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At least 73 records · Page 4
All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

Similarities and differences between nickelate and cuprate films grown on a SrTiO 3 substrate

The recent discovery of superconductivity in Sr-doped NdNiO 2 films grown on SrTiO 3 started a novel field within unconventional superconductivity. Therefore, to understand the similarities and differences between nickelate and cuprate layers on the same SrTiO 3 substrate, here based on the density functional theory we have systematically investigated the structural, electronic, and magnetic properties of NdNiO 2 / SrTiO 3 and CaCuO 2 / SrTiO 3 systems. Our results revealed a strong lattice reconstruction in the case of NdNiO 2 / SrTiO 3 , resulting in a polar film, with the surface and interfacial NiO 2 layers presenting opposite displacements. To avoid the “polar catastrophe,” the NiO 2 surface to the vacuum reconstructs as well. However, for CaCuO 2 / SrTiO 3 , the distortions of those same two CuO 2 layers were in the same direction. In addition, we found this distortion to be approximately independent of the studied range of film thickness for the nickelate films. Furthermore, we also observed a two-dimensional electron gas at the interface between NdNiO 2 and SrTiO 3 , caused by the polar discontinuity, in agreement with recent literature. For NdNiO 2 / SrTiO 3 the two-dimensional electron gas extends over several layers, while for CaCuO 2 / SrTiO 3 this electronic rearrangement is very localized at the interface between CaCuO 2 and SrTiO 3 . The electronic reconstruction found at the interface involves a strong occupation of the Ti 3 d x y state. In both cases, there is a significant electronic charge transfer from the surface Ni or Cu layers to the Ti interface layer. The interfacial Ni and Cu layers are hole and electron doped, respectively. By introducing magnetism and electronic correlation, we observed that the d 3 z 2 - r 2 orbital of Ni becomes itinerant while the same orbital for Cu remains doubly occupied, establishing a clear two- vs one-orbital active framework for the description of these systems. Furthermore, we also observed a strong magnetic reconstruction at the NdNiO 2 surface to vacuum layer where magnetism is basically suppressed.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2021

Emitter Reconstruction for Cleaved CdSexTe1-x Devices with Cu vs. As Doping

CdTe absorbers have had historically low carrier densities of ~10^14 cm-3 due to the self-compensating nature of copper dopants. Recent advances in group-V (e.g., arsenic) doping have increased this to 10^16-10^17 cm-3, but modeling suggests that the front interface and emitter properties become limiting in this case. By cleaving arsenic- and copper-doped CdTe device stacks at the emitter/absorber interface, we gain the ability to reconstruct emitters with known properties, which will not change during subsequent device processing, and directly test the modeling. By doing so, we find a much larger performance drop in arsenic devices; this is attributed to insufficient electron density in the emitter and increased sensitivity to interface changes due to collapsed depletion width. This work can help guide emitter engineering for highly-doped CdTe devices in both the as-grown-superstrate- and cleaved-substrate configurations.

As-doped↗
DOE OSTI2024

Engineering exchange bias at the interface of self-polarized ultrathin ferroelectric Ba⁢Ti⁢O 3 and ferromagnetic La 0.67⁢ Sr 0.33 ⁢Mn⁢O 3

We investigate the emergence and optimization of conventional exchange bias (EB) in ultrathin (<10 nm) ferroelectric (FE) Ba⁢Ti⁢O 3 (BTO)/ferromagnetic (FM) La 0.67 ⁢Sr 0.33⁢ Mn⁢O 3 (LSMO) epitaxial bilayers without an antiferromagnetic (AFM) material. The EB originates from the electronic orbital reconstruction at the FE-FM interface due to the ferroelectric polarization. We achieve maximum EB of approximately 42 Oe with single-domain polarization in nine-unit-cell-thick BTO, setting the BTO thickness above the critical threshold for ferroelectricity yet below the thickness of strain relaxation and multidomain breakdown. Furthermore, the LSMO layer needs to be thick enough to sustain both the FM layer and polarization-induced AFM spin configuration at the LSMO/BTO interface, yet as thin as possible to enable the EB loop shift. The temperature, training, field, and thickness dependence of the EB confirm that the LSMO/BTO interface exhibits conventional EB despite its unconventional origin. Using x-ray magnetic circular dichroism, scanning transmission electron microscopy, and density-functional-theory calculations, we confirm that the macroscopic EB effect originates from the interfacial AFM spin configuration in LSMO driven by FE-induced d-orbital modifications in interfacial Mn ions. Thus, we engineer strong interfacial EB coupling in artificial multiferroics without a conventional AFM material by controlling FE polarization, highlighting the potential for advanced spintronic applications.

