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DOE OSTI2025

Integrated process-structure–property–performance optimization of cold-sprayed zinc coatings on AZ91 magnesium alloy

High-pressure die cast (HPDC) AZ91 magnesium alloy is widely used in automotive components such as transmission housings and brackets for its excellent strength-to-weight ratio. Zinc-based cold spray coatings can be applied selectively to vulnerable areas to enhance corrosion resistance, minimize galvanic coupling with dissimilar metals, and eliminate the need for full-surface oxide coatings, making the process more efficient and targeted. A comprehensive evaluation of 16 combinations of nitrogen carrier gas temperatures and pressures led to the identification of an optimal range of process parameters, yielding Zn coatings with porosity <0.5 % by area, wear rates reduced by a factor of two compared to uncoated AZ91, and adhesion strengths up to 35 MPa. The enhanced mechanical performance of the coating is attributed to the low porosity and the formation of a metallurgical bond at the coating-substrate interface. Corrosion studies using macroscale potentiodynamic polarization (PDP) and electrochemical impedance spectroscopy (EIS) revealed a significant decrease in corrosion rate and a shift to more noble corrosion potentials (ZCP) for coated substrates. Furthermore, the Zn cold-sprayed samples exhibited significantly lower corrosion-induced evolved hydrogen content compared to the base AZ91 substrate and AZ91 coated with industrial coatings, demonstrating that the Zn layer effectively protects the substrate from the corrosive environment. Overall, cold spray Zn coatings significantly improve the mechanical and corrosion performance of AZ91 Mg alloys, addressing key material challenges and enabling their broader use in automotive applications.

Corrosion performance↗

DOE OSTI2023

Co 2 Mo 6 S 8 Catalyzes Nearly Exclusive Electrochemical Nitrate Conversion to Ammonia with Enzyme-like Activity

Electrocatalytic nitrate to ammonia conversion is a key reaction for energy and environmental sustainability. This reaction involves complex multi electron and proton transfer steps, and is impeded by the lack of catalyst for promoting both reactivity and ammonia selectivity. Here, we demonstrate active motifs based on the Chevrel phase Co 2 Mo 6 S 8 exhibit an enzyme-like high turnover frequency of ~95.1 s –1 for nitrate electroreduction to ammonia. We reveal strong synergy of multiple binding sites on this catalyst, such that the ligand effect of Co steers H ad* toward hydrogenation other than hydrogen evolution, the ensemble effect of Co, and the spatial confinement effect that promote the full hydrogenation of NO x to ammonia without N–N coupling. The catalyst exhibits almost exclusive ammonia conversion with a Faradaic efficiency of 97.1% and ammonia yielding rate of 115.5 mmol·g cat –1 ·h –1 in neutral electrolytes. The high activity was also confirmed in electrolytes with dilute nitrate and high chloride concentrations.

36 MATERIALS SCIENCE↗

DOE OSTI2025

Organophosphorus Binding Thermodynamics in Metal–Organic Frameworks: Interplay between Oxidation State, Lewis Acidity, and Node Structure

Organophosphorus compounds, including nerve agents and pesticides, represent a class of toxic chemicals causing harm to troops, civilians, and the environment. Metal–organic frameworks (MOFs) have emerged as a class of highly porous, crystalline, tunable materials adept at both capturing and catalytically neutralizing these harmful toxins. In particular, MOFs whose nodes display strong Lewis acidic character can hydrolyze such chemicals nearly instantaneously. However, without the help of a basic buffer to regenerate the active site, the benign organophosphorus product strongly binds to the node and prevents catalyst turnover. Here, we investigate a series of MOFs whose nodes contain metals of varying Lewis acidities and employ isothermal titration calorimetry (ITC) to directly measure the heat from the binding of an organophosphorus probe molecule, allowing the construction of a full thermodynamic binding profile (ΔH, ΔS, ΔG, K a ). We couple this with potentiometric titrations and solid state 31 P magic angle spinning (MAS) NMR to gain a clearer picture of how node identity, structure, and Lewis acidity interplay to impact binding strength and favorability. Furthermore, this study is the first to integrate these three complementary techniques to investigate binding interactions in MOFs, further showcasing the viability of ITC for probing MOF systems, which is still relatively underexplored.

