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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 973 records · Page 54
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Redox Defect Thermochemistry of FeAl 2 O 4 Hercynite in Water Splitting from First-Principles Methods

Solar thermochemical hydrogen (STCH) production is a promising route to produce fuels from sunlight via high-temperature water splitting. However, efficient and technologically viable implementations of this process only allow a narrow window of thermodynamic boundary conditions that can be used to cycle the system, thus limiting the design space for suitable metal oxide redox mediators. An oxygen defect redox mechanism can contribute a favorable reduction entropy to expand this window, and computational evaluation of materials with high oxygen defect entropies could play a pivotal role in guiding the discovery and design of suitable oxides. This study employs first-principles calculations to investigate the redox mediating defect mechanism of the STCH candidate material, hercynite (FeAl 2 O 4 ). We compare the results of total energy calculations from density functional theory (DFT) with beyond-DFT approaches, including hybrid functionals and the random phase approximation, which are among the most advanced methods currently feasible for supercell defect calculations. Using the predicted formation energies, we perform thermodynamic modeling of FeAl2O4 reduction and oxidation via free energy minimization that incorporates ideal gas, configurational, and vibrational entropy contributions evaluated within the quasi-harmonic approximation. Special attention is devoted to understanding interactions among co-existing defects, such as the association of pairs and complexes of O vacancies and cation antisite defects, and the effect of mutually compensating defect charges. Our results corroborate the notion that the details of defect interactions can be decisive for the viability of hydrogen production within the desirable STCH process window.

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

Quantum Many-Body Scars: A Quasiparticle Perspective

Weakly interacting quasiparticles play a central role in the low-energy description of many phases of quantum matter. At higher energies, however, quasiparticles cease to be well defined in generic many-body systems owing to a proliferation of decay channels. In this review, we discuss the phenomenon of quantum many-body scars, which can give rise to certain species of stable quasiparticles throughout the energy spectrum. This goes along with a set of unusual nonequilibrium phenomena including many-body revivals and nonthermal stationary states. We provide a pedagogical exposition of this physics via a simple yet comprehensive example, that of a spin-1 XY model. We place our discussion in the broader context of symmetry-based constructions of many-body scar states, projector embeddings, and Hilbert space fragmentation. We conclude with a summary of experimental progress and theoretical puzzles.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2022

Synthesizing Stellar Populations in South Pole Telescope Galaxy Clusters. I. Ages of Quiescent Member Galaxies at 0.3 < $\textit{z}$ < 1.4

Using stellar population synthesis models to infer star formation histories (SFHs), we analyze photometry and spectroscopy of a large sample of quiescent galaxies that are members of Sunyaev–Zel'dovich (SZ)-selected galaxy clusters across a wide range of redshifts. We calculate stellar masses and mass-weighted ages for 837 quiescent cluster members at 0.3 < $\textit{z}$ < 1.4 using rest-frame optical spectra and the Python-based Prospector framework, from 61 clusters in the SPT-GMOS Spectroscopic Survey (0.3 < $\textit{z}$ < 0.9) and three clusters in the SPT Hi-z cluster sample (1.25 < $\textit{z}$ < 1.4). We analyze spectra of subpopulations divided into bins of redshift, stellar mass, cluster mass, and velocity-radius phase-space location, as well as by creating composite spectra of quiescent member galaxies. We find that quiescent galaxies in our data set sample a diversity of SFHs, with a median formation redshift (corresponding to the lookback time from the redshift of observation to when a galaxy forms 50% of its mass, $t_{50}$) of $\textit{z}$ = 2.8 ± 0.5, which is similar to or marginally higher than that of massive quiescent field and cluster galaxy studies. We also report median age–stellar mass relations for the full sample (age of the universe at $t_{50}$ (Gyr) = 2.52 (±0.04)–1.66 (±0.12) log$_{10}(M/10^{11}M_⊙$)) and recover downsizing trends across stellar mass; we find that massive galaxies in our cluster sample form on aggregate ~0.75 Gyr earlier than lower-mass galaxies. We also find marginally steeper age–mass relations at high redshifts, and report a bigger difference in formation redshifts across stellar mass for fixed environment, relative to formation redshifts across environment for fixed stellar mass.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2022