exchange bias↗
DOE OSTI2022

Reconstruction of Thiospinel to Active Sites and Spin Channels for Water Oxidation

Water electrolysis is a promising technique for carbon neutral hydrogen production. A great challenge remains at developing robust and low-cost anode catalysts. Many pre-catalysts are found to undergo surface reconstruction to give high intrinsic activity in the oxygen evolution reaction (OER). The reconstructed oxyhydroxides on the surface are active species and most of them outperform directly synthesized oxyhydroxides. The reason for the high intrinsic activity remains to be explored. Here, a study is reported to showcase the unique reconstruction behaviors of a pre-catalyst, thiospinel CoFe 2 S 4 , and its reconstruction chemistry for a high OER activity. The reconstruction of CoFe 2 S 4 gives a mixture with both Fe–S component and active oxyhydroxide (Co(Fe)O x H y ) because Co is more inclined to reconstruct as oxyhydroxide, while the Fe is more stable in Fe–S component in a major form of Fe 3 S 4 . The interface spin channel is demonstrated in the reconstructed CoFe 2 S 4 , which optimizes the energetics of OER steps on Co(Fe)O x H y species and facilitates the spin sensitive electron transfer to reduce the kinetic barrier of O–O coupling. The advantage is also demonstrated in a membrane electrode assembly (MEA) electrolyzer. Finally, this work introduces the feasibility of engineering the reconstruction chemistry of the precatalyst for high performance and durable MEA electrolyzers.

36 MATERIALS SCIENCE↗
DOE OSTI2021

An efficient reconstruction algorithm for diffusion on triangular grids using the nodal discontinuous Galerkin method

High-energy-density (HED) hydrodynamics studies such as those relevant to inertial confinement fusion and astrophysics require highly disparate densities, temperatures, viscosities, and other diffusion parameters over relatively short spatial scales. This presents a challenge for high-order accurate methods to effectively resolve the hydrodynamics at these scales, particularly in the presence of highly disparate diffusion. A significant volume of engineering and physics applications use an unstructured discontinuous Galerkin (DG) method developed based on the finite element mesh generation and algorithmic framework. This work discusses the application of an affine reconstructed nodal DG method for unstructured grids of triangles. Solving the diffusion terms in the DG method is non-trivial due to the solution representations being piecewise continuous. Hence, the diffusive flux is not defined on the interface of elements. The proposed numerical approach reconstructs a smooth solution in a parallelogram that is enclosed by the quadrilateral formed by two adjacent triangle elements. The interface between these two triangles is the diagonal of the enclosed parallelogram. Similar to triangles, the mapping of parallelograms from a physical domain to a reference domain is an affine mapping, which is necessary for an accurate and efficient implementation of the numerical algorithm. Thus, all computations can still be performed on the reference domain, which promotes efficiency in computation and storage. This reconstruction does not make assumptions on choice of polynomial basis. Reconstructed DG algorithms have previously been developed for modal implementations of the convection–diffusion equations. However, to the best of the authors’ knowledge, this is the first practical guideline that has been proposed for applying the reconstructed algorithm on a nodal discontinuous Galerkin method with a focus on accuracy and efficiency. As a result, the algorithm is demonstrated on a number of benchmark cases as well as a challenging substantive problem in HED hydrodynamics with highly disparate diffusion parameters.

