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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 109 records · Page 6
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Efficient Topology Design Algorithms for Power Grid Stability

The dynamic response of power grids to small disturbances influences their overall stability. This letter examines the effect of network topology on the linearized time-invariant dynamics of electric power systems. The proposed framework utilizes H 2 -norm based stability metrics to study the optimal placement of lines on existing networks as well as the topology design of new networks. The design task is first posed as an NP-hard mixed-integer nonlinear program (MINLP) that is exactly reformulated as a mixed-integer linear program (MILP) using McCormick linearization. To improve computation time, graph-theoretic properties are exploited to derive valid inequalities (cuts) and tighten bounds on the continuous optimization variables. Moreover, a cutting plane generation procedure is put forth that is able to interject the MILP solver and augment additional constraints to the problem on-the-fly. Finally, the efficacy of our approach in designing optimal grid topologies is demonstrated through numerical tests on the IEEE 39-bus network.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2024

Characterization and classification of interacting ( 2 + 1 )-dimensional topological crystalline insulators with orientation-preserving wallpaper groups

While free fermion topological crystalline insulators have been largely classified, the analogous problem in the strongly interacting case has been only partially solved. In this work, we develop a characterization and classification of interacting, invertible fermionic topological phases in (2+1) dimensions with charge conservation, discrete magnetic translation and M-fold point group rotation symmetries, which form the group G f = U(1) f × Φ [Z 2 $\rtimes$Z M ] for M = 1,2,3,4, and 6. Φ is the magnetic flux per unit cell. We derive a topological response theory in terms of background crystalline gauge fields, which gives a complete classification of different phases and a physical characterization in terms of quantized response to symmetry defects. We then derive the same classification in terms of a set of real space invariants {$Θ^±_o$} that can be obtained from ground state expectation values of suitable partial rotation operators. We explicitly relate these real space invariants to the quantized coefficients in the topological response theory, and find the dependence of the invariants on the chiral central charge c – of the invertible phase. Finally, when Φ = 0 we derive an explicit map between the free and interacting classifications.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2025

Identifying Band Inversions in Topological Materials Using Diffusion Monte Carlo

Topological insulators are characterized by insulating bulk states and robust metallic surface states. Band inversion is a hallmark of topological insulators. At time-reversal invariant points in the Brillouin zone, spin–orbit coupling (SOC) induces a swapping of orbital character at the bulk band edges. Reliably detecting band inversion in solid-state systems with many-body methods would aid in identifying possible candidates for spintronics and quantum computing applications and improve our understanding of the physics behind topologically nontrivial systems. Density functional theory (DFT) methods are a well-established means of investigating these interesting materials due to their favorable balance of computational cost and accuracy but often struggle to accurately model the electron–electron correlations present in the many materials containing heavier elements. In this work, we develop a novel method to detect band inversion within continuum quantum Monte Carlo (QMC) methods that can accurately treat the electron correlation and spin–orbit coupling that are crucial to the physics of topological insulators. Our approach applies a momentum-space-resolved atomic population analysis throughout the first Brillouin zone utilizing the Löwdin method and the one-body reduced density matrix produced with diffusion Monte Carlo (DMC). We integrate this method into QMCPACK, an open source ab initio QMC package, so that these ground-state methods can be used to complement experimental studies and validate prior DFT work on predicting the band structures of correlated topological insulators. Here, we demonstrate this new technique on the topological insulator bismuth telluride, which displays band inversion between its Bi-p and Te-p states at the Γ-point. We show an increase in charge on the bismuth-p orbital and a decrease in charge on the tellurium-p orbital when comparing band structures with and without SOC. Additionally, we use our method to compare the degree of band inversion present in monolayer Bi 2 Te 3 , which has no interlayer van der Waals interactions, to that seen in the bilayer and bulk. The method presented here will enable future many-body studies of band inversion that can shed light on the delicate interplay between correlation and topology in correlated topological materials.

