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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.

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At least 523 records · Page 29
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Properties of a fading AGN from SDSS-IV MaNGA

ABSTRACT We identify a fading AGN SDSS J220141.64+115124.3 from the internal Product Launch-11 (MPL-11) in Mapping Nearby Galaxies at Apache Point Observatory (MaNGA) survey. The central region with a projected radius of $\sim$2.4 kpc is characterized as LINER-like line ratios while the outskirts extended to $\sim$15 kpc show Seyfert-like line ratios. The ${\rm{[O {\small III}]}}$$\lambda$5007 luminosity of the Seyfert regions is a factor of 37 (2) higher than the LINER regions without (with) dust attenuation correction, suggesting that the AGN activity decreases at least $\sim$8 $\times$ 10$^3$ yr ($\sim$2.4 kpc/light-speed) ago. We model the emission line spectra in the central region with double Gaussian components (a narrow core and a broad wing) and analyse the properties of each component. The narrow core component mostly co-rotates with the stellar disc, whereas the broad wing component with a median of the velocity dispersion $\sim$300 km s$^{-1}$ is related to a wind outflow. The kinematic position angle (PA) of the ionized gas shows an $\sim 20^{\circ }$ twist from the galaxy centre to 1.5 effective radius. The median of the PA difference between the gas and stellar components is as large as $\sim 50^{\circ }$ within 0.4 effective radius. The tidal feature in DESI image and star–gas misalignment suggest this galaxy is a merger remnant. Combining all these observational results as well as public available X-ray and MIR luminosities, we confirm this is a fading AGN, the merger process kick-started the central engine to quasar phase which ionized gas composed of tidal debris, and now the activity of the central black hole decreases. The discontinuity in ${\rm{[O {\small III}]}}$$\lambda$5007 flux and EQW maps is due to multiple AGN outbursts triggered by merger remnant gas inflows.

Mo, Hao (ORCID:0000000234430768)↗
DOE OSTI2025

Strange quark matter as dark matter: 40 yr later, a reappraisal

ABSTRACT Forty years ago Witten suggested that dark matter could be composed of macroscopic clusters of strange quark matter. This idea was very popular for several years, but it dropped out of fashion once lattice quantum chromodynamics calculations indicated that the confinement/deconfinement transition, at small baryonic chemical potential, is not first order, which seemed to be a crucial requirement in order to produce large clusters of quarks. Here, we revisit the conditions under which strangelets can be produced in the Early Universe. We discuss the impact of an instability in the hadronic phase separating a low density, positive-strange-charge phase from a high-density phase with a negative strange charge. This second phase can rapidly stabilize by forming colour-superconducting gaps. The strangelets then undergo partial evaporation. In this way, we obtain distributions of their sizes in agreement with the observational constraints and we discuss the many astrophysical and cosmological implications of these objects. Finally, we examine the most promising techniques to detect this type of strangelets. We also show that strangelets can exist with masses $\lesssim $1017 g, while primordial black holes are ruled out in that mass range, allowing us to distinguish between these two dark matter candidates.

Clemente, Francesco Di (ORCID:0000000282573819)↗
DOE OSTI2020

SDSS-IV MaNGA: when is morphology imprinted on galaxies?

ABSTRACT It remains an open question as to how long ago the morphology that we see in a present-day galaxy was typically imprinted. Studies of galaxy populations at different redshifts reveal that the balance of morphologies has changed over time, but such snapshots cannot uncover the typical time-scales over which individual galaxies undergo morphological transformation, nor which are the progenitors of today’s galaxies of different types. However, these studies also show a strong link between morphology and star formation rate (SFR) over a large range in redshift, which offers an alternative probe of morphological transformation. We therefore derive the evolution in SFR and stellar mass of a sample of 4342 galaxies in the SDSS-IV MaNGA survey through a stellar population ‘fossil record’ approach, and show that the average evolution of the population shows good agreement with known behaviour from previous studies. Although the correlation between a galaxy’s contemporaneous morphology and SFR is strong over a large range of lookback times, we find that a galaxy’s present-day morphology only correlates with its relatively recent ($\sim \! 2\, \textrm {Gyr}$) star formation history. We therefore find strong evidence that morphological transitions to galaxies’ current appearance occurred on time-scales as short as a few billion years.

