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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 775 records · Page 43
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Local atomic environment analysis of short and long-range solute-solute interactions in a symmetric tilt grain boundary

We develop an efficient molecular-statics algorithm for predicting local solute-solute interaction effects on grain-boundary segregation. This algorithm is applied to the segregation and interaction of Ni and Cu solutes in a Σ9 (221) symmetric tilt grain boundary in Ag. It is found that the strength of interaction between two solutes directly correlates with the change of average segregation energy in the local atomic environment of a fixed grain-boundary solute. It is shown that local interaction effects at grain boundaries can be either attractive or repulsive wherein long-range attractive effects increase the propensity for solute cluster nucleation. This study underscores the atomic nature of grain-boundary solute segregation and provides a tool that could yield meaningful insight into heterogeneous solute segregation phenomena in polycrystalline alloys beyond their dilute limit.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Shaker-structure interaction modeling and analysis for nonlinear force appropriation testing

Nonlinear force appropriation is an extension of its linear counterpart where sinusoidal excitation is applied to a structure with a modal shaker and phase quadrature is achieved between the excitation and response. While a standard practice in modal testing, modal shaker excitation has the potential to alter the dynamics of the structure under test. Previous studies have been conducted to address several concerns, but this work specifically focuses on a shaker-structure interaction phenomenon which arises during the force appropriation testing of a nonlinear structure. Under pure-tone sinusoidal forcing, a nonlinear structure may respond not only at the fundamental harmonic but also potentially at sub- or superharmonics, or it can even produce aperiodic and chaotic motion in certain cases. Shaker-structure interaction occurs when the response physically pushes back against the shaker attachment, producing non-fundamental harmonic content in the force measured by the load cell, even for pure tone voltage input to the shaker. This work develops a model to replicate these physics and investigates their influence on the response of a nonlinear normal mode of the structure. Experimental evidence is first provided that demonstrates the generation of harmonic content in the measured load cell force during a force appropriation test. This interaction is replicated by developing an electromechanical model of a modal shaker attached to a nonlinear, three-mass dynamical system. Several simulated experiments are conducted both with and without the shaker model in order to identify which effects are specifically due to the presence of the shaker. Finally, the results of these simulations are then compared to the undamped nonlinear normal modes of the structure under test to evaluate the influence of shaker-structure interaction on the identified system’s dynamics.

42 ENGINEERING↗
DOE OSTI2023

Tuning the Interaction between Platinum Single Atoms and Ceria by Zirconia Doping for Efficient Catalytic Ammonia Oxidation

Aiming at the development of an efficient NH 3 oxidation catalyst to eliminate the harmful NH 3 slip from the stationary flue gas denitrification system and diesel exhaust aftertreatment system, a facile ZrO 2 doping strategy was proposed to construct Pt 1 /Ce x Zr 1–x O 2 catalysts with a tunable Pt-CeO 2 interaction strength and Pt–O–Ce coordination environment. According to the results of systematic characterizations, Pt species supported on Ce x Zr 1–x O 2 were mainly in the form of single atoms when x ≥ 0.7, and the strength of the Pt-CeO 2 interaction and the coordination number of Pt–O–Ce bond (CN Pt–O–Ce ) on Pt 1 /Ce x Zr 1–x O 2 showed a volcanic change as a function of the ZrO 2 doping amount. Here, it was proposed that the balance between the reasonable concentration of oxygen defects and limited surface Zr–O x species well accounted for the strongest Pt-CeO 2 interaction and the highest CN Pt–O–Ce on Pt/Ce 0.9 Zr 0.1 O 2 . It was observed that the Pt/Ce 0.9 Zr 0.1 O 2 catalyst exhibited much higher NH 3 oxidation activity than other Pt/Ce x Zr 1–x O 2 catalysts. The mechanism study revealed that the Pt 1 species with the stronger Pt-CeO 2 interaction and higher CN Pt–O–Ce within Pt/Ce 0.9 Zr 0.1 O 2 could better activate NH 3 adsorbed on Lewis acid sites to react with O 2 thus resulting in superior NH 3 oxidation activity. This work provides a new approach for designing highly efficient Pt/CeO 2 based catalysts for low-temperature NH 3 oxidation.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Multipole Expansion of Atomic Electron Density Fluctuation Interactions in the Density-Functional Tight-Binding Method