Lewis acidity↗

DOE OSTI2026

Heteroepitaxial control of thickness, strain, and domain architecture in few-layer ferroelectric tin monochalcogenides

Thin-film epitaxy and epitaxial strain have been widely exploited to tune domain configurations, switching behavior, and ferroic properties in conventional three-dimensional ferroelectric thin films; however, its application to controlling the properties of two-dimensional (2D) ferroelectrics has remained largely unexplored. Here, using SnX (X = Se, S) as a model system, we demonstrate heteroepitaxial control of thickness, strain state, and domain architecture in few-layer ferroelectric SnX via growth on monolayer MoS2 van der Waals (vdW) templates. Compared with conventional growth, MoS2-templated heteroepitaxy promotes epitaxial alignment, yielding ultrathin SnSe films with improved crystalline quality, full areal coverage, and enlarged lateral dimensions. Strong interfacial epitaxial coupling induces pronounced in-plane strain and stabilizes a hierarchical ferroelastic domain architecture, in which long-range 90° stripe domains are further subdivided into nanoscale rotational variants, as revealed by scanning transmission electron microscopy and synchrotron X-ray microscopy. Piezoresponse force microscopy and second-harmonic polarimetry confirm robust in-plane polarization, while ferroelectricity in SnSe is established through polarization-electric field hysteresis and nonvolatile ferroelectric resistive switching with on/off ratios approaching 1000. A nonvolatile, switchable ferroelectric diode effect further evidences direct coupling between polarization and charge transport. Notably, ferroelectric switchability exhibits a strong thickness dependence and is preserved only below ∼10 layers. This vdW heteroepitaxial strategy is further extended to ferroelectric SnS. The seamless heteroepitaxial integration of 2D ferroelectrics with CMOS-compatible, wafer-scale MoS2 templates provides a general and scalable route for strain-enabled structural and ferroelectric engineering in emerging memory and low-power optoelectronic applications.

Wang, Yueyin↗

DOE OSTI2021

Strong interlayer charge transfer due to exciton condensation in an electrically isolated GaAs quantum well bilayer

We introduce a design of electrically isolated “floating” bilayer GaAs quantum wells (QW), in which application of a large gating voltage controllably and highly reproducibly induces charges that remain trapped in the bilayer after removal of the gating voltage. At smaller gate voltages, the bilayer is fully electrically isolated from external electrodes by thick insulating barriers. This design permits full control of the total and differential densities of two coupled 2D electron systems. The floating bilayer design provides a unique approach for studying systems inaccessible by simple transport measurements. It also provides the ability to measure the charge transfer between the layers, even when the in-plane resistivities of the 2D systems diverge. We measure the capacitance and inter-layer tunneling spectra of the QW bilayer with independent control of the top and bottom layer electron densities. Our measurements display strongly enhanced inter-layer tunneling current at v T =1, a signature of exciton condensation of a strongly interlayer-correlated bilayer system. With fully tunable densities of individual layers, the floating bilayer QW system provides a versatile platform to access previously unavailable information on the quantum phases in electron bilayer systems.

42 ENGINEERING↗

DOE OSTI2025

Reconstruction of current profiles from external magnetic and MSE measurements on DIII-D

