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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 631 records · Page 35
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Strategy for Direct Detection of Chiral Phonons with Phase-Structured Free Electrons

Chiral phonons possessing valley pseudoangular momentum (PAM) underlie a diversity of quantum phenomena of fundamental and applied importance, but are challenging to probe directly. We show that deficiencies of typical momentum-resolved electron energy loss measurements that make it impossible to distinguish the PAM of chiral phonons can be overcome by introducing pinwheel free electron states with well-defined PAM. Transitions between such states generate 2D periodic arrays of in-plane field vortices with polarization textures tailored to selectively couple to desired chiral mode symmetries.

chirality↗
NASA NTRS1992

The 10 kW power electronics for hydrogen arcjets

A combination of emerging mission considerations such as 'launch on schedule', resource limitations, and the development of higher power spacecraft busses has resulted in renewed interest in high power hydrogen arcjet systems with specific impulses greater than 1000 s for Earth-space orbit transfer and maneuver applications. Solar electric propulsion systems with about 10 kW of power appear to offer payload benefits at acceptable trip times. This work outlines the design and development of 10 kW hydrogen arcjet power electronics and results of arcjet integration testing. The power electronics incorporated a full bridge switching topology similar to that employed in state of the art 5 kW power electronics, and the output filter included an output current averaging inductor with an integral pulse generation winding for arcjet ignition. Phase shifted, pulse width modulation with current mode control was used to regulate the current delivered to arcjet, and a low inductance power stage minimized switching transients. Hybrid power Metal Oxide Semiconductor Field Effect Transistors were used to minimize conduction losses. Switching losses were minimized using a fast response, optically isolated, totem-pole gate drive circuit. The input bus voltage for the unit was 150 V, with a maximum output voltage of 225 V. The switching frequency of 20 kHz was a compromise between mass savings and higher efficiency. Power conversion efficiencies in excess of 0.94 were demonstrated, along with steady state load current regulation of 1 percent. The power electronics were successfully integrated with a 10 kW laboratory hydrogen arcjet, and reliable, nondestructive starts and transitions to steady state operation were demonstrated. The estimated specific mass for a flight packaged unit was 2 kg/kW.

Hamley, John A.↗
DOE OSTI2023

Melting, reentrant ordering and peak effect for Wigner crystals with quenched and thermal disorder

Abstract We consider simulations of Wigner crystals in solid state systems interacting with random quenched disorder in the presence of thermal fluctuations. When quenched disorder is absent, there is a well defined melting temperature determined by the proliferation of topological defects, while for zero temperature, there is a critical quenched disorder strength above which topological defects proliferate. When both thermal and quenched disorder are present, these effects compete, and the thermal fluctuations can reduce the effectiveness of the quenched disorder, leading to a reentrant ordered phase in agreement with the predictions of Nelson (1983 Phys. Rev. B 27 2902–14). There are two competing theories for the low temperature behavior, and our simulations show that both capture aspects of the actual response. The critical disorder strength separating ordered from disordered states remains finite as the temperature goes to zero, as predicted by Cha and Fertig (1995 Phys. Rev. Lett. 74 4867–70), instead of dropping to zero as predicted by Nelson. At the same time, the critical disorder strength decreases with decreasing temperature, as predicted by Nelson, instead of remaining constant, as predicted by Cha and Fertig. The onset of the reentrant phase can be deduced based on changes in the transport response, where the reentrant ordering appears as an increase in the mobility or the occurrence of a depinning transition. We also find that when the system is in the ordered state and thermally melts, there is an increase in the effective damping or pinning. This produces a drop in the electron mobility that is similar to the peak effect phenomenon found in superconducting vortices, where thermal effects soften the lattice or break down its elasticity, allowing the particles to better adjust their positions to take full advantage of the quenched disorder.