Computational efficiency↗
DOE OSTI2025

Predicting interface structure using the minima hopping method

Here, we adapt the minima hopping method (MHM) to the problem of interfacial structure prediction and apply it to study a canonical problem, the tilt grain boundaries in SrTiO 3 . Our method employs a hybrid approach by first exploring the potential energy surface (PES) of different grain boundary samplings with an empirical force field, among which the fifteen candidates with lower energies are then refined using ab initio density functional theory (DFT) calculations. During the exploratory stage, we bias the search using a local order parameter to primarily sample various reconstructions in the vicinity of the interface, while preserving the crystallinity of the bulk regions. We further enhance the search by incorporating initial structures with rigid body displacements to account for translational variations between bulk phases, enabling the MHM to effectively generate both stoichiometric and nonstoichiometric SrTiO 3 Σ⁢3(111)[110] and Σ⁢3(112)[110] grain boundaries. From an algorithmic standpoint, MHM outperforms earlier studies based on genetic algorithms (GA) by identifying more stable interfacial structures of several SrTiO 3 grain boundaries. The performance of the present implementation of the MHM approach is primarily limited by exploring an approximate description of the PES with a rather simple Buckingham potential. This limitation leads to variations in performance when compared to approaches utilizing more advanced surrogate PES models, such as direct DFT-PES sampling or GA with the embedded atom method (EAM). Despite the present limitations, the MHM approach is able to yield interfacial structures with comparable or lower interfacial energies in specific cases, such as Σ⁢3(111)[110] Γ=1, ±0.5 and Σ⁢3(112)[110] Γ= ±1, −2, underscoring the robustness of the MHM approach even with a simple approximation of the DFT PES. The MHM interfacial structure prediction method thus offers an efficient approach to understanding the grain boundaries and heterointerfaces at the atomic scale, providing an important prerequisite for effective materials design.

density functional theory↗
DOE OSTI2025

Subsurface Interface Structure Controlling Local Electronic Properties of Epitaxial Graphene on SiC(0001)

Recently realized high-mobility semiconducting epitaxial graphene on silicon carbide (SiC) [Zhao, J. Nature 2024, 625 (7993), 60−65, 10.1038/s41586-023-06811-0] provided an important step toward integration of the graphene-based system into active components in postsilicon micro- and nanoelectronics. However, the exact atomic-scale structure and complex bonding configurations of the first epitaxial graphene carbon layer (C buffer ) remain an open problem. Our recent report [Kolmer, M. Communications Physics 2024, 7 (1), 16, 10.1038/s42005-023-01515-3] has shed new light on understanding this interface, where the external transverse electric field-dependent dynamic switching behavior of the C buffer –SiC bonds was observed. Here, using scanning tunneling microscopy and spectroscopy (STM and STS), we present direct evidence of silicon (Si) vacancies at the interface and provide their distribution at the topmost reconstructed SiC(0001) layer. Bias voltage and epitaxial graphene thickness-dependent characterization of the collective C buffer –SiC interface showed that “Si” vacancy sites beneath C buffer are stable under STM electric fields. Moreover, the vacancies introduce localized electronic states below the Fermi level, thereby enhancing the charge-transfer phenomenon across the interface.

Thupakula, Umamahesh [Ames Laboratory (AMES), Ames↗
DOE OSTI2022

INTERFACES. A Program for Determining the 3D Structures of Surfaces Sites Using NMR Data

Dynamic nuclear polarization surface enhanced NMR spectroscopy has enabled the determination of high-resolution structures from surface-supported molecules, including singlesite heterogeneous catalysts. Structure determinations have largely mimicked the approaches used in biomolecular NMR spectroscopy, namely, using distance measurements to constrain a conformational search. These early demonstrations made use of purpose-built software, which has limited the adoption of the technique. Herein, we describe the open-source program INTERFACES (Interpret NMR to Elucidate or Reconstruct the Full Atomistic Configurations of External Surfaces) which automates the analysis of RE(SP)DOR data as well as the structure determination for surface sites. Distances, angles, dihedral angles, complex orientation, and distance from the support can all be sampled to find all structures that agree with the experimental data. A χ 2 metric is used to define the error ranges of the REDOR fits and produce structures with an arbitrary level of confidence. Structural solutions are then provided as both overlays and ORTEP-like probability ellipsoids.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