Band structure↗
DOE OSTI2021

Topological Defect Engineering and $\mathcal{PT}$ Symmetry in Non-Hermitian Electrical Circuits

In this work, we employ electric circuit networks to study topological states of matter in non-Hermitian systems enriched by parity-time symmetry $\mathcal{PT}$ and chiral symmetry anti-$\mathcal{PT (APT)}$. The topological structure manifests itself in the complex admittance bands which yields excellent measurability and signal to noise ratio. We analyze the impact of $\mathcal{PT}$-symmetric gain and loss on localized edge and defect states in a non-Hermitian Su-Schrieffer-Heeger (SSH) circuit. We realize all three symmetry phases of the system, including the $\mathcal{APT}$-symmetric regime that occurs at large gain and loss. We measure the admittance spectrum and eigenstates for arbitrary boundary conditions, which allows us to resolve not only topological edge states, but also a novel $\mathcal{PT}$-symmetric $\mathbb{Z}_2$ invariant of the bulk. We discover the distinct properties of topological edge states and defect states in the phase diagram. In the regime that is not $\mathcal{PT}$ symmetric, the topological defect state disappears and only reemerges when $\mathcal{APT}$ symmetry is reached, while the topological edge states always prevail and only experience a shift in eigenvalue. Our findings unveil a future route for topological defect engineering and tuning in non-Hermitian systems of arbitrary dimension.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2021

Quantum Computational Advantage with String Order Parameters of One-Dimensional Symmetry-Protected Topological Order

Nonlocal games with advantageous quantum strategies give arguably the most fundamental demonstration of the power of quantum resources over their classical counterparts. Recently, certain multiplayer generalizations of nonlocal games have been used to prove unconditional separations between limited computational complexity classes of shallow-depth circuits. Here, we show advantageous strategies for these nonlocal games for generic ground states of one-dimensional symmetry-protected topological orders (SPTOs), when a discrete invariant of a SPTO known as a twist phase is nontrivial and -1. Finally, our construction demonstrates that sufficiently large string order parameters of such SPTOs are indicative of globally constrained correlations useful for the unconditional computational separation.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Graph identification of proteins in tomograms ( GRIP‐Tomo )

Abstract In this study, we present a method of pattern mining based on network theory that enables the identification of protein structures or complexes from synthetic volume densities, without the knowledge of predefined templates or human biases for refinement. We hypothesized that the topological connectivity of protein structures is invariant, and they are distinctive for the purpose of protein identification from distorted data presented in volume densities. Three‐dimensional densities of a protein or a complex from simulated tomographic volumes were transformed into mathematical graphs as observables. We systematically introduced data distortion or defects such as missing fullness of data, the tumbling effect, and the missing wedge effect into the simulated volumes, and varied the distance cutoffs in pixels to capture the varying connectivity between the density cluster centroids in the presence of defects. A similarity score between the graphs from the simulated volumes and the graphs transformed from the physical protein structures in point data was calculated by comparing their network theory order parameters including node degrees, betweenness centrality, and graph densities. By capturing the essential topological features defining the heterogeneous morphologies of a network, we were able to accurately identify proteins and homo‐multimeric complexes from 10 topologically distinctive samples without realistic noise added. Our approach empowers future developments of tomogram processing by providing pattern mining with interpretability, to enable the classification of single‐domain protein native topologies as well as distinct single‐domain proteins from multimeric complexes within noisy volumes.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2020