36 MATERIALS SCIENCE↗
DOE OSTI2026

Characterizing skyrmion flow phases with principal component analysis

Principal component analysis (PCA) is a powerful method that can identify patterns in large, complex data sets by constructing low-dimensional order parameters from higher-dimensional feature vectors. There are increasing efforts to use space-and-time-dependent PCA to detect transitions in nonequilibrium systems that are difficult to characterize with equilibrium methods. Here, we demonstrate that feature vectors incorporating the position and velocity information of driven skyrmions moving through random disorder permit PCA to resolve different types of disordered skyrmion motion as a function of driving force and the ratio of the Magnus force to the dissipation. Since the Magnus force creates gyroscopic motion and a finite Hall angle, skyrmions can exhibit a greater range of flow phases than what is observed in overdamped driven systems with quenched disorder. We show that in addition to identifying previously known skyrmion flow phases, PCA detects several additional phases, including different types of channel flow, moving fluids, and partially ordered states. Guided by the PCA analysis, we further characterize the disordered flow phases to elucidate the different microscopic dynamics and show that the changes in the PCA-derived order parameters can be connected to features in bulk transport measures, including the transverse and longitudinal velocity-force curves, differential conductivity, topological defect density, and changes in the skyrmion Hall angle as a function of drive. We discuss how asymmetric feature vectors can be used to improve the resolution of the PCA analysis, and how this technique can be extended to find disordered phases in other nonequilibrium systems with time-dependent dynamics.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Directional effects of antiferromagnetic ordering on the electronic structure in NdSb

The recent discovery of unconventional surface-state pairs, which give rise to Fermi arcs and spin textures, in antiferromagnetically ordered NdBi raised the interest in rare-earth monopnictides. Several scenarios of antiferromagnetic (AFM) order have been suggested to explain the origin of these states with some of them being consistent with the presence of nontrivial topologies. Here, in this paper, we use angle-resolved photoemission spectroscopy (ARPES) and density-functional-theory (DFT) calculations to investigate the electronic structure of NdSb. We found the presence of distinct domains that have different electronic structures at the surface. These domains correspond to different orientations of magnetic moments in the AFM state with respect to the surface. We demonstrated remarkable agreement between DFT calculations and ARPES that capture all essential changes in the band structure caused by the transition to a magnetically ordered state.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2022

High-pressure control of optical nonlinearity in the polar Weyl semimetal TaAs

The transition metal monopnictide family of Weyl semimetals recently has been shown to exhibit anomalously strong second-order optical nonlinearity, which is theoretically attributed to a highly asymmetric polarization distribution induced by their polar structure. We experimentally test this hypothesis by measuring optical second harmonic generation (SHG) from TaAs across a pressure-tuned polar-to-nonpolar structural phase transition. Despite the high-pressure structure remaining noncentrosymmetric, the SHG yield is reduced by more than 60% by 20 GPa as compared to the ambient pressure value. By examining the pressure dependence of distinct groups of SHG susceptibility tensor elements, we find that the yield is primarily controlled by a single element that governs the response along the polar axis. Furthermore, our results confirm a connection between the polar axis and the giant optical nonlinearity of Weyl semimetals and demonstrate pressure as a means to tune this effect in situ.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2023

Real-space imaging of periodic nanotextures in thin films via phasing of diffraction data

New properties and exotic quantum phenomena can form due to periodic nanotextures, including Moire patterns, ferroic domains, and topologically protected magnetization and polarization textures. Despite the availability of powerful tools to characterize the atomic crystal structure, the visualization of nanoscale strain-modulated structural motifs remains challenging. Here, we develop nondestructive real-space imaging of periodic lattice distortions in thin epitaxial films and report an emergent periodic nanotexture in a Mott insulator. Specifically, we combine iterative phase retrieval with unsupervised machine learning to invert the diffuse scattering pattern from conventional X-ray reciprocal-space maps into real-space images of crystalline displacements. Our imaging in PbTiO 3 /SrTiO 3 superlattices exhibiting checkerboard strain modulation substantiates published phase-field model calculations. Furthermore, the imaging of biaxially strained Mott insulator Ca 2 RuO 4 reveals a strain-induced nanotexture comprised of nanometer-thin metallic-structure wires separated by nanometer-thin Mott-insulating-structure walls, as confirmed by cryogenic scanning transmission electron microscopy (cryo-STEM). The nanotexture in Ca 2 RuO 4 film is induced by the metal-to-insulator transition and has not been reported in bulk crystals. We expect the phasing of diffuse X-ray scattering from thin crystalline films in combination with cryo-STEM to open a powerful avenue for discovering, visualizing, and quantifying the periodic strain-modulated structures in quantum materials.