The Instability of Monolayer-Thick PbSe on VSe 2

Two-dimensional monolayers derived from 3D bulk structures remain a relatively unexplored class of materials because of the challenge of stabilizing non-epitaxial interfaces. Here, we report an unusual reconstruction during the deposition of precursors when targeting the synthesis of heterostructures with an odd number of PbSe monolayers. Multilayer elemental precursors of Pb|Se + V|Se were deposited to have correct number of atoms to form [(PbSe) 1+δ ] q (VSe 2 ) 1 where q is the number of PbSe monolayers in the heterostructure. Structural analysis of the self-assembled precursor via xray reflectivity, x-ray diffraction, and HAADF-STEM suggests three different behaviors upon deposition. Precursors with q 7 and even values of q have the targeted nanoarchitectures after deposition which are maintained as the products are selfassembled through a near diffusionless process. Significant lateral surface diffusion occurred during deposition of precursors with q = 1, 3, and 5 resulting in the precursor having a different nanoarchitecture than targeted. Additional perpendicular long range diffusion occurs during self-assembly of these precursors resulting in different final products than targeted. DFT calculations of PbSe blocks show that the odd numbered layers are less stable than even numbered layers, which suggests an energetic driving force for the observed rearrangement. This work highlights the importance of understanding the reaction mechanism when attempting to prepare 2D layers of constituents with bulk 3D structures.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Stability Enhancement and Microstructural Modification of Ni-Rich Cathodes via Halide Doping

In this study, elemental doping is an effective strategy to modify surface and bulk chemistry in NMC cathode materials. By adding small amounts of lithium halide salts during the calcination process, the Ni-rich NMC811 cathode is doped with Br, Cl, or F halogens. The dopant type has a significant impact on the lithiation process and heavily influences the final cathode porosity and surface morphology. Utilizing a variety of electrochemical, surface, and bulk characterization techniques, it is demonstrated that an initial content of 5 mol % LiBr or LiCl in the lithium source is effective in improving capacity retention while also providing excellent rate performance. The improvements are attributed to a substantial increase in specific surface area, the formation of a stable cathode electrolyte interface (CEI) layer, and suppressed surface reconstruction. In addition, the particle microstructure is better equipped to handle cyclic volume changes with increased values of critical crack lengths. Overall, it is demonstrated that anion doping via the addition of lithium halide salts is a facile approach toward Ni-rich NMC modification for enhanced cathode performance.

25 ENERGY STORAGE↗
NASA NTRS1988

Description of graphics translation software between Intergraph and Tektronix systems

The requirement for Marshall Space Flight Center's Photo Analysis to use existing 3-D Intergraph graphic files on an existing Tektronix 4129 3-D graphics workstation and the unavailability of an off-the-shelf Intergraph to Tektronix translator required the development of such a translater. Using the output of Intergraph's standard interchange format converter, the 3-D graphic information of Intergraph's files are reformatted and compressed. The 3-D image is reconstructed using Tektronix's software terminal interface graphic library (STI).

Rieckhoff, Tom↗
DOE OSTI2021

First-principles modeling of conductivity at the (001), (110), and (111) SrTiO 3 /LaAlO 3 heterointerfaces

Here, the complex polar oxide heterojunction of SrTiO 3 /LaAlO 3 (STO/LAO) is of great interest due to the emergent physical phenomena observed at the interface. STO and LAO separately are wide band-gap insulators. However, upon joining them at the 001, 110, and 111 crystallographic planes, the interface undergoes a transition to a conductive state. Although first-principles modeling of the 001 plane interface has been widely studied, there is a lack of reports regarding the 110 and 111. This paper expands the theoretical model of the STO/LAO heterointerface to the three crystallographic planes (001, 110, and 111) where the conductivity has been experimentally reported. The calculations showed that whereas at the 001 interface the conductivity appears at a critical thickness of 4 monolayers of LAO, the 110 and 111 planes have no clear critical thickness; these two interfaces were always conductive. Nevertheless, the number of conductive electrons per unit cell increases with the thickness of the LAO layer in the 110 and 111 interfaces. This is related to the energy levels downshifting due to the electrostatic potential buildup (which was in the opposite direction respect to the 001 interface), increasing the number of conductive sates below the Fermi level. Given the absence of a critical thickness and the fact that chemical intermixing and oxygen vacancies at the interface were not considered, the main mechanism responsible for the conductivity in the 110 and 111 planes was attributed to the large structure reconstruction that locally changes the energy levels at the interface causing charge transfer and accumulation at the layers close to the interface.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2024