This work introduces a new current model into the EFIT code for plasma current profile reconstruction. Using this model, edge-localized current density profiles are reconstructed solely from external magnetic measurements. Quantitative comparisons show that edge current profiles obtained with the new current model align closely with those from kinetic equilibrium reconstruction. The new model enables current density reconstruction with fewer diagnostics than kinetic equilibrium reconstruction (Lao et al 1990 Nucl. Fusion 30 1035–49), demonstrating that edge-localized current density information can be obtained from external magnetic measurements only, without the help of kinetic profiles and internal diagnostics, and without using the bootstrap current model. Furthermore, with the constraints of external magnetic and MSE measurements, current profiles in full radius obtained from the new model are in good agreement with the results of kinetic equilibrium reconstruction, which not only improves the efficiency of current reconstruction but also helps avoid possible errors caused by different kinds of diagnoses. Possible applications are also discussed, and a brief analysis of the evolution of the full-radius current density is performed. Noticeable decreases in both the magnitude and gradient of the edge current around the time of ELM bursts are observed. Moreover, analysis of the full radius current density profiles ( ρ N = 0 − 1.0, ρN denotes to square root of the normalized toroidal flux) reveals that as the edge current changes, the inner current also changes following a sinusoidal-like pattern at almost all time slices during four type-I ELMs in discharge 161493. The current evolution in the inner region ( ρ N = 0.2 − 0.6) is synchronized with the boundary region ( ρ N = 0.89 − 1.0), while the intermediate region ( ρ N = 0.6 − 0.89) shows opposite behavior. This sinusoidal-like variations in full-radius current density profile indicates strong core-pedestal coupling, suggesting ELMs significantly affect core plasmas, though current changes manifest differently across radial regions.

EFIT↗

DOE OSTI2020

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

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

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2020

Properties of La 0.7 Ca 0.3 MnO 3 under extreme tensile strain

The complex phase diagram of manganites with simultaneously active spin, charge, orbital, and lattice degrees of freedom continues providing surprises. In a recent groundbreaking experiment, membranes of the perovskite manganite La 0.7 Ca 0.3 MnO 3 (LCMO) deposited on a flexible polymer layer were strained up to 8% [S. S. Hong et al., Science 368, 71 (2020)], much more than achieved by regular strain induced by a rigid substrate. By increasing this strain, a metal-insulator transition was reported. Here we reproduce the results of the experiments using Monte Carlo simulations of the two-orbital double-exchange model including Jahn-Teller distortions at hole density x=1/3. The full phase diagram with varying temperature and Jahn-Teller coupling λ is presented. When the bandwidth W of mobile electrons is reduced, thus when the effective Jahn-Teller coupling λ/W is increased, a metal-insulator transition is found in our simulations, between a ferromagnetic metallic state with uniform charge distribution and an insulator with diagonal charge stripes that retains its ferromagnetic character. In between the hole-rich diagonals, staggered orbital order occurs. We also report resistivity and magnetization measurements alongside with spin correlations and charge structure factors. Our overall conclusions are in agreement with the recent experimental and density functional theory results by Hong et al., and we confirm much earlier ground state predictions of striped ferromagnetic order using energy optimization techniques by T. Hotta et al. [Phys. Rev. Lett. 86, 4922 (2001)]. The experimental observation of one of the states predicted by theory suggests that diagonal stripes could be achieved at other hole densities as well, such as x=1/4, if LCMO membranes with that hole doping were subject to similar strains.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2021

Phase diagram of the anisotropic triangular lattice Hubbard model

In a recent study [Phys. Rev. X 10, 021042 (2020)], we showed using large-scale density matrix renormalization group (DMRG) simulations on infinite cylinders that the triangular lattice Hubbard model has a chiral spin liquid phase. In this work, we introduce hopping anisotropy in the model, making one of the three distinct bonds on the lattice stronger or weaker compared with the other two. We implement the anisotropy in two inequivalent ways, one which respects the mirror symmetry of the cylinder and one which breaks this symmetry. In the full range of anisotropy, from the square lattice to weakly coupled one-dimensional chains, we find a variety of phases. Near the isotropic limit we find the three phases identified in our previous work: metal, chiral spin liquid, and 120$^\circ$ spiral order; we note that a recent paper suggests the apparently metallic phase may actually be a Luther-Emery liquid, which would also be in agreement with our results. Furthermore, when one bond is weakened by a relatively small amount, the ground state quickly becomes the square lattice N\'{e}el order. When one bond is strengthened, the story is much less clear, with the phases that we find depending on the orientation of the anisotropy and on the cylinder circumference. While our work is to our knowledge the first DMRG study of the anisotropic triangular lattice Hubbard model, the overall phase diagram we find is broadly consistent with that found previously using other methods, such as variational Monte Carlo and dynamical mean field theory.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2020

Penetration Through Slots in Cylindrical Cavities Operating at Fundamental Cavity Modes