Peterken, Thomas↗
DOE OSTI2020

Co-locality to co-functionality: Eukaryotic gene neighborhoods as a resource for function

Diverging from the classic paradigm of random gene order in eukaryotes, gene proximity can be leveraged to systematically identify functionally related gene neighborhoods in eukaryotes, utilizing techniques pioneered in bacteria. Current methods of identifying gene neighborhoods typically rely on sequence similarity to characterized gene products. However, this approach is not robust for non model organisms like algae, which are evolutionarily distant from well-characterized model organisms. Here, we utilize a comparative genomic approach to identify evolutionarily conserved Proximal Orthologous Gene (POG) pairs conserved across at least two taxonomic classes of green algae. A total of 317 gene neighborhoods were identified. In some cases, gene proximity appears to have been conserved since before the streptophyte-chlorophyte split, 1,000 million years ago. Using functional inferences derived from reconstructed evolutionary relationships, we identified several novel functional clusters. A putative mycosporine-like amino acid (MAA), "sunscreen", neighborhood contains genes similar to either vertebrate or cyanobacterial pathways, suggesting a novel mosaic biosynthetic pathway in green algae. One of two putative arsenic-detoxification neighborhoods includes an organoarsenical transporter (ArsJ), a glyceraldehyde 3-phosphate dehydrogenase-like gene, homologs of which are involved in arsenic detoxification in bacteria, and a novel algal-specific phosphoglycerate kinase-like gene (PGK). Mutants of the ArsJ-like transporter and PGK-like genes in Chlamydomonas reinhardtii were found to be sensitive to arsenate, providing experimental support for the role of these identified neighbors in resistance to arsenate. Potential evolutionary origins of neighborhoods are discussed, and updated annotations for formerly poorly annotated genes are presented, highlighting the potential of this strategy for functional annotation.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2020

Crystal structure of an atypical cobalamin riboswitch reveals RNA structural adaptability as basis for promiscuous ligand binding

Cobalamin riboswitches encompass a structurally diverse group of cis-acting, gene regulatory elements found mostly in bacterial messenger RNA and are classified into subtypes based on secondary and tertiary characteristics. An unusual variant of the cobalamin riboswitch with predicted structural features was identified in Bacillus subtilis over a decade ago, but its structure and mechanisms of cobalamin selectivity and translational control have remained unsolved. We present the crystal structure of the aptamer domain of this atypical cobalamin riboswitch and a model for the complete riboswitch, including its expression platform domain. We demonstrate that this riboswitch binds to multiple cobalamin derivatives and correlate its promiscuous behavior to its structure and unique arrangement of peripheral elements. Comparative structural analyses between conventional cobalamin riboswitches and the B. subtilis cobalamin riboswitch reveal that the likely basis for this promiscuous ligand binding is intrinsic structural adaptability encoded in the RNA structure. It suggests that cobalamin selectivity might ultimately be viewed as existing on a spectrum of affinity for each derivative rather than as belonging to distinct types based on ligand specificities. Our work provides an interesting and notable example of functional coupling of ligand-sensing and adaptive folding by a structured RNA molecule.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2024

The N-terminal domains of NLR immune receptors exhibit structural and functional similarities across divergent plant lineages

Nucleotide-binding domain and leucine-rich repeat (NLR) proteins are a prominent class of intracellular immune receptors in plants. However, our understanding of plant NLR structure and function is limited to the evolutionarily young flowering plant clade. Here, we describe an extended spectrum of NLR diversity across divergent plant lineages and demonstrate the structural and functional similarities of N-terminal domains that trigger immune responses. We show that the broadly distributed coiled-coil (CC) and toll/interleukin-1 receptor (TIR) domain families of nonflowering plants retain immune-related functions through translineage activation of cell death in the angiosperm Nicotiana benthamiana. We further examined a CC subfamily specific to nonflowering lineages and uncovered an essential N-terminal MAEPL motif that is functionally comparable with motifs in resistosome-forming CC-NLRs. Consistent with a conserved role in immunity, the ectopic activation of CC MAEPL in the nonflowering liverwort Marchantia polymorpha led to profound growth inhibition, defense gene activation, and signatures of cell death. Moreover, comparative transcriptomic analyses of CC MAEPL activity delineated a common CC-mediated immune program shared across evolutionarily divergent nonflowering and flowering plants. Collectively, our findings highlight the ancestral nature of NLR-mediated immunity during plant evolution that dates its origin to at least ~500 million years ago.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2021