The accuracy of the density-functional tight-binding (DFTB) method in describing noncovalent interactions is limited due to its reliance on monopole-based spherical charge densities. In this study, we present a multipole-extended second-order DFTB (mDFTB2) method that takes into account atomic dipole and quadrupole interactions. Furthermore, we combine the multipole expansion with the monopole-based third-order contribution, resulting in the mDFTB3 method. To assess the accuracy of mDFTB2 and mDFTB3, we evaluate their performance in describing noncovalent interactions, proton transfer barriers, and dipole moments. Here, our benchmark results show promising improvements even when using the existing electronic parameters optimized for the original DFTB3 model. Both mDFTB2 and mDFTB3 outperform their monopole-based counterparts, DFTB2 and DFTB3, in terms of accuracy. While mDFTB2 and mDFTB3 perform comparably for neutral and positively charged systems, mDFTB3 exhibits superior performance over mDFTB2 when dealing with negatively charged systems and proton transfers. Overall, the incorporation of the multipole expansion significantly enhances the accuracy of the DFTB method in describing noncovalent interactions and proton transfers.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

COCOMO2: A Coarse-Grained Model for Interacting Folded and Disordered Proteins

Biomolecular interactions are essential in many biological processes, including complex formation and phase separation processes. Coarse-grained computational models are especially valuable for studying such processes via simulation. Here, we present COCOMO2, an updated residue-based coarse-grained model that extends its applicability from intrinsically disordered peptides to folded proteins. This is accomplished with the introduction of a surface exposure scaling factor, which adjusts interaction strengths based on solvent accessibility, to enable the more realistic modeling of interactions involving folded domains without additional computational costs. COCOMO2 was parametrized directly with solubility and phase separation data to improve its performance on predicting concentration-dependent phase separation for a broader range of biomolecular systems compared to the original version. COCOMO2 enables new applications including the study of condensates that involve IDPs together with folded domains and the study of complex assembly processes. COCOMO2 also provides an expanded foundation for the development of multiscale approaches for modeling biomolecular interactions that span from residue-level to atomistic resolution.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Correction to “COCOMO2: A Coarse-Grained Model for Interacting Folded and Disordered Proteins”

Biomolecular interactions are essential in many biological processes, including complex formation and phase separation processes. Coarse-grained computational models are especially valuable for studying such processes via simulation. Here, we present COCOMO2, an updated residue-based coarse-grained model that extends its applicability from intrinsically disordered peptides to folded proteins. This is accomplished with the introduction of a surface exposure scaling factor, which adjusts interaction strengths based on solvent accessibility, to enable the more realistic modeling of interactions involving folded domains without additional computational costs. COCOMO2 was parametrized directly with solubility and phase separation data to improve its performance on predicting concentration-dependent phase separation for a broader range of biomolecular systems compared to the original version. COCOMO2 enables new applications including the study of condensates that involve IDPs together with folded domains and the study of complex assembly processes. COCOMO2 also provides an expanded foundation for the development of multiscale approaches for modeling biomolecular interactions that span from residue-level to atomistic resolution.

Molecular interactions↗
DOE OSTI2024

Probing Interactions between Adsorbed Polymers and γ-Al 2 O 3 Using Solid-State NMR

The interactions between polymers and metal oxide surfaces affect the physical properties of polymer composites and the selectivity of catalysts used for plastic conversion. Gauging the strengths of these interactions and how they depend on adsorption conformations and polymer structure is nevertheless quite challenging. Herein, we evaluate whether a recently introduced dynamic nuclear polarization-based surface-to-atom distance measurement method can be used to gauge the specific interactions between five vinyl polymers and an oxide support (alumina). The adsorption conformations of polymer monolayers were studied using site-specific 13 C{ 27 Al} rotational-echo saturation-pulse double-resonance (RESPDOR) experiments. The method is effective in revealing the average distance between the adsorbed polymer and the surface, as well as the fraction of the monomers that are adsorbed. Polymers that possess larger side chains are more weakly adsorbed, as evidenced by their formation of more numerous loop and tail structures. In conclusion, the measured RESPDOR dephasing data further reveals that polymer adsorption conformations are largely disordered and involve few hydrogen bonding interactions.