Realistic simulations of spin squeezing and cooperative coupling effects in large ensembles of interacting two-level systems

We describe an efficient numerical method for simulating the dynamics of interacting spin ensembles in the presence of dephasing and decay. The method builds on the discrete truncated Wigner approximation for isolated systems, which combines the mean-field dynamics of a spin ensemble with a Monte Carlo sampling of discrete initial spin values to account for quantum correlations. Here we show how this approach can be generalized for dissipative spin systems by replacing the deterministic mean-field evolution by a stochastic process, which describes the decay of coherences and populations while preserving the length of each spin. We demonstrate the application of this technique for simulating nonclassical spin-squeezing effects or the dynamics and steady states of cavity QED models with 10 5 interacting two-level systems. This opens up the possibility to perform accurate real-scale simulations of a diverse range of experiments in quantum optics or with solid-state spin ensembles under realistic laboratory conditions.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Bayesian optimization to design a novel x-ray shaping device

In radiation therapy, x-ray dose must be precisely sculpted to the tumor, while simultaneously avoiding surrounding organs at risk. This requires modulation of x-ray intensity in space and/or time. Typically, this is achieved using a multi leaf collimator (MLC) - a complex mechatronic device comprising over one hundred individually powered tungsten ‘leaves’ that move in or out of the radiation field as required. Here, an all-electronic x-ray collimation concept with no moving parts is presented, termed “SPHINX”: Scanning Pencil-beam High-speed Intensity-modulated X-ray source. SPHINX utilizes a spatially distributed bremsstrahlung target and collimator array in conjunction with magnetic scanning of a high energy electron beam to generate a plurality of small x-ray “beamlets.” A simulation framework was developed in Topas Monte Carlo incorporating a phase space electron source, transport through user defined magnetic fields, bremsstrahlung x-ray production, transport through a SPHINX collimator, and dose in water. This framework was completely parametric, meaning a simulation could be built and run for any supplied geometric parameters. This functionality was coupled with Bayesian optimization to find the best parameter set based on an objective function which included terms to maximize dose rate for a user defined beamlet width while constraining inter-channel cross talk and electron contamination. Designs for beamlet widths of 5, 7, and 10 mm 2 were generated. Each optimization was run for 300 iterations and took approximately 40 h on a 24-core computer. For the optimized 7-mm model, a simulation of all beamlets in water was carried out including a linear scanning magnet calibration simulation. Finally, a back-of-envelope dose rate formalism was developed and used to estimate dose rate under various conditions. The optimized 5–, 7–, and 10-mm models had beamlet widths of 5.1 , 7.2 , and 10.1 mm 2 and dose rates of 3574, 6351, and 10 015 Gy/C, respectively. The reduction in dose rate for smaller beamlet widths is a result of both increased collimation and source occlusion. For the simulation of all beamlets in water, the scanning magnet calibration reduced the offset between the collimator channels and beam centroids from 2.9 ±1.9 mm to 0.01 ±0.03 mm. A slight reduction in dose rate of approximately 2% per degree of scanning angle was observed. Based on a back-of-envelope dose rate formalism, SPHINX in conjunction with next-generation linear accelerators has the potential to achieve substantially higher dose rates than conventional MLC-based delivery, with delivery of an intensity modulated 100 x 100 mm 2 field achievable in 0.9 to 10.6 s depending on the beamlet widths used. Bayesian optimization was coupled with Monte Carlo modeling to generate SPHINX geometries for various beamlet widths. A complete Monte Carlo simulation for one of these designs was developed, including electron beam transport of all beamlets through scanning magnets, x-ray production and collimation, and dose in water. These results demonstrate that SPHINX is a promising candidate for sculpting radiation dose with no moving parts, and has the potential to vastly improve both the speed and robustness of radiotherapy delivery. A multi-beam SPHINX system may be a candidate for delivering magavoltage FLASH RT in humans.