Science & Technology - Other Topics↗
NASA NTRS1990

Analysis and design of a high power, digitally-controlled spacecraft power system

The progress to date on the analysis and design of a high power, digitally controlled spacecraft power system is described. Several battery discharger topologies were compared for use in the space platform application. Updated information has been provided on the battery voltage specification. Initially it was thought to be in the 30 to 40 V range. It is now specified to be 53 V to 84 V. This eliminated the tapped-boost and the current-fed auto-transformer converters from consideration. After consultations with NASA, it was decided to trade-off the following topologies: (1) boost converter; (2) multi-module, multi-phase boost converter; and (3) voltage-fed push-pull with auto-transformer. A non-linear design optimization software tool was employed to facilitate an objective comparison. Non-linear design optimization insures that the best design of each topology is compared. The results indicate that a four-module, boost converter with each module operating 90 degrees out of phase is the optimum converter for the space platform. Large-signal and small-signal models were generated for the shunt, charger, discharger, battery, and the mode controller. The models were first tested individually according to the space platform power system specifications supplied by NASA. The effect of battery voltage imbalance on parallel dischargers was investigated with respect to dc and small-signal responses. Similarly, the effects of paralleling dischargers and chargers were also investigated. A solar array and shunt model was included in these simulations. A model for the bus mode controller (power control unit) was also developed to interface the Orbital replacement Unit (ORU) model to the platform power system. Small signal models were used to generate the bus impedance plots in the various operating modes. The large signal models were integrated into a system model, and time domain simulations were performed to verify bus regulation during mode transitions. Some changes have subsequently been incorporated into the models. The changes include the use of a four module boost discharger, and a new model for the mode controller, which includes the effects of saturation. The new simulations for the boost discharger show the improvement in bus ripple that can be achieved by phase-shifted operation of each of the boost modules.

Lee, F. C.↗
DOE OSTI2023

YbV 3 ⁢Sb 4 and EuV 3 ⁢Sb 4 vanadium-based kagome metals with Yb 2+ and Eu 2+ zigzag chains

Here, in this work, we present Yb⁢V 3 ⁢Sb 4 and Eu⁢V 3 ⁢Sb 4 , two compounds exhibiting slightly distorted vanadium-based kagome nets interleaved with zigzag chains of divalent Yb 2+ and Eu 2+ ions. Single crystal growth methods are reported alongside magnetic, electronic, and heat capacity measurements. Yb⁢V 3⁢ Sb 4 is a nonmagnetic metal with no collective phase transitions observed between 60 mK and 300 K. Conversely, Eu⁢V 3 ⁢Sb 4 is a magnetic kagome metal exhibiting easy-plane ferromagneticlike order below T C =32 K with hints of modulated spin texture under low field. With Yb⁢V 3 ⁢Sb 4 and Eu⁢V 3 ⁢Sb 4 we demonstrate another direction for the discovery and development of vanadium-based kagome metals while incorporating the chemical and magnetic degrees of freedom offered by a rare-earth sublattice.

36 MATERIALS SCIENCE↗
NASA NTRS1999

Phase Diagrams of Electric-Fduced Aggregation in Conducting Colloids

Under the application of a sufficiently strong electric field, a suspension may undergo reversible phase transitions from a homogeneous random arrangement of particles into a variety of ordered aggregation patterns. The surprising fact about electric-field driven phase transitions is that the aggregation patterns, that are observed in very diverse systems of colloids, display a number of common structural features and modes of evolution thereby implying that a universal mechanism may exist to account for these phenomena. It is now generally believed that this mechanism emanates from the presence of the long-range anisotropic interactions between colloidal particles due to their polarization in an applied field. But, in spite of numerous applications of the electric-field-driven phenomena in biotechnology, separation, materials engineering, chemical analysis, etc. our understanding of these phenomena is far from complete. Thus, it is the purpose of the proposed research to develop a theory and then test experimentally, under normal- and low-gravity conditions, the accuracy of the theoretical predictions regarding the effect of the synergism of the interparticle electric and hydrodynamic interactions on the phase diagram of a suspension. The main results from our theoretical studies performed to-date enable one to trace how the variations of the electrical properties of the constituent materials influence the topology of the suspension phase diagram and then, by using an appropriate phase diagram, to evaluate how the electric-field-induced transformations will depend on the frequency and the strength of the applied field.