The metabolic origins of non-photorespiratory CO 2 release during photosynthesis: a metabolic flux analysis

Respiration in the light (R L ) releases CO 2 in photosynthesizing leaves and is a phenomenon that occurs independently from photorespiration. Since R L lowers net carbon fixation, understanding R L could help improve plant carbon-use efficiency and models of crop photosynthesis. Although R L was identified more than 75 years ago, its biochemical mechanisms remain unclear. To identify reactions contributing to R L , we mapped metabolic fluxes in photosynthesizing source leaves of the oilseed crop and model plant camelina (Camelina sativa). We performed a flux analysis using isotopic labeling patterns of central metabolites during 13 CO 2 labeling time course, gas exchange, and carbohydrate production rate experiments. To quantify the contributions of multiple potential CO 2 sources with statistical and biological confidence, we increased the number of metabolites measured and reduced biological and technical heterogeneity by using single mature source leaves and quickly quenching metabolism by directly injecting liquid N 2 ; we then compared the goodness-of-fit between these data and data from models with alternative metabolic network structures and constraints. Our analysis predicted that R L releases 5.2 μmol CO2 g –1 FW h –1 of CO 2 , which is relatively consistent with a value of 9.3 μmol CO 2 g –1 FW h –1 measured by CO 2 gas exchange. The results indicated that ≤10% of R L results from TCA cycle reactions, which are widely considered to dominate R L . Further analysis of the results indicated that oxidation of glucose-6-phosphate to pentose phosphate via 6-phosphogluconate (the G6P/OPP shunt) can account for >% of CO 2 released by R L .

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2024

The end game(s) of photosynthetic carbon metabolism

Abstract The year 2024 marks 70 years since the general outline of the carbon pathway in photosynthesis was published. Although several alternative pathways are now known, it is remarkable how many organisms use the reaction sequence described 70 yrs ago, which is now known as the Calvin–Benson cycle or variants such as the Calvin–Benson–Bassham cycle or Benson–Calvin cycle. However, once the carbon has entered the Calvin–Benson cycle and is converted to a 3-carbon sugar, it has many potential fates. This review will examine the last stages of photosynthetic metabolism in leaves. In land plants, this process mostly involves the production of sucrose provided by an endosymbiont (the chloroplast) to its host for use and transport to the rest of the plant. Photosynthetic metabolism also usually involves the synthesis of starch, which helps maintain respiration in the dark and enables the symbiont to supply sugars during both the day and night. Other end products made in the chloroplast are closely tied to photosynthetic CO2 assimilation. These include serine from photorespiration and various amino acids, fatty acids, isoprenoids, and shikimate pathway products. I also describe 2 pathways that can short circuit parts of the Calvin–Benson cycle. These final processes of photosynthetic metabolism play many important roles in plants.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2024

Phylogenomic Insights into the Evolution and Origin of Nematoda

Abstract The phylum Nematoda represents one of the most cosmopolitan and abundant metazoan groups on Earth. In this study, we reconstructed the phylogenomic tree for phylum Nematoda. A total of 60 genomes, belonging to 8 nematode orders, were newly sequenced, providing the first low-coverage genomes for the orders Dorylaimida, Mononchida, Monhysterida, Chromadorida, Triplonchida, and Enoplida. The resulting phylogeny is well-resolved across most clades, with topologies remaining consistent across various reconstruction parameters. The subclass Enoplia is placed as a sister group to the rest of Nematoda, agreeing with previously published phylogenies. While the order Triplonchida is monophyletic, it is not well-supported, and the order Enoplida is paraphyletic. Taxa possessing a stomatostylet form a monophyletic group; however, the superfamily Aphelenchoidea does not constitute a monophyletic clade. The genera Trichinella and Trichuris are inferred to have shared a common ancestor approximately 202 millions of years ago (Ma), a considerably later period than previously suggested. All stomatostylet-bearing nematodes are proposed to have originated ~305 Ma, corresponding to the transition from the Devonian to the Permian period. The genus Thornia is placed outside of Dorylaimina and Nygolaimina, disagreeing with its position in previous studies. In addition, we tested the whole genome amplification method and demonstrated that it is a promising strategy for obtaining sufficient DNA for phylogenomic studies of microscopic eukaryotes. This study significantly expanded the current nematode genome dataset, and the well-resolved phylogeny enhances our understanding of the evolution of Nematoda.

