Search NASA⌕ Search

SEARCH · Search NASA

Results for “Symmetry functions”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 145 records · Page 8
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Response functions and giant monopole resonances for light to medium-mass nuclei from the ab initio symmetry-adapted no-core–shell model

Using the ab initio symmetry-adapted no-core–shell model, we compute sum rules and response functions for light to medium-mass nuclei, starting from interactions that are derived in the chiral effective field theory. Specifically, we investigate electromagnetic transitions of monopole, dipole and quadrupole nature for 4 He, and explore dominant features of giant monopole resonances in symmetric nuclei such as the closed-shell 4 He and 16 O light nuclei, the intermediate-mass open-shell 20 Ne and the medium-mass closed-shell 40 Ca. Furthermore, for the NNLO opt chiral potential, we determine parameter-free monopole sum rules, which can provide information on the incompressibility of symmetric nuclear matter. Here, we report 213(10) MeV as an estimate for the compression modulus for infinite nuclear matter, which overlaps with the lower range of values often used in current astrophysical applications.

ab initio nuclear structure↗
DOE OSTI2025

Raman Digital Twin of Monolayer Janus Transition Metal Dichalcogenides

Monolayer transition metal dichalcogenides (TMDs) are a key class of two-dimensional (2D) materials with broad technological potential. Their Janus counterparts exhibit unique properties due to broken out-of-plane symmetry and further enrich the functionalities of TMDs. However, experimental synthesis and identification of Janus TMDs remain challenging. It is thus highly desirable to have a rapid, simple, and in situ characterization technique to monitor, in real time, the conversion process from the parent to Janus structure. Raman spectroscopy stands out for such a task as it is a powerful, nondestructive, and very commonly used tool to characterize 2D materials both in situ and ex situ. To realize the full potential of Raman spectroscopy on rapid characterization of Janus TMDs, we present a computational “Raman digital twin” library for various monolayer Janus TMDs in both 2H and Td phases. We focus on group-6 TMDs: MoS 2 , WS 2 , MoSe 2 , WSe 2 , MoTe 2 , WTe 2 and their Janus variants: MoSSe, MoSTe, MoSeTe, WSSe, WSTe, and WSeTe. Using first-principles density functional theory (DFT), we calculate their vibrational properties and predict distinct Raman fingerprints. These phonon and Raman signatures reflect each material’s structural symmetry and atomic composition, enabling clear identification via Raman spectroscopy. Our theoretical work supports experimental efforts by providing benchmarks for material identification, structural analysis, and quality control. In conclusion, the computational library expedites the discovery and development of Janus 2D materials, facilitating tighter integration between theoretical predictions and experimental validation.

Chalcogenides↗
DOE OSTI2021

Calculating the hyperfine tensors for group-IV impurity-vacancy centers in diamond using hybrid density functional theory

The hyperfine interaction is an important probe for understanding the structure and symmetry of defects in a semiconductor. Density functional theory has shown that it can provide useful first-principles predictions for both the hyperfine tensor and the hyperfine constants that arise from it. Recently there has been great interest in using group-IV impurity-vacancy color centers XV – (where X = Si, Ge, Sn, or Pb and V is a carbon vacancy) for important applications in quantum computing and quantum information science. In this paper we have calculated the hyperfine tensors for these XV – color centers using the HSE06 screened Hartree-Fock hybrid exchange-correlation functional with the inclusion of core electron spin polarization. We have compared our results to calculations which only use the PBE exchange-correlation functional without the inclusion of core electron spin polarization and we have found that our results are in very good agreement with available experimental results. Lastly, we have theoretically shown that these XV – color centers exhibit a Jahn-Teller distortion which explains the observed anisotropic distribution of the hyperfine constants among the neighboring 13 C nuclear spins.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2025