62 RADIOLOGY AND NUCLEAR MEDICINE↗
DOE OSTI2020

Predicting metal–metal interactions. II. Accelerating generalized schemes through physical insights

Operando-computational frameworks that integrate descriptors for catalyst stability within catalyst screening paradigms enable predictions of rates and selectivity on chemically faithful representations of nanoparticles under reaction conditions. These catalyst stability descriptors can be efficiently predicted by density functional theory (DFT)-based models. The alloy stability model, for example, predicts the stability of metal atoms in nanoparticles with site-by-site resolution. In this work, we use physical insights to present accelerated approaches of parameterizing this recently introduced alloy-stability model. These accelerated approaches meld quadratic functions for the energy of metal atoms in terms of the coordination number with linear correlations between model parameters and the cohesive energies of bulk metals. By interpolating across both the coordination number and chemical space, these accelerated approaches shrink the training set size for 12 fcc p- and d-block metals from 204 to as few as 24 DFT calculated total energies without sacrificing the accuracy of our model. We validate the accelerated approaches by predicting adsorption energies of metal atoms on extended surfaces and 147 atom cuboctahedral nanoparticles with mean absolute errors of 0.10 eV and 0.24 eV, respectively. This efficiency boost will enable a rapid and exhaustive exploration of the vast material space of transition metal alloys for catalytic applications.

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

Efficient and universal characterization of atomic structures through a topological graph order parameter

Abstract A graph-based order parameter, based on the topology of the graph itself, is introduced for the characterization of atomistic structures. The order parameter is universal to any material/chemical system and is transferable to all structural geometries. Four sets of data are used to validate both the generalizability and accuracy of the algorithm: (1) liquid lithium configurations spanning up to 300 GPa, (2) condensed phases of carbon along with nanotubes and buckyballs at ambient and high temperature, (3) a diverse set of aluminum configurations including surfaces, compressed and expanded lattices, point defects, grain boundaries, liquids, nanoparticles, all at nonzero temperatures, and (4) eleven niobium oxide crystal phases generated with ab initio molecular dynamics. We compare our proposed method to existing, state-of-the-art methods for the cases of aluminum and niobium oxide. Our order parameter uniquely classifies every configuration and outperforms all studied existing methods, opening the door for its use in a multitude of complex application spaces that can require fine structure-level characterization of atomistic graphs.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Approximate two-body generating Hamiltonian for the particle-hole Pfaffian wave function

We present two two-body Hamiltonians that approximate the exact particle-hole Pfaffian wave function with their ground states for all the system sizes where this wave function has been numerically constructed to date. The approximate wave functions have high overlap with the original and reproduce well the low-lying entanglement spectrum and structure factor. The approximate generating Hamiltonians are obtained by an optimization procedure where three to four pseudopotentials are varied in the neighbourhood of second Landau level Coulomb interaction or of a noninteracting model. They belong to a finite region in the variational space of Hamiltonians where each point approximately generates the particle-hole Pfaffian. Here we diagonalize the identified Hamiltonians for up to 20 electrons and find that for them the particle-hole Pfaffian shift appears energetically more favorable. The possibility to interpret the data in terms of composite fermions is discussed.

36 MATERIALS SCIENCE↗
DOE OSTI2025

A new tubular ironless linear induction motor using non-interrupted winding method

The ironless linear induction motor device can be used for any application which requires a large motion span or rotation restrictedly by the ironless feature due to the strong magnetic field environment. One of the possible applications is ITER diagnostics shutters. The tokamak reactor systems have a severe radiation issue during the operation. The traditional Kapton-insulated wires have significantly lower radiation resistance than an expected large radiation dose at ITER Motion Stark Effect (MSE) shutter location. Furthermore, the traditional single-sided linear induction motor winds the wire to make the N-turn pitch coils independently and then connect them in series to make a one-phase winding. Therefore, it is a big challenge to make so many radiation-protection connectors in such a limited space as inside the vacuum vessel of fusion reactors. The approved mineral-insulated kinds of cables need a large bend radius for the end turns, so the traditional single-sided linear motor with two-layer three-phase windings need to be upgraded to the tubular linear motors. The new proposed tubular ironless linear induction motor can not only overcome the large bend radius issue with the mineral-insulated cables but also allow the motor coils wound continuously around the tubular-shaped stator, forward and backward N times to make a N-turn winding for each phase, in order to resolve the radiation protection issue with the winding connection. The 3D transient Maxwell electromagnetic model with a tubular three-phase linear induction motor has been analyzed. Furthermore, this paper will present the detailed design and winding method of ironless linear induction motor actuators, and results of the 3D transient numerical simulation of the actuator performance.