Hofstadter Topology: Noncrystalline Topological Materials at High Flux

he Hofstadter problem is the lattice analog of the quantum Hall effect and is the paradigmatic example of topology induced by an applied magnetic field. Conventionally, the Hofstadter problem involves adding ~10 4 T magnetic fields to a trivial band structure. In this work, we show that when a magnetic field is added to an initially topological band structure, a wealth of possible phases emerges. Remarkably, we find topological phases that cannot be realized in any crystalline insulators. We prove that threading magnetic flux through a Hamiltonian with a nonzero Chern number or mirror Chern number enforces a phase transition at fixed filling and that a 2D Hamiltonian with a nontrivial Kane–Mele invariant can be classified as a 3D topological insulator (TI) or 3D weak TI phase in periodic flux. We then study fragile topology protected by the product of twofold rotation and time reversal and show that there exists a higher order TI phase where corner modes are pumped by flux. We show that a model of twisted bilayer graphene realizes this phase. Our results rely primarily on the magnetic translation group that exists at rational values of the flux. The advent of Moiré lattices renders our work relevant experimentally. Due to the enlarged Moiré unit cell, it is possible for laboratory-strength fields to reach one flux per plaquette and allow access to our proposed Hofstadter topological phase.

36 MATERIALS SCIENCE↗
DOE OSTI2024

FORESTR: Finding, Organizing, Representing, Explaining, Summarizing, and Thinning Random forests

Random forests have become popular models used for data driven predictions. As a result, random forests are currently used or being considered for high-consequence mission applications in national security, such as the prediction of yield from optical signals and malware detection. While random forests may provide accurate predictions, the complexity of the algorithm causes a lack of interpretability. Random forests are an ensemble of regression or decision trees. Individual regression and decision trees are interpretable, but ensembles are inherently difficult to interpret due to the compilation of many models. We aim to increase the interpretability of random forests by finding patterns in the ensemble of trees that can be used to “thin” (or remove) trees. As a starting point, in this report, we develop a new distance metric for quantifying the similarity between trees based on their topologies (i.e., shapes). We base the metric on a novel distance metric for graphs that is a proper mathematical distance, is invariant to transformations, has registration between graphs, and computes topological evolutions between graphs. We use the tree distance metric to compute tree statistics such as a “mean tree” and to identify clusters of trees. We apply the developed methodology to a toy dataset and a mission relevant product inspection dataset to demonstrate how the metric can provide insight into random forests. Furthermore, we discuss the limitations of the approach and ideas for future research into how the metric could be used as a thinning tool to develop less complex models.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Multipartite edge modes and tensor networks

Holographic tensor networks model AdS/CFT, but so far they have been limited by involving only systems that are very different from gravity. Unfortunately, we cannot straightforwardly discretize gravity to incorporate it, because that would break diffeomorphism invariance. In this note, we explore a resolution. In low dimensions gravity can be written as a topological gauge theory, which can be discretized without breaking gauge-invariance. However, new problems arise. Foremost, we now need a qualitatively new kind of “area operator,” which has no relation to the number of links along the cut and is instead topological. Secondly, the inclusion of matter becomes trickier. We successfully construct a tensor network both including matter and with this new type of area. Notably, while this area is still related to the entanglement in “edge mode” degrees of freedom, the edge modes are no longer bipartite entangled pairs. Instead they are highly multipartite. Along the way, we calculate the entropy of novel subalgebras in a particular topological gauge theory. We also show that the multipartite nature of the edge modes gives rise to non-commuting area operators, a property that other tensor networks do not exhibit.

Akers, Chris (ORCID:0000000227929827)↗
DOE OSTI2024

Group IV topological quantum alloy and the role of short-range order: the case of Ge-rich Ge 1– x Pb x

Despite the explosion of interest in topological materials over the last decades, their applications remain limited due to challenges in growth and incorporation with today’s microelectronics. As a potential bridge to close this gap, we investigate the group-IV alloy Ge 1–x Pb x , in the Ge-rich condition using density functional theory and show that relatively low concentrations of Pb (~9.4%) can lead to a topological phase transition. Furthermore, the calculation of the Z 2 invariant for both the random alloy and the alloy with short-range order (SRO) indicate that the topological phase of the material can be directly modified by the degree of SRO. These findings are understood in terms of local structural relaxation, which decreases the bandgap in the random alloy. However, in the SRO case, the mutual avoidance of Pb leads to minimal structural relaxation, alleviating strain. Our findings not only highlight the emerging importance of SRO in alloy properties but also indicate the possibility of constructing topological interfaces between materials of identical composition (and nominally identical structure). Moreover, they uncover a viable avenue toward the monolithic integration of quantum materials with today’s semiconductor industry.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Hybridization of colloidal handlebodies with singular defects and topological solitons in chiral liquid crystals