Large critical fields in superconducting Ti 4 ⁢Ir 2⁢ O from spin-orbit coupling

The recently synthesized 𝜂-carbide-type superconductors exhibit large critical fields. A notable example is Ti 4 ⁢Ir2⁢ O, for which the upper critical field strongly violates the Pauli paramagnetic limit, a behavior that is unusual for cubic materials that preserve inversion symmetry. Here, by combining density functional theory (DFT) and analytic modeling, we provide an explanation for this enhanced Pauli limiting field. We show that the nonsymmorphic Fd⁢-3 ⁢m symmetry implies that the electronic states near the X points exhibit strong spin-orbit coupling (SOC), which leads to a vanishing effective 𝑔 factor and enables the enhanced Pauli limiting field. Furthermore, our DFT results reveal a Van Hove singularity peak near the X points, accounting for ∼65% of the total density of states (DOS), occurring near the chemical potential. We propose that the strong SOC and enhanced DOS in the vicinity of the X points provide the origin of the observed enhancement of the critical field. This leads to a prediction that the magnetic field will lead to a strongly momentum-dependent gap suppression. As a result, the gap due to electronic states away from (near to) the X points will be rapidly (slowly) suppressed by fields.

Critical field↗
DOE OSTI2025

A two-loop four-point form factor at function level

Recently, the maximally-helicity-violating four-point form factor for the chiral stress-energy tensor in planar $\mathcal{N}$ = 4 super Yang-Mills was computed to three loops at the level of the symbol associated with multiple polylogarithms. It exhibits antipodal self-duality, or invariance under the combined action of a kinematic map and reversing the ordering of letters in the symbol. Here we lift the two-loop form factor from symbol level to function level. We provide an iterated representation of the function’s derivatives (coproducts). In order to do so, we find a three-parameter limit of the five-parameter phase space where the symbol’s letters are all rational. We also use function-level information about dihedral symmetries and the soft, collinear, and factorization limits, as well as limits governed by the form-factor operator product expansion (FFOPE). We provide plots of the remainder function on several kinematic slices, and show that the result is compatible with the FFOPE data. We further verify that antipodal self-duality is valid at two loops beyond the level of the symbol.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2024

Edge supercurrent reveals competition between condensates in a Weyl superconductor

In topological materials, the edge states are readily distinguished from the bulk states. The situation where a topological semimetal becomes superconducting so that Cooper pairs occupy both the bulk and the edge states is not well understood. In particular, we do not know if we can force their pairing symmetries to be different. Here we show that, when supercurrent is injected into the superconducting Weyl semimetal MoTe 2 from Nb contacts, the invasive s-wave pairing potential from Nb is incompatible with the intrinsic Cooper pair condensate in MoTe 2 . This incompatibility leads to strong stochasticity in the switching current and an unusual anti-hysteretic behaviour in the current–voltage loops. There is also an asymmetry in the edge oscillations where, as the magnetic field crosses zero, the phase noise switches from one with a noisy spectrum to one that is noise free. Furthermore, using the noise spectrum as a guide, we track the anomalous features to field-induced switching of the device gap function between s-wave symmetry and the unconventional symmetry intrinsic to MoTe 2 . We infer that the behaviour of the gap function along the edges is different from that in the bulk.

Superconducting properties and materials↗
DOE OSTI2021

Strong influence of nonmagnetic ligands on the momentum-dependent spin splitting in antiferromagnets