Qing, Xue (ORCID:0000000203559956)↗
DOE OSTI2024

Conversion of Site-Specific Meteorological Data for use in CAP-88 PC

CAP-88 PC is a commonly used radiological atmospheric dispersion model. This US EPA-approved model is used to demonstrate compliance with atmospheric emission regulations for radionuclides. While the model includes a large library of meteorological data for use across the United States, there are applications when users may wish to use onsite meteorological data as an input to the CAP-88 PC model. Here, in this work, we present a work-around process for preparing and converting onsite data for use in CAP-88 PC. However, the use of local data should provide a more realistic estimate of doses to members of the public in the immediate vicinity of a facility, although the regulatory agency having jurisdiction may not accept the use of local data for compliance. Additionally, the historical meteorological records from 20+ years ago (at a site many kilometers away) might not be representative of current local weather patterns, highlighting another benefit of using local meteorological data.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2025

Possible Spin-Triplet Excitonic Insulator in the Ultraquantum Limit of HfTe 5

More than 50 years ago, excitonic insulators formed by the pairing of electrons and holes due to Coulomb interactions were first predicted [A. N. Kozlov and L. A. Maksimov, Sov. J. Exp. Theor. Phys. 21, 790 (1965); L. V. Keldysh and Y. V. Kopaev, Sov. Phys. Solid State 6, 2219 (1965); D. Jérome, T. M. Rice, and W. Kohn, Phys. Rev. 158, 462 (1967)]. Since then, excitonic insulators have been observed in various classes of materials, including quantum Hall bilayers, graphite, transition metal chalcogenides, and more recently in moiré superlattices. In these excitonic insulators, an electron and a hole with the same spin bind together, and the resulting exciton is a spin singlet. Here, we report the experimental observation of a spin-triplet excitonic insulator in the ultra-quantum limit of a three-dimensional topological material HfTe 5 . We observe that the spin-polarized zeroth Landau bands dispersing along the field direction cross each other beyond a characteristic magnetic field in HfTe 5 , forming the one-dimensional Weyl mode. Transport measurements reveal the emergence of a gap of about 2⁢5⁢0 μ⁢eV when the field surpasses a critical threshold. By performing the material-specific modeling, we identify this gap as a consequence of a spin-triplet exciton formation, where electrons and holes with opposite spin form bound states, and the translational symmetry is preserved. The system reaches charge neutrality following the gap opening, as evidenced by the zero Hall conductivity over a wide magnetic field range (10–72 T). In conclusion, our finding of the spin-triplet excitonic insulator paves the way for studying novel spin transport including spin superfluidity, spin Josephson currents, and Coulomb drag of spin currents in analogy to the transport properties associated with the layer pseudospin in quantum Hall bilayers.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Rethinking 𝛼−RuCl 3 : Parameters, models, and phase diagram