Topology can manifest itself in colloids when quantified by invariants like Euler characteristics of nonzero-genus colloidal surfaces, albeit spherical colloidal particles are most often studied, and colloidal particles with complex topology are rarely considered. On the other hand, singular defects and topological solitons often define the physical behavior of the molecular alignment director fields in liquid crystals. Interestingly, nematic liquid crystalline dispersions of colloidal particles allow for probing the interplay between topologies of surfaces and fields, but only a limited number of such cases have been explored so far. Here, we study the hybridization of topological solitons, singular defects, and topologically nontrivial colloidal particles with the genus of surfaces different from zero in a chiral nematic liquid crystal phase. Hybridization occurs when distortions separately induced by colloidal particles and LC solitons overlap, leading to energy minimization-driven redistribution of director field deformations and defects. As a result, hybrid director configurations emerge, combining topological features from both components. We uncover a host of director field configurations complying with topological theorems, which can be controlled by applying electric fields. Rotational and translational dynamics arise due to the nonreciprocal evolution of the director fields in response to alternating electric fields of different frequencies. These findings help define a platform for controlling topologically hyper-complex colloidal structures and dynamics with electrically reconfigurable singular defects and topological solitons induced by colloidal handlebodies.

Lee, Jun-Yong [Hiroshima Univ. (Japan)]↗
DOE OSTI2026

Symmetry-protected topological polarons

Emergent quasiparticles in solids often exhibit unique topological properties as a result of the complex interplay between charge, orbital, spin, and lattice degrees of freedom. Among these quasiparticles, the polaron occupies a special place as the first known manifestation of the interaction between a fermion and a boson field. While polarons have been investigated for almost a century, whether these quasiparticles exhibit topological properties and why remain open questions. Here, we establish the universal symmetry principles governing the topology of polar textures in large polarons. Using a group-theoretic analysis, we identify four distinct classes of polar textures in time-reversal-invariant systems, and we show that they carry integer topological charges. We validate this classification by performing state-of-the-art first-principles calculations of materials representative of each class. For these materials, we compute the fingerprints of polaron topology in Huang diffuse scattering and propose ultrafast electron and X-ray scattering experiments to detect these quasiparticles.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2020

Phase-matching analysis in high-order harmonic generation with nonzero orbital angular momentum Laguerre-Gaussian beams

Through high-order harmonic generation driven by intense ultrashort vortex infrared or midinfrared lasers, a nonzero orbital angular momentum can be imprinted onto extreme ultraviolet (XUV) or soft-x-ray (SXR) light pulses. Here we simulate the generation of vortex XUV harmonics in the gas medium as well as their propagation in vacuum till reaching the far field. In this work, we find that the intensity and phase of generated high harmonics are very sensitive to the position of gas jet with respect to the laser focus. The topological charge of the $\textit{q}$th harmonic is found to be $\textit{q}$ times that of the driving Laguerre-Gaussian beam. Each harmonic in the far field appears as a single ring in the transverse plane with an invariant diameter which is scalable with the fundamental topological charge only when the gas jet is placed after the laser focus. The underlying phase-matching mechanism is analyzed by examining the spatial map of the coherence length and by calculating the evolution of harmonic emission in the medium. We anticipate this work to stimulate interest in generating intense vortex XUV or SXR attosecond pulses for probing dynamics of molecules where special molecular features are difficult to be detected with linear or circular XUV or SXR pulses.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Fermi surfaces of the topological semimetal CaSn 3 probed through de Haas van Alphen oscillations