Here, recent studies show the nonrelativistic antiferromagnetic ordering could generate momentum-dependent spin splitting analogous to the Rashba effect but free from the requirement of relativistic spin-orbit coupling. Whereas the classification of such compounds can be illustrated by different spin-splitting prototypes (SSTs) from symmetry analysis and density-functional-theory calculations, the huge variation in chemical bonding and structures of these diverse compounds possibly clouds the issue of how much of the variation in spin splitting can be traced back to the symmetry-defined characteristics, rather to the underlining chemical and structural diversity. The alternative model Hamiltonian approaches do not confront the issues of chemical and structural complexity but often consider only the magnetic sublattice, dealing with the all-important effects of the nonmagnetic ligands via renormalizing the interactions between the magnetic sites. To this end, we constructed a DFT model Hamiltonian that allows us to study SSTs at constant chemistry while retaining the realistic atomic-scale structure including ligands. This is accomplished by using a single, universal magnetic skeletal lattice (Ni 2+ ions in rocksalt NiO) and designing small displacements of the nonmagnetic (oxygen) sublattice which produce, by design, the different SST magnetic symmetries. We show that (i) even similar crystal structures having very similar band structures can lead to contrasting behavior of spin splitting vs momentum, and (ii) even subtle deformations of the nonmagnetic ligand sublattice could cause a giant spin splitting in AFM-induced SST. This is a paradigm shift relative to the convention of modeling magnets without considering the nonmagnetic ligand that mediates indirect magnetic interaction (e.g., superexchange).

36 MATERIALS SCIENCE↗
DOE OSTI2023

An empirical method for geometric calibration of a photon counting detector-based cone beam CT system

BACKGROUND: Geometric calibration is essential in developing a reliable computed tomography (CT) system. It involves estimating the geometry under which the angular projections are acquired. Geometric calibration of cone beam CTs employing small area detectors, such as currently available photon counting detectors (PCDs), is challenging when using traditional-based methods due to detectors’ limited areas. OBJECTIVE: This study presented an empirical method for the geometric calibration of small area PCD-based cone beam CT systems. METHODS: Unlike the traditional methods, we developed an iterative optimization procedure to determine geometric parameters using the reconstructed images of small metal ball bearings (BBs) embedded in a custom-built phantom. An objective function incorporating the sphericities and symmetries of the embedded BBs was defined to assess performance of the reconstruction algorithm with the given initial estimated set of geometric parameters. The optimal parameter values were those which minimized the objective function. The TIGRE toolbox was employed for fast tomographic reconstruction. To evaluate the proposed method, computer simulations were carried out using various numbers of spheres placed in various locations. Furthermore, efficacy of the method was experimentally assessed using a custom-made benchtop PCD-based cone beam CT. RESULTS: Computer simulations validated the accuracy and reproducibility of the proposed method. The precise estimation of the geometric parameters of the benchtop revealed high-quality imaging in CT reconstruction of a breast phantom. Within the phantom, the cylindrical holes, fibers, and speck groups were imaged in high fidelity. The CNR analysis further revealed the quantitative improvements of the reconstruction performed with the estimated parameters using the proposed method. CONCLUSION: Apart from the computational cost, we concluded that the method was easy to implement and robust.

Instruments & Instrumentation↗
DOE OSTI2023

Group-equivariant autoencoder for identifying spontaneously broken symmetries

We introduce the group-equivariant autoencoder (GE autoencoder), a deep neural network (DNN) method that locates phase boundaries by determining which symmetries of the Hamiltonian have spontaneously broken at each temperature. We use group theory to deduce which symmetries of the system remain intact in all phases, and then use this information to constrain the parameters of the GE autoencoder such that the encoder learns an order parameter invariant to these “never-broken” symmetries. This procedure produces a dramatic reduction in the number of free parameters such that the GE-autoencoder size is independent of the system size. We include symmetry regularization terms in the loss function of the GE autoencoder so that the learned order parameter is also equivariant to the remaining symmetries of the system. By examining the group representation by which the learned order parameter transforms, we are then able to extract information about the associated spontaneous symmetry breaking. We test the GE autoencoder on the 2D classical ferromagnetic and antiferromagnetic Ising models, finding that the GE autoencoder (1) accurately determines which symmetries have spontaneously broken at each temperature; (2) estimates the critical temperature in the thermodynamic limit with greater accuracy, robustness, and time efficiency than a symmetry-agnostic baseline autoencoder; and (3) detects the presence of an external symmetry-breaking magnetic field with greater sensitivity than the baseline method. Lastly, we describe various key implementation details, including a quadratic-programming-based method for extracting the critical temperature estimate from trained autoencoders and calculations of the DNN initialization and learning rate settings required for fair model comparisons.

