the Yb-terminated surface. Our study demonstrates unambiguously the reconstruction of surface electronic structure due to the valence transition of the lanthanide element in a Kondo lattice system.

36 MATERIALS SCIENCE↗
DOE OSTI2020

MIRaGE: Design Software for Metamaterials

Metamaterials are artificial optical structures that allow control of light in ways not found in, or offered by, naturally occurring materials. Sandia's Multiscale Inverse Rapid Group-theory for Engineered-metamaterials (MIRaGE) software, which won an R&D100 award in 2019, allows researchers to deterministically design and produce metamaterials with unique characteristics. MIRaGE also provides powerful autonomous optimization techniques for real-world performance in a rigorous, robust, and accurate manner.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Theory of optical responses in clean multi-band superconductors

Electromagnetic responses in superconductors provide valuable information on the pairing symmetry as well as physical quantities such as the superfluid density. However, at the superconducting gap energy scale, optical excitations of the Bogoliugov quasiparticles are forbidden in conventional Bardeen-Cooper-Schrieffer superconductors when momentum is conserved. Accordingly, far-infrared optical responses have been understood in the framework of a dirty-limit theory by Mattis and Bardeen for over 60 years. Here we show, by investigating the selection rules imposed by particle-hole symmetry and unitary symmetries, that intrinsic momentum-conserving optical excitations can occur in clean multi-band superconductors when one of the following three conditions is satisfied: (i) inversion symmetry breaking, (ii) symmetry protection of the Bogoliubov Fermi surfaces, or (iii) simply finite spin-orbit coupling with unbroken time reversal and inversion symmetries. This result indicates that clean-limit optical responses are common beyond the straightforward case of broken inversion symmetry. We apply our theory to optical responses in FeSe, a clean multi-band superconductor with inversion symmetry and significant spin-orbit coupling. This result paves the way for studying clean-limit superconductors through optical measurements.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2021

Tuning valley degeneracy with band inversion

Valley degeneracy is a key feature of the electronic structure that benefits the thermoelectric performance of a material. Despite recent studies which claim that high valley degeneracy can be achieved with inverted bands, our analysis of rock-salt IV–VI compounds using first-principles calculations and k•p perturbation theory demonstrates that mere band inversion is an insufficient condition for high valley degeneracy; rather, there is a critical degree to which the bands must be inverted to induce multiple carrier pockets. The so-called “band inversion parameter” is formalized as a chemically-tunable property, offering a design route to achieving high valley degeneracy in compounds with inverted bands. In conclusion, we predict that the valley degeneracy of rock-salt IV–VI compounds can be increased from N V = 4 to N V = 24, which could result in a corresponding increase in the thermoelectric figure of merit zT .

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

Stochastic Inversion of Gaussian Random Media Using Transverse Coherence Functions for Reflected Waves: Theory and Method

The transverse coherence functions (TCFs) of phase and amplitude fluctuations of a seismic wave are powerful to estimate the spatial distribution, length scales, and strength of random heterogeneities. However, TCFs have been formulated for transmitted waves only, not for reflected waves. In this paper, we derive reflection TCFs for Gaussian random media. Furthermore, we propose to invert for Gaussian random media using the reflection TCFs based on the grid search. We validate the new reflection TCF formulas using 2D finite-difference numerical experiments. The numerical example also illustrates the feasibility and efficiency of the inversion. The stochastic inversion using reflected waves can be used in both exploration and global seismology.

58 GEOSCIENCES↗
DOE OSTI2024

Thermal quasiparticle theory

The widely used thermal Hartree–Fock (HF) theory is generalized to include the effect of electron correlation while maintaining its quasi-independent-particle framework. An electron-correlated internal energy (or grand potential) is postulated in consultation with the second-order finite-temperature many-body perturbation theory (MBPT), which then dictates the corresponding thermal orbital (quasiparticle) energies in such a way that all fundamental thermodynamic relations are obeyed. The associated density matrix is of a one-electron type, whose diagonal elements take the form of the Fermi–Dirac distribution functions, when the grand potential is minimized. The formulas for the entropy and chemical potential are unchanged from those of Fermi–Dirac or thermal HF theory. The theory thus stipulates a finite-temperature extension of the second-order Dyson self-energy of one-particle many-body Green’s function theory and can be viewed as a second-order, diagonal, frequency-independent, thermal inverse Dyson equation. At low temperatures, the theory approaches finite-temperature MBPT of the same order, but it may outperform the latter at intermediate temperatures by including additional electron-correlation effects through orbital energies. Here, a physical meaning of these thermal orbital energies is proposed (encompassing that of thermal HF orbital energies, which has been elusive) as a finite-temperature version of Janak’s theorem.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2023