Ironless↗
DOE OSTI2020

Chemical Robotics Enabled Exploration of Stability in Multicomponent Lead Halide Perovskites via Machine Learning

Metal halide perovskites have attracted immense interest as a promising material for a variety of optoelectronic and sensing applications. However, issues regarding long-term stability have emerged as the key bottleneck for commercialization. Here, we develop an automated experimental workflow based on combinatorial synthesis and rapid throughput characterization to explore long-term stability of these materials in ambient conditions. We apply it to four model perovskite systems: MA x FA y Cs 1–x–y PbBr 3 , MA x FA y Cs 1–x–y PbI 3 , Cs x FA y MA 1–x–y Pb(Br x+y I 1–x–y ) 3 , and Cs x MA y FA 1–x–y Pb(I x+y Br 1–x–y ) 3 . Non-negative matrix factorization and Gaussian process regression are used to interpolate the photoluminescent behavior of the phase diagram. This interpolative regression analysis helps to distinguish mixtures that form solid solutions from those that segregate into multiple materials, pointing out the most stable regions of the phase diagram. Here, we find stability dependence on composition to be nonuniform within the composition space, suggesting the presence of potential preferential compositional regions. This proposed workflow is universal and can be applied to other solution-processable materials.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Data-driven design of novel halide perovskite alloys

The great tunability of the properties of halide perovskites presents new opportunities for optoelectronic applications as well as significant challenges associated with exploring combinatorial chemical spaces. Here, in this work, we develop a framework powered by high-throughput computations and machine learning for the design and prediction of mixed cation halide perovskite alloys. In a chemical space of ABX 3 perovskites with a selected set of options for A, B, and X species, pseudo-cubic structures with B-site mixing are simulated using density functional theory (DFT) and several properties are computed, including stability, lattice constant, band gap, vacancy formation energy, refractive index, and optical absorption spectrum, using both semi-local and hybrid functionals. Neural networks (NN) are used to train predictive models for every property using tabulated elemental properties of A, B, and X site species as descriptors. Starting from a DFT dataset of 229 points, we use the trained NN models to predict the structural, energetic, electronic, and optical properties of an extensive dataset of 17955 compounds, and perform high-throughput screening in terms of stability, band gap, and defect tolerance, to obtain 392 promising compounds that are ranked as potential absorbers according to their photovoltaic figure of merit. Compositional trends in the screened set of attractive mixed cation halide perovskites are revealed and additional computations are performed on selected compounds. The data-driven design framework developed here is promising for designing novel mixed compositions and can be extended to a wider perovskite chemical space in terms of A, B, and X species, different kinds of mixing at the A, B, or X sites, non-cubic phases, and other properties of interest.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Neutrino energy reconstruction from semi-inclusive samples

We study neutrino-nucleus charged-current reactions on finite nuclei for the situation in which an outgoing muon and a proton are detected in coincidence, {\it i.e.,} we focus on semi-inclusive cross sections. We limit our attention to one-body current interactions (quasielastic scattering) and assess the impact of different nuclear effects in the determination of the neutrino energy. We identify the regions in phase space where the neutrino energy can be reconstructed relatively well, and study whether the cross section in those regions is significant. Our results indicate that it is possible to filter more than 50\% of all events according to the muon and proton kinematics, so that for the DUNE and T2K fluxes the neutrino energy can be determined with an uncertainty of less than 1\% and 3\%, respectively. Furthermore, we find that the reconstructed neutrino energy does not depend strongly on how one treats the final-state interactions and is not much affected by the description of the initial state. On the other hand, the estimations of the uncertainty on the neutrino energy show important sensitivity to the modeling of the initial state.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2022