In this article, we examine the coupling into an electrically short azimuthal slot on a cylindrical cavity operating at fundamental cavity modal frequencies. We first develop a matched bound formulation through which we can gather information for maximum achievable levels of interior cavity fields. Actual field levels are below this matched bound; therefore, we also develop an unmatched formulation for frequencies below the slot resonance to achieve a better insight on the physics of this coupling. Good agreement is observed between the unmatched formulation, full-wave simulations, and experimental data, providing a validation of our analytical models. We then extend the unmatched formulation to treat an array of slots, found again in good agreement with full-wave simulations. These analytical models can be used to investigate ways to mitigate electromagnetic interference and electromagnetic compatibility effects within cavities.

42 ENGINEERING↗

DOE OSTI2023

Cross-Scale Land-Atmosphere Experiment (CSLAEX) (Final Report)

It is now well recognized that land-atmosphere interactions play an important role in both weather and climate. These interactions take place over a wide range of spatial and temporal scales. Most of the current formulations of the momentum, heat and moisture transport laws are informed by observations with a limited temporal or spatial scale, and hence may have limited applicability. The objective of this work is to improve the multi-scale representation of the near-surface heat transfer in the ground and in the atmosphere using a combination of modeling and field observations. Our knowledge and predictive capacity in land-atmosphere coupling is limited by our capacity to observe the full-scale spectrum at play. In order to bridge this fundamental gap in our observation capacity I will work to: create the first long-term Integrated Cross-Scale land-Atmosphere Experiment (CSLAEX) since I will work to: measure the components of the surface energy balance at a spatial scale relevant to remote sensing and meteorological applications (5km), along with observations of the nested subscale processes with Distributed Temperature Sensors (DTS). This proposal aims to fill the gaps in modeling and observing land-atmosphere interactions across scales via a novel Cross-Scale Land-Atmosphere Experiment (CSLAEX) to be implemented as part of the Department of Energy (DOE) Atmospheric Radiation Measurement (ARM) Southern Great Plains (SGP) site near Lamont, Oklahoma. The proposed research effort aims at exploring land-atmosphere processes across multiple spatial scales and to investigate the effect of landscape heterogeneity using Distributed Temperature Sensor measurements. The novel instrumentation of the Surface Energy Balance and simultaneous observations of the atmospheric state (boundary layer, cloud, convection) available at the DOE ARM SGP site will be used to create CSLAEX. This dataset will be used to frame and evaluate new transport laws and parameterizations for the boundary layer and the land surface, which can be implemented into the Weather and Research Forecasting (WRF) model and Community Atmospheric Model (CAM). The result of this study should impact multiple fields: meteorology, climate, and hydrology.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2025

SCM overview & the EBR-II shutdown heat removal tests validation.

Pronghorn is an engineering-scale, coarse-mesh, thermal-hydraulics tool for supporting reactor-core simulations of advanced nuclear reactors. Most of the current efforts in Pronghorn have been devoted in developing porous finite-volume capabilities and adapting closure correlations for coarse-mesh thermal-hydraulics modeling. However, for liquid-metal reactors (LMRs) with wire-wrapped fuel pin assemblies, a pin-level thermal-hydraulic resolution is required for most safety case studies (pin rupture, channel blockage, etc.). For this purpose, a new Subchannel application is developed in MOOSE, which affords the required flow field resolution, while still preserving an engineering-scale approach. This new solver can be natively coupled to Pronghorn and other MOOSE objects to enable full-core, multi-physics, multi-scale engineering studies. This presentation presents the main features of the SCM code and demonstrates a validation case based on the EBR-II SHRT tests.