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

Complex pH-Dependent Interactions between Weak Polyelectrolyte Block Copolymer Micelles and Molecular Fluorophores

Amphiphilic block copolymers with weak polyelectrolyte blocks can assemble stimulus-responsive nanostructures and interfaces. Applications of these materials in drug delivery, biomimetics, and sensing largely rely on the well-understood swelling of polyelectrolyte chains upon deprotonation, often induced by changes in pH or ionic strength. This deprotonation can also tune interfacial interactions between the polyelectrolyte blocks and surrounding solution, an effect which is less studied than morphological swelling of polyelectrolytes but can be just as critical for intended function. Here, we investigate whether the pH-driven morphological response of polyelectrolyte-bearing nanostructures also affects the interactions of these nanostructures with molecules in solution, using micelles of a short-chain polybutadiene-block-poly(acrylic acid) (pBd–pAA) as a model system. Here we introduce a Förster resonance energy transfer (FRET) approach to probe interactions between micelles and fluorescent molecular solutes as a function of solution pH. As expected, the pAA corona of these pBd–pAA micelles increases in thickness monotonically as a function of pH. However, FRET efficiency, which provides a metric of the spatial proximity of fluorescently labeled micelles and freely diffusing fluorophores, exhibits complex nonmonotonic behavior as a function of pH, indicating that the average separation of micelles and acceptor fluorophores is not strictly correlated with micelle swelling. Dialysis experiments quantify the affinity of fluorophores for micelles as a function of pH, confirming that changes in FRET are driven almost entirely by the pH-dependent affinity of the pAA block for the investigated molecular fluorophores, not simply by a shape change of the pAA corona. This study provides key insights into the interfacial interactions between weak-polyelectrolyte-bearing nanostructures and molecular solutes, of importance for the development of their stimulus-responsive applications.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Reassembly of Peptide Nanofibrils on Live Cell Surfaces Promotes Cell–Cell Interactions

Nature regulates cellular interactions through the cell-surface molecules and plasma membranes. Despite advances in cell-surface engineering with diverse ligands and reactive groups, modulating cell–cell interactions through scaffolds of the cell-binding cues remains a challenging endeavor. Here, we assembled peptide nanofibrils on live cell surfaces to present the ligands that bind to the target cells. Surprisingly, with the same ligands, reducing the thermal stability of the nanofibrils promoted cellular interactions. Characterizations of the system revealed a thermally induced fibril disassembly and reassembly pathway that facilitated the complexation of the fibrils with the cells. Using the nanofibrils of varied stabilities, the cell–cell interaction was promoted to different extents with free-to-bound cell conversion ratios achieved at low (31%), medium (54%), and high (93%) levels. Further, this study expands the toolbox to generate desired cell behaviors for applications in many areas and highlights the merits of thermally less stable nanoassemblies in designing functional materials.

77 NANOSCIENCE AND NANOTECHNOLOGY↗
DOE OSTI2022

Understanding the Impacts of Support–Polymer Interactions on the Dynamics of Poly(ethyleneimine) Confined in Mesoporous SBA-15