Representations and strategies for transferable machine learning improve model performance in chemical discovery

Strategies for machine-learning (ML)-accelerated discovery that are general across material composition spaces are essential, but demonstrations of ML have been primarily limited to narrow composition variations. By addressing the scarcity of data in promising regions of chemical space for challenging targets such as open-shell transition-metal complexes, general representations and transferable ML models that leverage known relationships in existing data will accelerate discovery. Over a large set (~1000) of isovalent transition-metal complexes, we quantify evident relationships for different properties (i.e., spin-splitting and ligand dissociation) between rows of the Periodic Table (i.e., 3d/4d metals and 2p/3p ligands). We demonstrate an extension to the graph-based revised autocorrelation (RAC) representation (i.e., eRAC) that incorporates the group number alongside the nuclear charge heuristic that otherwise overestimates dissimilarity of isovalent complexes. To address the common challenge of discovery in a new space where data are limited, we introduce a transfer learning approach in which we seed models trained on a large amount of data from one row of the Periodic Table with a small number of data points from the additional row. We demonstrate the synergistic value of the eRACs alongside this transfer learning strategy to consistently improve model performance. Analysis of these models highlights how the approach succeeds by reordering the distances between complexes to be more consistent with the Periodic Table, a property we expect to be broadly useful for other material domains.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Dynamics of dark matter misalignment through the Higgs portal

A light singlet scalar field feebly coupled through the super-renormalizable Higgs portal provides a minimal and well-motivated realization of ultra-light bosonic dark matter. We study the cosmological production of dark matter in this model by elucidating the dynamics of two sources of scalar field misalignment generated during the radiation era. For large scalar masses (above $\mathcal{O}$ (10 −3 eV)), dark matter is produced through thermal misalignment, by which the scalar field is driven towards large field values as a result of the finite-temperature effective potential. The dominance of thermal misalignment in this mass range leads to a sharp relic abundance prediction which is, to a significant extent, insensitive to the initial conditions of the scalar field. On the other hand, for low mass scalars (below $\mathcal{O}$ (10 −5 eV)), dark matter is produced via VEV misalignment, which is caused by the induced scalar field vacuum expectation value triggered by the electroweak phase transition. We show that the relic abundance in this low mass range is sensitive to the scalar field initial conditions. In the intermediate mass range, the relic abundance is a consequence of a competition between thermal misalignment and VEV misalignment, which can potentially lead to novel forced resonance effects which cause a recurring enhancement and suppression in the late time oscillation amplitude as a function of the scalar mass. We compare our relic abundance predictions with constraints and projections from equivalence principle and inverse square law tests, stellar cooling, resonant molecular absorption, and observations of extra-galactic background light and diffuse X-ray backgrounds. New experimental ideas are needed to probe most of the cosmologically motivated regions of parameter space.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2020

Di-Higgs production in the 4b channel and gravitational wave complementarity

We present a complementarity study of gravitational waves and double Higgs production in the 4 b channel, exploring the gauge singlet scalar extension of the SM. This new physics extension serves as a simplified benchmark model that realizes a strongly first-order electroweak phase transition necessary to generate the observed baryon asymmetry in the universe. In calculating the signal-to-noise ratio of the gravitational waves, we incorporate the effect of the recently discovered significant suppression of the gravitational wave signals from sound waves for strong phase transitions, make sure that supercooled phase transitions do complete and adopt a bubble wall velocity that is consistent with a successful electroweak baryogenesis by solving the velocity profiles of the plasma. The high-luminosity LHC sensitivity to the singlet scalar extension of the SM is estimated using a shape-based analysis of the invariant 4 b mass distribution. We find that while the region of parameter space giving detectable gravitational waves is shrunk due to the new gravitational wave simulations, the qualitative complementary role of gravitational waves and collider searches remain unchanged.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2024

Correction to “Frank–Kasper Phases of Diblock Copolymer Melts Studied with the DPD Model: SCF Results”