21 - SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLAN↗

DOE OSTI2023

Nonvolatile Magnetoelectric Switching of Magnetic Tunnel Junctions with Dipole Interaction

The magnetoelectric effect is technologically appealing because of its ability to manipulate magnetism using an electric field rather than magnetic field or current, thus providing a promising solution for the development of energy-efficient spintronics. Although 180° magnetization switching is vital to spintronic devices, the achievement of 180° magnetization switching via magnetoelectric coupling is still a fundamental challenge. Here, in this work, voltage-driven full resistance switching of a magnetic tunnel junction (MTJ) with dipole interaction on a ferroelectric substrate through switchable parallel/antiparallel magnetization alignment is demonstrated. Parallel magnetization alignment along the y direction is obtained under a bias magnetic field. By rotating the magnetic easy axis via strain-mediated magnetoelectric coupling, the parallel magnetizations in the MTJ reorient to the x axis with opposite paths because of dipole interaction, thus resulting in antiparallel alignment. Moreover, this voltage switching of MTJs is nonvolatile owing to variations in dipole interaction and can be well understood via phase field simulations. The results provide an avenue to realize electrical switching of MTJs and are significant for exploring energy-efficient spintronic devices.

36 MATERIALS SCIENCE↗

DOE OSTI2022

Driving Zn-MnO2 grid-scale batteries: A roadmap to cost-effective energy storage

Highlights Zn-MnO 2 batteries promise safe, reliable energy storage, and this roadmap outlines a combination of manufacturing strategies and technical innovations that could make this goal achievable. Approaches such as improved efficiency of manufacturing and increasing active material utilization will be important to getting costs as low as $100/kWh, but key materials innovations that facilitate the full 2-electron capacity utilization of MnO 2 , the use of high energy density 3D electrodes, and the promise of a separator-free battery with greater than 2V potential offer a route to batteries at $50/kWh or less. Abstract Large-scale energy storage is certain to play a significant, enabling role in the evolution of the emerging electrical grid. Battery-based storage, while not a dominant form of storage today, has opportunity to expand its utility through safe, reliable, and cost-effective technologies. Here, secondary Zn–MnO 2 batteries are highlighted as a promising extension of ubiquitous primary alkaline batteries, offering a safe, environmentally friendly chemistry in a scalable and practical energy dense technology. Importantly, there is a very realistic pathway to also making such batteries cost-effective at price points of $50/kWh or lower. By examining manufacturing examples at the Zn–MnO 2 battery manufacturer Urban Electric Power, a roadmap has been created to realize such low-cost systems. By focusing on manufacturing optimization through reduced materials waste, scalable manufacturing, and effective materials selection, costs can be significantly reduced. Ultimately, though, coupling these approaches with emerging research and development advances to enable full capacity active materials utilization and battery voltages greater than 2V are likely needed to drive costs below a target of $50/kWh. Reaching this commercially important goal, especially with a chemistry that is safe, well-known, and reliably effective stands to inject Zn–MnO 2 batteries in the storage landscape at a critical time in energy storage development and deployment. Graphical abstract

Spoerke, Erik D. (ORCID:0000000322862560)↗

DOE OSTI2026

Robust qubit interactions mediated by photonic topological edge states

Here, we investigate the coupling of two spatially separated qubits via topologically protected edge states in a two-dimensional Hofstadter lattice. In this hybrid platform, the qubits are coupled to distinct edge sites of the lattice, enabling long-range interactions mediated by topological edge modes. We solve the full system Hamiltonian and analyze the resulting eigenstate structure to uncover the conditions under which coherent qubit interactions emerge. Our analysis reveals that the effective coupling is highly sensitive to the qubit placement, energy detuning, and the topological character of the edge spectrum. We obtain an analytical solution that goes beyond the perturbative regime, capturing the full interplay between the qubits and edge modes. These results provide a foundation for exploring information transport and many-body effects in engineered quantum systems where interactions are mediated by topological edge modes.

Chern insulators↗

DOE OSTI2023

Implementation and verification of a user-defined element (UEL) for coupled thermal-hydraulic-mechanical-chemical (THMC) processes in saturated geological media