Khusid, B.↗
DOE OSTI2024

Discovering Classical Spin Liquids by Topological Search of High Symmetry Nets

Spin liquids are a paradigmatic example of a nontrivial state of matter. The search for new spin liquids is a key interdisciplinary challenge. Geometrical frustration-where the geometry of the net that the spins occupy precludes the generation of a simple ordered state-is a particularly fruitful way to generate these intrinsically disordered states. Prior focus has been on a handful of high symmetry nets. There are, however, many three-dimensional nets, each of which has the potential to form unique states. In this paper, we investigate the high symmetry nets-those which are both vertex- and edge-transitive-for the simplest possible interaction sets: nearest-neighbor couplings of antiferromagnetic Heisenberg and Ising spins. While the well-known crs (pyrochlore) net is the only nearest-neighbor Heisenberg antiferromagnet which does not order, we identify two new frustrated nets (lcx and thp) possessing finite temperature Heisenberg spin-liquid states with strongly suppressed magnetic ordering and noncollinear ground states. With Ising spins, we identify three new classical spin liquids that do not order down to T/J = 0.01. We highlight materials that contain these high symmetry nets, and which could, if substituted with appropriate magnetic ions, potentially host these unusual states. Our systematic survey will guide searches for novel magnetic phases.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Potential Skyrmion Host Fe(IO3)3: Connecting Stereoactive Lone-Pair Electron Effects to the Dzyaloshinskii-Moriya Interaction

Magnetic skyrmions, which are topologically distinct magnetic spin textures, are gaining increased attention for their unique physical properties and potential applications in spintronic devices. Here we present a design strategy for skyrmion host candidates based on combinations of magnetic spin, asymmetric building units having stereoactive lone-pair electrons, and polar lattice symmetry. To demonstrate the viability of the proposed rational design principles, we successfully synthesized a Fe(IO 3 ) 3 polycrystalline sample and single crystals by using a new simplified low-temperature pathway, which is experimentally feasible for extending materials growth of transition metal iodates. Single crystal X-ray and powder synchrotron X-ray diffraction measurements demonstrated that Fe(IO 3 ) 3 crystallizes in the polar chiral hexagonal lattice with space group P63. The combined structural features of the macroscopic electric polarization along the c-axis stemming from the coalignment of the stereoactive lone-pairs of the IO 3 – trigonal pyramid and the magnetic Fe 3+ cation residing on the 3-fold rotation axis were selected to promote asymmetric exchange coupling. We find evidence of a predicted skyrmion phase at 14 K ≤ T ≤ 16 K and 2.5 T ≤ μ 0 H ≤ 3.2 T driven by a Dzyaloshinskii–Moriya (DM) interaction, a conclusion supported by the appreciable DM exchange and the zero-field spiral antiferromagnetic ground state of Fe(IO 3 ) 3 deduced from neutron diffraction experiments. The associated magnetic modulation wavelength of the putative skyrmions is expected to be short ~18 nm, comparable to the period of the DM-driven incommensurate order. This work links stereoactive lone-pair electron effects to enhanced DM interaction, demonstrating a new approach for chemical guidelines in the search for skyrmionic states of matter.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Computationally Directed Discovery of MoBi 2