Analyticity of replica correlators and modular ETH

We study the two point correlation function of a local operator on an n -sheeted replica manifold corresponding to the half-space in the vacuum state of a conformal field theory. In analogy with the inverse Laplace transform, we define the Renyi transform of this correlation function, which is a function of one complex variable w, dual to the Renyi parameter n . Inspired by the inversion formula of Caron-Huot, we argue that if the Renyi transform ƒ(w) has bounded behavior at infinity in the complex w plane, the discontinuity of the Renyi transform disc ƒ(w) provides the unique analytic continuation in n of the original replica correlation function. We check our formula by explicitly calculating the Renyi transform of a particular replica correlator in a large N holographic CFT d in dimensions d > 2. We also discover that the discontinuity of the Renyi transform is related to the matrix element of local operators between two distinct eigenstates of the modular Hamiltonian. We calculate the Renyi transform in 2 d conformal field theories, and use it to extract the off-diagonal elements of (modular) ETH. We argue that in 2 d , this is equivalent to the off-diagonal OPE coefficients of a CFT and show that our technique exactly reproduces recent results in the literature.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2024

Analysis of a Computational Framework for Bayesian Inverse Problems: Ensemble Kalman Updates and MAP Estimators under Mesh Refinement

This paper analyzes a popular computational framework to solve infinite-dimensional Bayesian inverse problems, discretizing the prior and the forward model in a finite-dimensional weighted inner product space. We demonstrate the benefit of working on a weighted space by establishing operator-norm bounds for finite element and graph-based discretizations of Matérn-type priors and deconvolution forward models. For linear-Gaussian inverse problems, we develop a general theory to characterize the error in the approximation to the posterior. We also embed the computational framework into ensemble Kalman methods and MAP estimators for nonlinear inverse problems. Furthermore, our operator-norm bounds for prior discretizations guarantee the scalability and accuracy of these algorithms under mesh refinement.

Bayesian inverse problem↗
DOE OSTI2024

Evolution of the Electronic and Excitonic Properties in 2D Ruddlesden–Popper Perovskites Induced by Bifunctional Ligands

2D Ruddlesden–Popper metal‐halide perovskites exhibit structural diversity due to a variety of choices of organic ligands. Incorporating bifunctional ligands in such materials is particularly intriguing since it can result in novel electronic properties and functions. However, an in‐depth understanding of the effects of bifunctional ligands on perovskite structures and, consequently, their electronic and excitonic properties, is still lacking. Here, in this work, n = 1 2D perovskites built with organic ligands containing ─CN, ─OH, ─COOH, ─phenyl (Ph), and ─CH 3 functional groups are investigated using ultraviolet and inverse photoemission spectroscopies, density functional theory calculations, and tight‐binding model analyses. The experimentally determined electronic gaps of the ─CN, ─COOH, ─Ph, and ─CH 3 based perovskites exhibit a strong correlation with the in‐plane Pb─I─Pb bond angle, while the ─OH based perovskite deviates from the linear trend. Based on the band structure calculations, this anomaly is attributed to the out‐of‐plane dispersion, caused predominantly by significant interlayer electronic coupling that is present in ─OH based perovskites. These results highlight the complex and diverse impacts of organic ligands on electronic properties, especially in terms of the involvement of strong interlayer electronic coupling. The impact of the bifunctional ligands on the evolution of the exciton binding energy is also addressed.

2D perovskites↗
DOE OSTI2025

Conjugation effect of amine molecules in non-aqueous Mg redox flow batteries

Nonaqueous magnesium redox flow batteries (Mg RFBs) are attractive for low-cost, high-energy-density and long-cycle-life stationary energy storage applications. However, state-of-the-art cathode redox-active molecules suffer from low solubility and low redox potential. Herein, we screened a range of cathode redox-active molecules and identified amine molecules as optimal to couple with the Mg anode. The properties of amine derivatives and their performances were collected to establish the correlation between molecular structures and electrochemical performances. The redox potential and solubility of these amine molecules were influenced by the π-conjugated and non-conjugated structures of amine derivatives. Density functional theory (DFT) simulations and the inverse aromatic fluctuation index (FLU −1 ) verified that conjugation had an important role in stabilizing the molecule and increasing its redox potential. Notably, tris[4-(diethylamino)phenyl]amine (TDPA) achieved the highest theoretical energy density (∼120 Wh L −1 ) due to its high solubility (∼0.9 M) and voltage (∼2.5 V vs. Mg/Mg 2+ ). We also demonstrated that ether solvents were crucial for stable, high-solubility catholytes, while bulk anions did not affect the redox potential of these p-type molecules. In a Mg-amine RFB configuration, the battery delivered 2.50 V, a specific discharge capacity of 106.5 mAh g −1 , an initial coulombic efficiency of 90.74%, and a capacity retention of 93.88% after 150 cycles.

Qin, Yunan [University of Utah, Salt Lake City, UT↗