42 ENGINEERING↗
NASA NTRS1981

An algorithm for the rapid location of an extreme of a function subject only to geometric restrictions

The requirements of symmetry and convexity in the application of algorithms for the minimization or maximization of a function are discussed. It is argued that if a function of a single variable is convex and symmetric in a neighborhood of an extremum, the extremum may be approximated to the precision that increases by at least a power of two per functional evaluation. The procedure may be used to drive a complex optimization procedure in the multivariate area estimation problem encountered in remote sensing.

Terrell, G. R.↗
DOE OSTI2025

Role of magnetic and structural symmetry breaking in forming the Mott insulating gap in Nb 3 ⁢Cl 8

The α-phase of the gapped insulator Nb 3 Cl 8 has recently emerged as the long-sought critical testing bed for examining the importance of strong interelectronic correlation vs symmetry breaking in understanding insulation of such Mott compounds. Structural symmetry breaking detected by density functional theory (DFT) energy lowering (such as dimer formation, disproportionation, or Jahn-Teller distortions) explains insulation in both d-electron Mott-like systems and in non-d-electron cases without recourse to strong correlation. Yet, in Nb 3 Cl 8 , structural symmetry breaking alone (viz. formation of Nb trimers) fails to explain insulation, leading instead to a partially occupied metallic flat band, in contrast with experimental observations. We examine the role of magnetic symmetry breaking, noting that Nb 3 Cl 8 is an observed paramagnet (not an antiferromagnet), thus potentially carrying also short-range ordered magnetic moments. Describing the latter as a polymorphous distribution of nonzero local moments with total zero net magnetization is demonstrated to lower the DFT total energy, while gapping the system without recourse to strong correlation or long-range magnetic order. This suggests that degeneracy removal by symmetry breaking in mean-field-like approaches—either structural, or magnetic, or both—can reduce or eliminate the need for strong correlation, allowing the use of DFT for such Mott systems.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2022

Magnetic chirality

Abstract Chirality with all broken mirror symmetries matters ubiquitously from DNA functionality, vine climbing, to the piezoelectricity of quartz crystals. Magnetic chirality means chirality in spin-ordered states or (atomic-scale or mesoscopic) spin textures. Magnetic chirality does not change with time-reversal operation, and chirality prime ( $${\mathcal{C}}^\prime$$ C ′ ) means that time-reversal symmetry in addition to all mirror symmetries is broken with free spatial rotations. We will discuss a few examples of magnetic chirality and $${\mathcal{C}}^\prime$$ C ′ , and their emergent physical properties. Some of these exotic properties have been recently observed, and many of them need to be experimentally confirmed.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Poincaré constraints on celestial amplitudes

The functional structure of celestial amplitudes as constrained by Poincare symmetry is investigated in 2, 3, and 4-point cases for massless external particles of various spin, as well as massive external scalars. Functional constraints and recurrence relations are found (akin to the findings in [24]) that must be obeyed by the respective permissible correlator structures and function coefficients. In specific three-point cases involving massive scalars the resulting recurrence relations can be solved, e.g., reproducing purely from symmetry a three-point function coefficient known in the literature. Additionally, as a byproduct of the analysis, the three-point function coefficient for gluons in Minkowski signature is obtained from an amplitude map to the celestial sphere.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS1990

Self-collimated electromagnetic jets from magnetized accretion disks - The even-symmetry case

This paper extends the previous treatment (Lovelace et al., 1987) of the origin of self-collimated EM jets to the case of even field symmetry, where the magnetic flux function Psi(r, z) is an even function of z. A viscous resistive accretion disk is assumed to surround a black hole with a force-free plasma outside of the disk. Inside the disk, the induction equation is solved for Psi(r, z) and the toroidal magnetic field. Outside the disk, previous results are used to study the formation of self-collimated EM jets. In contrast with the odd-symmetry case, for even symmetry the toroidal magnetic field acts to vertically compress the disk; a comparatively large toroidal magnetic field can exist inside the disk; and an appreciable fraction (possibly all) of the available accretion power can go into the jets.