Incorporating bismuth, the heaviest element stable to radioactive decay, into new materials enables the creation of emergent properties such as permanent magnetism, superconductivity, and nontrivial topology. Understanding the factors that drive Bi reactivity is critical for the realization of these properties. Using pressure as a tunable synthetic vector, we can access unexplored regions of phase space to foster reactivity between elements that do not react under ambient conditions. Furthermore, combining computational and experimental methods for materials discovery at high-pressures provides broader insight into the thermodynamic landscape than can be achieved through experiment alone, informing our understanding of the dominant chemical factors governing structure formation. Herein, we report our combined computational and experimental exploration of the Mo–Bi system, for which no binary intermetallic structures were previously known. Using the ab initio random structure searching (AIRSS) approach, we identified multiple synthetic targets between 0–50 GPa. Highpressure in situ powder X-ray diffraction experiments performed in diamond anvil cells confirmed that Mo–Bi mixtures exhibit rich chemistry upon the application of pressure, including experimental realization of the computationally predicted CuAl 2 -type MoBi 2 structure at 35.8(5) GPa. Electronic structure and phonon dispersion calculations on MoBi 2 revealed a correlation between valence electron count and bonding in high-pressure transition metal–Bi structures as well as identified two dynamically stable ambient pressure polymorphs. Our study demonstrates the power of the combined computational–experimental approach in capturing highpressure reactivity for efficient materials discovery.

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

Time-reversal symmetry-breaking charge order in a kagome superconductor

The kagome lattice 1 , which is the most prominent structural motif in quantum physics, benefits from inherent non-trivial geometry so that it can host diverse quantum phases, ranging from spin-liquid phases, to topological matter, to intertwined orders 2,3,4,5,6,7,8 and, most rarely, to unconventional superconductivity 6,9 . Recently, charge sensitive probes have indicated that the kagome superconductors AV 3 Sb 5 (A = K, Rb, Cs) 9,10,11 exhibit unconventional chiral charge order 12,13,14,15,16,17,18,19, which is analogous to the long-sought-after quantum order in the Haldane model 20 or Varma model 21 . However, direct evidence for the time-reversal symmetry breaking of the charge order remains elusive. Here we use muon spin relaxation to probe the kagome charge order and superconductivity in KV 3 Sb 5 . We observe a noticeable enhancement of the internal field width sensed by the muon ensemble, which takes place just below the charge ordering temperature and persists into the superconducting state. Notably, the muon spin relaxation rate below the charge ordering temperature is substantially enhanced by applying an external magnetic field. We further show the multigap nature of superconductivity in KV 3 Sb 5 and that the T c /λ$^{-2}_{ab}$ ratio (where T c is the superconducting transition temperature and λ ab is the magnetic penetration depth in the kagome plane) is comparable to those of unconventional high-temperature superconductors. Our results point to time-reversal symmetry-breaking charge order intertwining with unconventional superconductivity in the correlated kagome lattice.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
NASA NTRS1991

Chemical spray pyrolysis of Tl-Ba-Ca-Cu-O high-T(sub c) superconductors for high-field bitter magnets

The deposition of Tl-Ba-Ca-Cu-O thick films by spray pyrolyzing a Ba-Ca-Cu-O precursor film and diffusing thallium into the film to form the superconducting phase is examined. This approach was taken to reduce exposure to thallium and its health and safety hazards. The Tl-Ba-Ca-Cu-O system was selected because it has very attractive features which make it appealing to device and manufacturing engineering. Tl-Ba-Ca-Cu-O will accommodate a number of superconducting phases. This attribute makes it very forgiving to stoichiometric fluctuations in the bulk and film. It has excellent thermal and chemical stability, and appears to be relatively insensitive to chemical impurities. Oxygen is tightly bound into the systems, consequently there is no orthorhombic (conductor) to tetragonal (insulator) transition which would affect a component's lifetime. More significantly, the thallium based superconductors appear to have harder magnetic properties than the other high-Tc oxide ceramics. Estimates using magnetoresistance measurements indicate that at 77 K Tl2Ba2CaCu2O10 will have an upper critical field, H(sub c2) fo 26 Tesla for applied fields parallel to the c-axis and approximately 1000 Tesla for fields oriented in the a-b plane. Results to date have shown that superconducting films can be reproducibly deposited on 100 oriented MgO substrates. One film had a zero resistance temperature of 111.5 K. Furthermore, x ray diffraction analysis of the films showed preferential c-axis orientation parallel to the plane of the substrate. These results have now made it possible to consider the manufacture of a superconducting tape wire which can be configured into a topology useful for high-field magnet designs. The research which leads to the preparation of these films and plans for further development are reviewed.