RuCl 3 was likely the first ever deliberately synthesized ruthenium compound, following the discovery of the 44 Ru element in 1844. For a long time it was known as an oxidation catalyst, with its physical properties being discrepant and confusing, until a decade ago when its allotropic form 𝛼−RuCl 3 rose to exceptional prominence. This “rediscovery” of 𝛼−RuCl 3 has not only reshaped the hunt for a material manifestation of the Kitaev spin liquid, but it has opened the floodgates of theoretical and experimental research in the many unusual phases and excitations that the anisotropic-exchange magnets as a class of compounds have to offer. Given its importance for the field of Kitaev materials, it is astonishing that the low-energy spin model that describes this compound and its possible proximity to the much-desired spin-liquid state is still a subject of significant debate ten years later. In the present study, we argue that the existing key phenomenological observations put strong natural constraints on the effective microscopic spin model of 𝛼−RuCl 3 , and specifically on its spin-orbit-induced anisotropic-exchange parameters that are responsible for the nontrivial physical properties of this material. These constraints allow one to focus on the relevant region of the multidimensional phase diagram of the 𝛼−RuCl 3 model, suggest an intuitive description of it via a different parametrization of the exchange matrix, offer a unifying view on the earlier assessments of its parameters, and bring closer together several approaches to the derivation of anisotropic-exchange models. We explore extended phase diagrams relevant to the 𝛼−RuCl 3 parameter space using quasiclassical, Luttinger-Tisza, exact diagonalization, and density-matrix renormalization-group methods, demonstrating a remarkably close quantitative accord between them on the general structure and hierarchy of the phases, with the zigzag, ferromagnetic, and incommensurate phases that are proximate to each other. As a result, one of the highlights is the detailed agreement on the nature of the incommensurate phases that realize two distinct counterrotating helical states.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2020

Modeling the pseudogap metallic state in cuprates: Quantum disordered pair density wave

We present a way to quantum-disorder a pair density wave and propose it to be a candidate of the effective low-energy description of the pseudogap metal which may reveal itself in a sufficiently high magnetic field that suppresses the d-wave pairing. The ground state we construct is a small-pocket Fermi liquid with a bosonic Mott insulator in the density-wave-enlarged unit cell. At low energy, the charge density is mainly carried by charge 2e bosons, which develop a small insulating gap. As an intermediate step, we discuss the quantum disordering of a fully gapped superconductor and its excitation spectrum. A simplified 1D model, which we solve numerically, is used to illustrate the introduced concepts. Here, we discuss a number of experimental consequences. The interplay between the electron and the small-gap boson results in a step-function background in the electron spectral function which may be consistent with existing angle-resolved photoemission spectroscopy data. Optical excitation across the boson gap can explain the onset and the magnitude of the mid infrared absorption reported long ago.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2020

Experimental demonstration and analysis of random field effects in ferromagnet/antiferromagnet bilayers

More than 30 years ago, Malozemoff [Phys. Rev. B 35, 3679 (1987)] hypothesized that exchange interaction at the interface between a ferromagnet (F) and an antiferromagnet (AF) can act as an effective random field, which can profoundly affect the magnetic properties of the system. However, until now this hypothesis has not been directly experimentally tested. We utilize magnetoelectronic measurements to analyze the effective exchange fields at permalloy/CoO interface. Our results cannot be explained in terms of quasiuniform effective exchange fields but are in agreement with the random-field hypothesis of Malozemoff. Finally, the presented approach opens a new route for the quantitative analysis of effective exchange fields and anisotropies in magnetic heterostructures for memory, sensing and computing applications.

36 MATERIALS SCIENCE↗
DOE OSTI2020

$\testit{d}$-wave superconductivity and Bogoliubov-Fermi surfaces in Rarita-Schwinger-Weyl semimetals

In this work, we uncover the properties of complex tensor ($\textit{d}$-wave) superconducting order in three-dimensional Rarita-Schwinger-Weyl semimetals that host pseudospin-$\frac{3}{2}$ fermions at a fourfold linear band-crossing point. Although the general theory of $\textit{d}$-wave order was originally developed for materials displaying quadratic band touching, it directly applies to the case of semimetals with linear dispersion, several candidate compounds of which have been discovered experimentally very recently. The spin-$\frac{3}{2}$ nature of the fermions allows for the formation of spin-2 Cooper pairs which may be described by a complex second-rank tensor order parameter. In the case of linear dispersion, for the chemical potential at the Fermi point and at strong coupling, the energetically preferred superconducting state is the uniaxial nematic state, which preserves time-reversal symmetry and provides a full (anisotropic) gap for quasiparticle excitations. In contrast, at a finite chemical potential, we find that the usual weak-coupling instability is toward the “cyclic state,” well known from the studies of multicomponent Bose-Einstein condensates, which breaks time-reversal symmetry maximally, has vanishing average value of angular momentum, and features 16 small Bogoliubov-Fermi surfaces. The Rarita-Schwinger-Weyl semimetals provide therefore the first example of weakly coupled, three-dimensional, isotropic $\textit{d}$-wave superconductors where the $\textit{d}$-wave superconducting phase is uniquely selected by the quartic expansion of the mean-field free energy, and is not afflicted by the accidental degeneracy first noticed by Mermin over 40 years ago. We discuss the appearance and stability of the Bogoliubov-Fermi surfaces in absence of inversion symmetry in the electronic Hamiltonian, as in the case at hand.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2021