Supported amines are a promising class of CO 2 sorbents offering large uptake capacities and fast uptake rates. Additionally, among supported amines, poly(ethyleneimine) (PEI) physically impregnated in the mesopores of SBA-15 silica is widely used. Within these composite materials, the chain dynamics and morphologies of PEI strongly influence the CO 2 capture performance, yet little is known about chain and macromolecule mobility in confined pores. Here, we probe the impact of the support–PEI interactions on the dynamics and structures of PEI at the support interface and the corresponding impact on CO 2 uptake performance, which yields critical structure–property relationships. The pore walls of the support are grafted with organosilanes with different chemical end groups to differentiate interaction modes (spanning from strong attraction to repulsion) between the pore surface and PEI. Combinations of techniques, such as quasi-elastic neutron scattering (QENS), 1 H T 1 –T 2 relaxation correlation solid-state NMR, and molecular dynamics (MD) simulations, are used to comprehensively assess the physical properties of confined PEI. We hypothesized that PEI would have faster dynamics when subjected to less attractive or repulsive interactions. However, we discover that complex interfacial interactions resulted in complex structure–property relationships. Indeed, both the chain conformation of the surface-grafted chains and of the PEI around the surface influenced the chain mobility and CO 2 uptake performance. By coupling knowledge of the dynamics and distributions of PEI with CO 2 sorption performance and other characteristics, we determine that the macroscopic structures of the hybrid materials dictate the first rapid CO 2 uptake, and the rate of CO 2 sorption during the subsequent gradual uptake stage is determined by PEI chain motions that promote diffusive jumps of CO 2 through PEI-packed domains.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Combining Force Fields and Neural Networks for an Accurate Representation of Chemically Diverse Molecular Interactions

A key goal of molecular modeling is the accurate reproduction of the true quantum mechanical potential energy of arbitrary molecular ensembles with a tractable classical approximation. The challenges are that analytical expressions found in general purpose force fields struggle to faithfully represent the intermolecular quantum potential energy surface at close distances and in strong interaction regimes; that the more accurate neural network approximations do not capture crucial physics concepts, e.g., nonadditive inductive contributions and application of electric fields; and that the ultra-accurate narrowly targeted models have difficulty generalizing to the entire chemical space. We therefore designed a hybrid wide-coverage intermolecular interaction model consisting of an analytically polarizable force field combined with a short-range neural network correction for the total intermolecular interaction energy. Here, we describe the methodology and apply the model to accurately determine the properties of water, the free energy of solvation of neutral and charged molecules, and the binding free energy of ligands to proteins. The correction is subtyped for distinct chemical species to match the underlying force field, to segment and reduce the amount of quantum training data, and to increase accuracy and computational speed. For the systems considered, the hybrid ab initio parametrized Hamiltonian reproduces the two-body dimer quantum mechanics (QM) energies to within 0.03 kcal/mol and the nonadditive many-molecule contributions to within 2%. Simulations of molecular systems using this interaction model run at speeds of several nanoseconds per day.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Attractive Noncovalent Interactions versus Steric Confinement in Asymmetric Supramolecular Catalysis

The remarkable catalytic performance of enzymes stems from their ability to engage in precise noncovalent interactions (NCIs) within a sterically confined space. Supramolecular catalysis seeks to emulate and understand these strategies through the rational design of simple and controlled catalyst microenvironments. While both steric confinement and attractive interactions have been invoked as key to host activity, their relative contribution to rate enhancement and selectivity, as well as potential trade-offs, remains an outstanding question. Here, we address this question by systematically comparing two metal–organic supramolecular catalysts, which differ in the strength of their attractive noncovalent interactions and in their cavity volume. Our findings reveal that the catalyst with the larger cavity, and with stronger available NCIs, exhibits both significant rate acceleration (100-fold) and enhanced enantioselectivity (84% vs 14% ee) in a model ketone reduction compared to its smaller analogue. Mechanistic analysis, binding competition experiments, and computational modeling indicate that these differences predominantly stem from stabilizing noncovalent interactions in the larger catalyst, a result that challenges existing steric-based models of supramolecular stereoinduction. Understanding the governing factors of asymmetric induction and rate acceleration in supramolecular hosts will undoubtedly inform future catalyst design.