Derochemont, L. Pierre↗
DOE OSTI2022

Optical control of topological memory based on orbital magnetization

Under suitable conditions, some twisted graphene multilayers and transition-metal dichalcogenides become Chern insulators, exhibiting the anomalous quantum Hall effect and orbital magnetization due to spontaneous valley polarization. We study the interaction of a Chern insulator with circularly polarized light. Here, the interaction energy contains an antisymmetric term that couples to the helicity of incident light. For a two-band Chern insulator, this term is expressed as an integral involving the Berry curvature of the system. Taking advantage of this interaction, we propose an experimental protocol for switching topological memory based on orbital magnetization by circularly polarized light. Moreover, two laser beams of opposite circular polarization can nucleate domains of opposite magnetization and thus produce an optically configurable domain wall carrying topologically protected chiral edge modes.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Control over emergence and alignment of transient blisters in thermo-responsive gels using hierarchically patterned substrates

Surfaces with tunable microscale textures are vital in a large variety of technological applications, including heat transfer, antifouling and adhesion. To facilitate such broad-scale use, there is a need to create surfaces that undergo reconfigurable changes in topology and thus, enable switchable functionality. To date, there is a relative dearth of methods for engineering surfaces that can be actuated to change topography over a range of length scales, and hence, form tunable hierarchically structured layers. Combining modeling and experiments, we design a geometrically patterned, thermo-responsive poly (N-isopropylacrylamide) gel film that undergoes controllable hierarchical changes in topology with changes in temperature. At the bottom, the film is covalently bound to a solid, curved substrate; at the top, the film encompasses longitudinal rectangular ridges that are oriented perpendicular to the underlying cylindrical curves. At temperatures below lower critical solution temperature (LCST), the swollen gel exhibits 3D variations in polymer density and thickness defined by the gel's top and bottom topography. As the temperature rises above LCST, the interplay between the upper ridges and lower curves in the gel drives non-uniform, directional solvent transport, the nucleation and propagation of a phase-separated higher-density skin layer, and the resulting pressure buildup within the film. These different, interacting kinetic processes lead to an instability, which produces transient microscopic blisters in the film. Through simulations, we show how tuning the width of the ridges modifies the propagation of a skin layer and creates localized pressure build-up points, which enables control over the emergence, distribution, and alignment of the microscopic blisters. Futhermore, we provide a simple argument to predict the size of such microscopic features. Experiments confirm our predictions and further highlight how our computational model enables the rational design of topographical transitions in these tunable films. The development of actuatable, hierarchically structured films provides new routes for achieving switchable functionality in actuators, drug release systems and adhesives.

42 ENGINEERING↗
DOE OSTI2022

First-principles calculation of gate-tunable ferromagnetism in magic-angle twisted bilayer graphene under pressure

Magic-angle twisted bilayer graphene (MATBG) is notable as a highly tunable platform for investigating strongly correlated phenomena such as unconventional superconductivity and quantum spin liquids, due to easy control of doping level through gating and sensitive dependence of the magic angle on hydrostatic pressure. Experimental observations of correlated insulating states, unconventional superconductivity and ferromagnetism in MATBG indicate that this system exhibits rich exotic phases. In this work, using density functional theory calculations in conjunction with the effective screening medium method, we find the MATBG under pressure at a twisting angle of 2.88 °and simulate how its electronic states evolve when doping level and electric field perpendicular to plane are tuned by gating. Our calculations show that, at doping levels between two electrons and four holes per moiré unit cell, a ferromagnetic (FM) solution with spin density localized at AA stacking sites is lower in energy than the nonmagnetic solution. The magnetic moment of this FM state decreases with both electron and hole doping and vanishes at four electrons/holes doped per moiré unit cell. Hybridization between the flat bands at the Fermi level and the surrounding dispersive bands can take place at finite doping. On increasing the out-of-plane electric field at zero doping, a transition from the FM state to the nonmagnetic one is seen. An investigation of impurity effects shows that both absorption of O 2 molecules and occurrence of Stone–Wales impurities suppress the FM state, and the mechanisms are understood from our calculations. We also analyze the interlayer bonding character due to flat bands via Wannier functions. Finally, we report trivial band topology of the flat bands in the FM state at a certain doping level.

Physics↗