Origin of the $ν$ = 1/2 fractional quantum Hall effect in wide quantum wells

The nature of the fractional quantum Hall effect at ν = 1/2, observed in wide quantum wells al- most three decades ago, is still under debate. Previous studies have investigated it by the variational Monte Carlo method, which assumes that the transverse wave function and the gap between the symmetric and antisymmetric subbands obtained in a local density approximation at zero magnetic field remain valid even at high perpendicular magnetic fields; this method also ignores the effect of Landau level mixing. We develop in this work a three-dimensional fixed phase diffusion Monte Carlo method, which gives, in a single framework, the total energies of various candidate states in a finite width quantum well, including Landau level mixing, directly in a large magnetic field. This method can be applied to one-component states, and also to two-component states in the limit where the symmetric and antisymmetric bands are nearly degenerate. Our three-dimensional fixed-phase diffusion Monte Carlo calculations find that the one-component composite-fermion Fermi sea and the one-component Pfaffian states are very close in energy for a range of quantum well widths and densities, suggesting that the observed 1/2 fractional quantum Hall state in wide quantum wells is likely to be the one-component Pfaffian state. Furthermore, we hope that this will motivate further experimental studies of this state.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2021

Candidate structure for the H 2 -PRE phase of solid hydrogen

Experimental progress finally reached the metallic solid hydrogen phase, which was predicted by Wigner and Huntington over 80 years ago. However, the different structures in the phase diagram are still being debated due to the difficulty of diffraction experiments for high-pressured hydrogen. The determination of crystal structures under extreme condition is both of the basic condensed matter physics, and in planetary science: the behavior of giant gaseous planets (e.g., Jupiter and Saturn) strongly depends on the properties of inner high-pressured hydrogen. This work describes possible structures appearing under high pressures of 400~600 GPa. We applied a structural search using particle swarm optimization with density functional theory (DFT) to propose several candidate structures. For these structures, we performed fixed-node diffusion Monte Carlo simulations combined with DFT zero-point energy corrections to confirm their relative stability. We found P2 1 /c-8 as a promising candidate structure for the H 2 -PRE phase. P2 1 /c-8 is predicted the most stable at 400 and 500 GPa. P2 1 /c-8 reproduces qualitatively the IR spectrum peaks observed in the H 2 -PRE phase.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2022

Local magnetic moments due to loop currents in metals

We present Hartree-Fock calculations on a simple model to obtain the conditions of formation of local magnetic moments due to loop currents $L$ $o$ and spin-loop currents $L$ $s$ and compare them to the conditions of formation of local spin moments $M$ which were given long ago in a similar approximation by Anderson. A model with three degenerate orbitals sitting on an equilateral triangle, with on-site and nearest-neighbor repulsions $U$ and $V$, respectively, and intersite kinetic energy, hybridizing with conduction electrons with a parameter $Δ$ is investigated. $L$ $o$ and $L$ $s$ are promoted by large $V$/$Δ$ and their magnitude is relatively unaffected by $U$/$Δ$. Spin-magnetic moments $M$ promoted by large $U$/$Δ$ on the other hand are adversely affected by $V$/$Δ$. In this model, $L$ $o$ for $V$ multiplied by the number of neighbors is approximately the same as the $M$ promoted by $U$ in Anderson’s local model for $M$. $L$ $o$ and $L$ $s$ are degenerate if exchange interactions and Hund’s rule are neglected but $L$ $o$ is favored when they are included. Many of the qualitative results are visible in an expression for the Hartree-Fock ground state energy derived as a function of small $L$ $o$ , $L$ $s$ , and $M$. Numerical minimization of the Hartree-Fock energy is presented for larger values. Additionally, we also briefly discuss the connection and differences of the interaction-generated orbital currents and spin currents discussed here and generalized to a lattice with the topological states in metals and semiconductors.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