Catalysts↗
DOE OSTI2025

Quantifying the Resolution Sensitivity of the Kain–Fritsch Scheme Across the Gray Zone by Isolating Interactions: A TWP‐ICE Case Study

The resolution sensitivity of the Kain–Fritsch (KF) convection scheme and the role of interactions between the physics and dynamics within the gray zone (<10 km) were investigated using the Separate Physics and Dynamics Experiment (SPADE) framework. Two groups of experiments were conducted using the Weather Research and Forecasting (WRF) model via traditional (Tradition) runs and SPADE runs with resolutions of 1, 2, 4, and 8 km during the wet period of the Tropical Warm Pool–International Cloud Experiment (TWP‐ICE). Results show that the KF scheme simulates the weakened convective processes well as the resolution increases in both groups, and the changes in the convective variables with resolution in SPADE are smaller than in the Tradition group. This indicates the important effects of interactions between model components on convection parameterizations as the resolution changes. Additionally, the microphysics variables remain nearly unchanged with resolution in SPADE and weaken slightly in Tradition as the resolution decreases, suggesting the relatively weaker influences of model interactions for the resolved‐cloud parameterization. Therefore, the scale‐aware behavior of KF scheme is further strengthened in Tradition runs, primarily through inhibiting the strength of stratiform processes through physics–dynamics interactions and physical components.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2020

Impacts of hydrogen bonding interactions with Np(v/vi)O 2 Cl 4 complexes: vibrational spectroscopy, redox behavior, and computational analysis

The neptunyl (Np(V)O 2 + /Np(VI)O 2 2+ ) cation is the dominant form of 237 Np in acidic aqueous solutions and the stability of the Np(V) and Np(VI) species is driven by the specific chemical constituents present in the system. Hydrogen bonding with the oxo group may impact the stability of these species, but there is limited understanding of how these intermolecular interactions influence the behavior of both solution and solid-state species. In the current study, we systematically evaluate the interactions between the neptunyl tetrachloride species and hydrogen donors in coordination complexes and in the related aqueous solutions. Both Np(V) compounds (N 2 C 4 H 12 ) 2 [Np(V)O 2 Cl 4 ]Cl (Np(V)pipz) and (NOC 4 H 10 ) 3 [Np(V)O 2 Cl 4 ] (Np(V)morph) exhibit directional hydrogen bonding to the neptunyl oxo group while Np(VI) compounds (NC 5 H 6 ) 2 [Np(VI)O 2 Cl 4 ] (Np(VI)pyr) and (NOC 4 H 10 ) 4 [Np(VI)O 2 Cl 4 ]·2Cl (Np(VI)morph) assemble via halogen interactions. Here, the Raman spectra of the solid-state phases indicate the activation of vibrational bands when there is asymmetry of the neptunyl bond, while these spectral features are not observed within the related solution phase spectra. Density functional theory calculations of the Np(V)pipz system suggest that activation of the ν 3 asymmetric stretch and other combination modes lead to additional complexity within the solid-state spectra. Electrochemical analyses of complexes in the solution phases are consistent with the results of the crystallization experiments as the voltammetric potentials of Np(V)/Np(VI) complexes in the presence of protonated heterocycles differ from the potentials of pure Np(V) and may correlate with the hydrogen bonding interactions.

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

Floquet control of indirect exchange interaction in periodically driven two-dimensional electron systems

We present a theory for the Ruderman–Kittel–Kasuya–Yosida (RKKY) interaction mediated by a two-dimensional (2D) electron system subjected to periodic driving. This is demonstrated for a 2D metal with two ferromagnetic chains deposited in parallel. Our calculations reveal new non-analytic features in the time-averaged spin susceptibility. For weak light–matter coupling, the RKKY interaction shows oscillations with a period tunable by the light amplitude and frequency. For stronger light–matter coupling, the interaction becomes non-oscillatory and remains purely ferromagnetic. Our findings open a path forward for realizing dynamic control of the indirect exchange interaction in 2D magnetic structures.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2025