Efficient and accurate modeling of the coupled thermal-hydraulic-mechanical-chemical (THMC) processes in various rock formations is indispensable for designing energy geo-structures such as underground repositories for high-level nuclear wastes. Here, this work focuses on developing and verifying an implicit finite element solver for generic coupled THMC problems in geological settings. Starting from the mass, momentum, and energy balance laws, a specialized set of governing equations and a thermoporoelastic constitutive model is derived. This system is then solved by an implicit finite element (FE) scheme. Specifically, the residuals and the Jacobians are scripted in a user-defined element (UEL) subroutine which is then combined with the general-purpose FE software Abaqus Standard to solve initial-boundary value problems. Considering the complexity of the system, the UEL development follows a stepwise manner by first solving the coupled hydraulic-mechanical (HM) and thermal-hydraulic-mechanical (THM) equations before moving on to the full THMC problem. Each implementation step consists of at least one verification test by comparing computed results with closed-form analytical solutions to ensure that the various coupling effects are correctly realized. To demonstrate the robustness of the algorithm and to validate the UEL, a three-dimensional case study is performed with reference to the in-situ heating test of ATLAS at Belgium in 1980s. A hypothetical radionuclide leakage event is then simulated by activating the chemical-concentration degree of freedom and prescribing a constant high concentration at the heater's surface. The model predicts a limited contaminated regime after six years considering both diffusion and advection effects on species transport.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

DOE OSTI2024

Chemical bonding dictates drastic critical temperature difference in two seemingly identical superconductors

Though YB 6 and LaB 6 share the same crystal structure, atomic valence electron configuration, and phonon modes, they exhibit drastically different phonon-mediated superconductivity. YB 6 superconducts below 8.4 K, giving it the second-highest critical temperature of known borides, second only to MgB 2 . LaB 6 does not superconduct until near-absolute zero temperatures (below 0.45 K), however. Though previous studies have quantified the canonical superconductivity descriptors of YB 6 ’s greater Fermi-level (E f ) density of states and higher electron–phonon coupling (EPC), the root of this difference has not been assessed with full detail of the electronic structure. Through chemical bonding, we determine low-lying, unoccupied 4f atomic orbitals in lanthanum to be the key difference between these superconductors. These orbitals, which are not accessible in YB 6 , hybridize with π B–B bonds and bring this π-system lower in energy than the σ B–B bonds otherwise at E f . This inversion of bands is crucial: the optical phonon modes we show responsible for superconductivity cause the σ-orbitals of YB 6 to change drastically in overlap, but couple weakly to the π-orbitals of LaB 6 . These phonons in YB 6 even access a crossing of electronic states, indicating strong EPC. No such crossing in LaB 6 is observed. Finally, a supercell (the M k-point) is shown to undergo Peierls-like effects in YB 6 , introducing additional EPC from both softened acoustic phonons and the same electron-coupled optical modes as in the unit cell. Overall, we find that LaB 6 and YB 6 have fundamentally different mechanisms of superconductivity, despite their otherwise near-identity.

Science & Technology - Other Topics↗

DOE OSTI2021

Twisted symmetric trilayer graphene: Single-particle and many-body Hamiltonians and hidden nonlocal symmetries of trilayer moiré systems with and without displacement field

Here, we derive the Hamiltonian for trilayer moiré systems with the Coulomb interaction projected onto the bands near the charge neutrality point. Motivated by the latest experimental results, we focus on the twisted symmetric trilayer graphene (TSTG) with a mirror symmetry with respect to the middle layer. We provide a full symmetry analysis of the noninteracting Hamiltonian with a perpendicular displacement field coupling the band structure made otherwise of the twisted bilayer graphene (TBG) and the high-velocity Dirac fermions, and we identify a hidden nonlocal symmetry of the problem. In the presence of this displacement field, we construct an approximate single-particle model, akin to the tripod model for TBG, capturing the essence of noninteracting TSTG. We also derive more quantitative perturbation schemes for the low-energy physics of TSTG with displacement field, obtaining the corresponding eigenstates. This allows us to obtain the Coulomb interaction Hamiltonian projected in the active band TSTG wave functions and derive the full many-body Hamiltonian of the system. We also provide an efficient parametrization of the interacting Hamiltonian. Finally, we show that the discrete symmetries at the single-particle level promote the U (2) × U (2) spin-valley symmetry to enlarged symmetry groups of the interacting problem under different limits. The interacting part of the Hamiltonian exhibits a large U (4) × U (4) × U (4) × U (4) symmetry in the chiral limit. Moreover, by identifying a symmetry which we dub spatial many-body charge conjugation, we show that the physics of TSTG is symmetric around charge neutrality.

2-dimensional systems↗