Abstract In the search of topological superconductors, nailing down the Fermiology of the normal state is as crucial a prerequisite as unraveling the superconducting pairing symmetry. In particular, the number of time-reversal-invariant momenta (TRIM) in the Brillouin zone enclosed by Fermi surfaces is closely linked to the topological class of time-reversal-invariant systems, and can experimentally be investigated. We report here a detailed study of de Haas van Alphen quantum oscillations in single crystals of the topological semimetal CaSn 3 with torque magnetometry in high magnetic fields up to 35 T. In conjunction with density functional theory based calculations, the observed quantum oscillations frequencies indicate that the Fermi surfaces of CaSn 3 enclose an odd number of TRIM, satisfying one of the proposed criteria to realize topological superconductivity. Nonzero Berry phases extracted from the magnetic oscillations also support the nontrivial topological nature of CaSn 3 .

Physics↗
DOE OSTI2022

Data-Driven Operator Theoretic Methods for Phase Space Learning and Analysis

This paper uses data-driven operator theoretic approaches to explore the global phase space of a dynamical system. In this work, we defined conditions for discovering new invariant subspaces in the state space of a dynamical system starting from an invariant subspace based on the spectral properties of the Koopman operator. When the system evolution is known locally in several invariant subspaces in the state space of a dynamical system, a phase space stitching result is derived that yields the global Koopman operator. Additionally, in the case of equivariant systems, a phase space stitching result is developed to identify the global Koopman operator using the symmetry properties between the invariant subspaces of the dynamical system and time-series data from any one of the invariant subspaces. Finally, these results are extended to topologically conjugate dynamical systems; in particular, the relation between the Koopman tuple of topologically conjugate systems is established. The proposed results are demonstrated on several second-order nonlinear dynamical systems including a bistable toggle switch. Our method elucidates a strategy for designing discovery experiments: experiment execution can be done in many steps, and models from different invariant subspaces can be combined to approximate the global Koopman operator.

42 ENGINEERING↗
DOE OSTI2021

4-manifolds and topological modular forms

We build a connection between topology of smooth 4-manifolds and the theory of topological modular forms by considering topologically twisted compactification of 6d (1, 0) theories on 4-manifolds with flavor symmetry backgrounds. The effective 2d theory has (0, 1) supersymmetry and, possibly, a residual flavor symmetry. The equivariant topological Witten genus of this 2d theory then produces a new invariant of the 4-manifold equipped with a principle bundle, valued in the ring of equivariant weakly holomorphic (topological) modular forms. We describe basic properties of this map and present a few simple examples. As a byproduct, we obtain some new results on ’t Hooft anomalies of 6d (1, 0) theories and a better understanding of the relation between 2d (0, 1) theories and TMF spectra.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

Exact non-symmetric closed line vacuum magnetic fields in a topological torus

Non-symmetric vacuum magnetic fields with closed magnetic field lines are of interest in the construction of stellarator equilibria. Beyond the result of D. Lortz, Z. Angew Math. Phys. 21, 196 (1970), few results are available. This work presents a closed-form expression for a class of vacuum magnetic fields in a topological torus with closed field lines. We explicitly obtain the invariants of such a field. We finally show that a three-dimensional low beta magnetohydrodynamic equilibrium may be constructed in a topological torus, starting with these closed line vacuum magnetic fields.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2023

On Galilean invariance of mean kinetic helicity

While kinetic helicity is not Galilean invariant locally, it is known [Moffatt, J. Fluid Mech. 35, 117 (1969)] that its spatial integral quantifies the degree of knottedness of vorticity field lines. Being a topological property of the flow, mean kinetic helicity is Galilean invariant. Here, we provide a direct mathematical proof that kinetic helicity is Galilean invariant when spatially integrated over regions enclosed by vorticity surfaces, i.e., surfaces of zero vorticity flux. Here, we also discuss so-called relative kinetic helicity, which is Galilean invariant when integrated over any region in the flow.

42 ENGINEERING↗