Mitigation of ICRF—edge plasma interaction in Alcator C-Mod

The parasitic interaction between ion cyclotron range of frequencies (ICRF) waves and the edge plasma has long limited high-power ICRF utilization in magnetically confined fusion plasmas. In this paper, we report on the successful mitigation of this interaction by power tapering a four-strap field-aligned (FA) antenna in the Alcator C-Mod tokamak. With the antenna operated in dipole phasing ($0\pi0\pi$), the ratio of the power coupled by the central two straps ($P_\mathrm {cent}$) to the power coupled by the outer two straps was varied at fixed total coupled ICRF power ($P_\mathrm {tot}$). With $P_\mathrm {cent}$/$P_\mathrm {tot} \approx 0.8-0.9$, no enhancement of the plasma potential was measured despite 1 MW of coupled ICRF power. When the antenna is powered, energy deposition increases on its four corners and on neighboring limiter tiles magnetically connected to some of those corners. The energy deposited on the antenna and limiter is minimized together with near-field plasma potentials. Additionally, we show that deviation from $P_\mathrm {cent}$/$P_\mathrm {tot} \approx 0.8$ enhances wave-plasma interactions in places not magnetically connected to the antenna. These far-field effects are correlated with changes in the antenna spectrum. Hence, on C-Mod, near-field and far-field interactions were minimized for about the same range of $P_\mathrm {cent}$/$P_\mathrm {tot}$. Optimal power tapering was also found to improve ICRF heating efficiency and facilitate H-mode access. Finally, we show that the heat flux pattern on the toroidally aligned antennas reverses with the direction of the RF-induced E×B flow in front of the antenna, a correlation not observed for the FA antenna. We argue that the RF-induced E×B flow, which carries high-density plasma from the near-SOL, is aligned with the FA antenna and does not intercept its corners, where the plasma potential is large. This could explain the previously reported smaller impurity generation by the FA antenna (Wukitch et al 2013 Phys. Plasmas 20 056117).

Alcator C-Mod↗
DOE OSTI2021

Attractive and repulsive dipolar interaction in bilayers of indirect excitons

We explore attractive dipolar interaction in indirect excitons (IXs). For one layer of IXs in a single pair of coupled quantum wells (CQWs), the out-of-plane IX electric dipoles lead to repulsive dipolar interaction between IXs. The attractive dipolar interaction between IXs is realized in a two-CQW heterostructure with two IX layers in two separated CQW pairs. We found both in experimental measurements and theoretical simulations that increasing density of IXs in one layer causes a monotonic energy reduction for IXs in the other layer. We also found an in-plane shift of a cloud of IXs in one layer towards a cloud of IXs in the other layer. This behavior is qualitatively consistent with attractive dipolar interaction. In conclusion, the measured IX energy reduction and IX cloud shift are higher than the values given by the correlated liquid theory.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2021

Twisted bilayer graphene. III. Interacting Hamiltonian and exact symmetries

We derive the explicit Hamiltonian of twisted bilayer graphene (TBG) with Coulomb interaction projected into the flat bands and study the symmetries of the Hamiltonian. First, we show that all projected TBG Hamiltonians can be written as positive semidefinite Hamiltonians, an example of which was found in work by Kang and Vafek [Phys. Rev. Lett. 122, 246401 (2019)]. We then prove that the interacting TBG Hamiltonian exhibits an exact U(4) symmetry in the exactly flat band (nonchiral-flat) limit. We further define, besides a first chiral limit where the AA stacking hopping is zero, a second chiral limit where the AB/BA stacking hopping is zero. In the first chiral-flat limit (or second chiral-flat limit) with exactly flat bands, the TBG is enhanced to have an exact U(4) × U(4) symmetry, whose generators are different between the two chiral limits. While in the first chiral limit and in the nonchiral case these symmetries have been found in work by Bultinck et al. [Phys. Rev. X 10, 031034 (2020)], for the eight lowest bands, we here prove that they are valid for projection into any 8 n max particle-hole symmetric TBG bands, with n max > 1 being the practical case for small twist angles < 1°. Furthermore, in the first or second chiral-nonflat limit without flat bands, an exact U(4) symmetry still remains. We also elucidate the link between the U(4) symmetry presented here and the similar but different U(4) of Kang and Vafek [Phys. Rev. Lett. 122, 246401 (2019)]. Additionally, we show that our projected Hamiltonian can be viewed as the normal-ordered Coulomb interaction plus a Hartree-Fock term from passive bands, and exhibits a many-body particle-hole symmetry which renders the physics symmetric around charge neutrality. We also provide an efficient parametrization of the interacting Hamiltonian. The existence of two chiral limits with an enlarged symmetry suggests a possible duality of the model yet undiscovered.

2-dimensional systems↗