In a recent study, (1) we performed the self-consistent field (SCF) calculations of a dissipative particle dynamics (DPD) model of conformationally asymmetric diblock copolymer A-B melts to study the stability of various Frank–Kasper (FK) phases formed by such A-B melts. While all the equations in ref (1) are correct, we did not calculate the dimensionless (mean-field) Helmholtz free energies per chain βf c = βu c,χ + βu c,κ – s c /k B and the dimensionless stresses dβf c /dθ of ordered phases accurately. For example, the dimensionless (nonbonded) internal energy per chain due to the system compressibility βu c,κ = (N/2κ)∑ q βû 0 (|q|)(ϕ̂ A (q) + ϕ̂ B (q) – δ q,0 )(ϕ̂ A (−q) + ϕ̂ B (−q) – δ– q,0 ) should be calculated in the reciprocal space as given (note that βû 0 (|q|) is obtained analytically, and that since ϕ A (r) is real 𝜙̂ A (−𝐪)= $\overline{𝜙̂ A}$(𝐪), i.e., the complex conjugate of ϕ̂ A (q)); this corresponds to numerically evaluating βu c,κ = (N/2κ)∫dr(ϕ A (r) + ϕ B (r) – 1)ψ(r) with ψ(r) ≡ (∫dr′βu 0 (|r–r′|)(ϕ A (r′) + ϕ B (r′) – 1)/V in the real space via the (composite) trapezoidal rule. While the trapezoidal rule is less accurate than the Romberg integration (2) in general, the opposite occurs when the integration domain is periodic; this was pointed out by Matsen in ref (3) and explained in detail in refs (4and5). With our ignorance of this exceptional convergence property of the trapezoidal rule for periodic functions, we calculated all convolutions having the form of ψ(r) in the reciprocal space via the fast Fourier transforms (6) but those having the form of βu c,κ in the real space via Romberg integration; the latter leads to inaccurate results and unfortunately incorrect phase diagrams reported in ref (1), which are corrected here.

He, Juntong↗
DOE OSTI2026

Data mining and computational screening of Rashba-Dresselhaus splitting and optoelectronic properties in two-dimensional perovskite materials

Recent developments highlighting the promise of two-dimensional perovskites have vastly increased the compositional search space in the perovskite family. This presents a great opportunity for the realization of highly performant devices and practical challenges associated with the identification of candidate materials. High-fidelity computational screening offers great value in this regard. In this study, we carry out a multiscale computational workflow, generating a dataset of two-dimensional perovskites in the Dion-Jacobson and Ruddlesden-Popper phases. Our dataset comprises ten B-site cations, four halogens, and over 20 organic cations across over 2000 materials. We compute electronic properties, thermoelectric performance, and numerous geometric characteristics. Furthermore, we introduce a framework for the high-throughput computation of Rashba-Dresselhaus splitting. Finally, we use this dataset to train machine learning models for the accurate prediction of band gaps, candidate Rashba-Dresselhaus materials, and partial charges. The work presented herein can aid future investigations of two-dimensional perovskites with targeted applications in mind.

14 SOLAR ENERGY↗
DOE OSTI2022

Superfluid Weight Bounds from Symmetry and Quantum Geometry in Flat Bands

Flat-band superconductivity has theoretically demonstrated the importance of band topology to correlated phases. In two dimensions, the superfluid weight, which determines the critical temperature through the Berezinksii-Kosterlitz-Thouless criteria, is bounded by the Fubini-Study metric at zero temperature. We show this bound is nonzero within flat bands whose Wannier centers are obstructed from the atoms—even when they have identically zero Berry curvature. Next, we derive general lower bounds for the superfluid weight in terms of momentum space irreps in all 2D space groups, extending the reach of topological quantum chemistry to superconducting states. We find that the bounds can be naturally expressed using the formalism of real space invariants (RSIs) that highlight the separation between electronic and atomic degrees of freedom. Finally, using exact Monte Carlo simulations on a model with perfectly flat bands and strictly local obstructed Wannier functions, we find that an attractive Hubbard interaction results in superconductivity as predicted by the RSI bound beyond mean field. Hence, obstructed bands are distinguished from trivial bands in the presence of interactions by the nonzero lower bound imposed on their superfluid weight.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