Wang, J. C. L.↗
DOE OSTI2024

Controlling topology through targeted composite symmetry manipulation in magnetic systems

The possibility of selecting magnetic space groups by orienting the magnetization direction or tuning magnetic orders offers a vast playground for engineering symmetry-protected topological phases in magnetic materials. In this work, we study how selective tuning of symmetry and magnetism can influence and control the resulting topology in a two-dimensional magnetic system, and we illustrate such a procedure in the ferromagnetic monolayer MnPSe 3 . Density functional theory calculations reveal a symmetry-protected accidental semimetallic (SM) phase for out-of-plane magnetization, which becomes an insulator when the magnetization is tilted in-plane, reaching band-gap values close to 100 meV. We identify an order-2 composite antiunitary symmetry and threefold rotational symmetry that induce the band crossing, and we classify the possible topological phases using symmetry analysis, which we support with tight-binding and k · p models. Breaking of inversion symmetry opens a gap in the SM phase, giving rise to a Chern insulator. We demonstrate this explicitly in the isostructural Janus compound Mn 2 ⁢P 2 ⁢S 3 ⁢Se 3 , which naturally exhibits Rashba spin-orbit coupling that breaks inversion symmetry. Our results map out the phase space of topological properties of ferromagnetic transition-metal phosphorus trichalcogenides, and they demonstrate the potential of the magnetization-dependent metal-to-insulator transition as a spin switch in integrated two-dimensional electronics.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2024

Modulation of Electrostatic Potential in 2D Crystal Engineered by an Array of Alternating Polar Molecules

The moiré potential in rotationally misfit two-dimensional (2D) heterostructures has been used to build artificial exciton and electron lattices, which have become platforms for realizing exotic electronic phases. Here, we demonstrate a different approach to create a superlattice potential in 2D crystals by using the near field of an array of polar molecules. Here, a bilayer of titanyl phthalocyanine (TiOPc), consisting of alternating out-of-plane dipoles, is deposited on monolayer MoS 2 . Time-resolved two-photon photoemission spectroscopy reveals a pair of interlayer exciton states with an energy difference of ~0.1 eV, which is consistent with the electrostatic potential modulation induced by the TiOPc bilayer as determined by density functional theory calculations. Because the symmetry and the period of this potential superlattice can be changed readily by using molecules of different shapes and sizes, molecule/2D heterostructures can be promising platforms for designing artificial exciton and electron lattices.

2D heterostructures↗
DOE OSTI2024

Imaging and structure analysis of ferroelectric domains, domain walls, and vortices by scanning electron diffraction

Direct electron detectors in scanning transmission electron microscopy give unprecedented possibilities for structure analysis at the nanoscale. In electronic and quantum materials, this new capability gives access to, for example, emergent chiral structures and symmetry-breaking distortions that underpin functional properties. Quantifying nanoscale structural features with statistical significance, however, is complicated by the subtleties of dynamic diffraction and coexisting contrast mechanisms, which often results in a low signal-to-noise ratio and the superposition of multiple signals that are challenging to deconvolute. Here we apply scanning electron diffraction to explore local polar distortions in the uniaxial ferroelectric Er(Mn,Ti)O 3 . Using a custom-designed convolutional autoencoder with bespoke regularization, we demonstrate that subtle variations in the scattering signatures of ferroelectric domains, domain walls, and vortex textures can readily be disentangled with statistical significance and separated from extrinsic contributions due to, e.g., variations in specimen thickness or bending. The work demonstrates a pathway to quantitatively measure symmetry-breaking distortions across large areas, mapping structural changes at interfaces and topological structures with nanoscale spatial resolution.

36 MATERIALS SCIENCE↗