Capping Effects on Spin and Charge Excitations in Parent and Superconducting Nd 1-x Sr x⁢ NiO 2

Superconductivity in infinite layer nickelates Nd 1-x⁢ Sr x NiO 2 has so far been achieved only in thin films, raising questions on the role of substrates and interfaces. Given the challenges associated with their synthesis it is imperative to identify their intrinsic properties. We use resonant inelastic x-ray scattering to investigate the influence of the SrTiO 3 capping layer on the excitations of Nd 1-x ⁢Sr x⁢ NiO 2 (x =0 and 0.2). Spin excitations are observed in parent and 20% doped Nd 1-x Sr x ⁢NiO 2 regardless of capping, proving that magnetism is intrinsic to infinite-layer nickelates and appears in a significant fraction of their phase diagram. In parent and superconducting Nd 1-x Sr x ⁢NiO 2 , the spin excitations are slightly hardened in capped samples compared to the noncapped ones. Additionally, a weaker Ni-Nd charge transfer peak at ~0.6 eV suggests that the hybridization between Ni 3⁢d and Nd 5⁢d orbitals is reduced in capped samples. In conclusion, from our data, capping induces only minimal differences in Nd 1-x Sr x NiO 2 and we phenomenologically discuss these differences based on the reconstruction of the SrTiO 3 -NdNiO 2 interface and other mechanisms such as crystalline disorder.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Interface-induced sign reversal of the anomalous Hall effect in magnetic topological insulator heterostructures

The Berry phase picture provides important insights into the electronic properties of condensed matter systems. The intrinsic anomalous Hall (AH) effect can be understood as the consequence of non-zero Berry curvature in momentum space. Here, we fabricate TI/magnetic TI heterostructures and find that the sign of the AH effect in the magnetic TI layer can be changed from being positive to negative with increasing the thickness of the top TI layer. Our first-principles calculations show that the built-in electric fields at the TI/magnetic TI interface influence the band structure of the magnetic TI layer, and thus lead to a reconstruction of the Berry curvature in the heterostructure samples. Based on the interface-induced AH effect with a negative sign in TI/V-doped TI bilayer structures, we create an artificial “topological Hall effect”-like feature in the Hall trace of the V-doped TI/TI/Cr-doped TI sandwich heterostructures. Our study provides a new route to create the Berry curvature change in magnetic topological materials that may lead to potential technological applications.

36 MATERIALS SCIENCE↗
DOE OSTI2025

MoRE-Brain: Routed Mixture of Experts for Interpretable and Generalizable Cross-Subject fMRI Visual Decoding

Decoding visual experiences from fMRI offers a powerful avenue to understand human perception and develop advanced brain-computer interfaces. However, current progress often prioritizes maximizing reconstruction fidelity while overlooking interpretability, an essential aspect for deriving neuroscientific insight. To address this gap, we propose MoRE-Brain, a neuro-inspired framework designed for high-fidelity, adaptable, and interpretable visual reconstruction. MoRE-Brain uniquely employs a hierarchical Mixture-of-Experts architecture where distinct experts process fMRI signals from functionally related voxel groups, mimicking specialized brain networks. The experts are first trained to encode fMRI into the frozen CLIP space. A finetuned diffusion model then synthesizes images, guided by expert outputs through a novel dual-stage routing mechanism that dynamically weighs expert contributions across the diffusion process. MoRE-Brain offers three main advancements: First, it introduces a novel Mixture-of-Experts architecture grounded in brain network principles for neuro-decoding. Second, it achieves efficient cross-subject generalization by sharing core expert networks while adapting only subject-specific routers. Third, it provides enhanced mechanistic insight, as the explicit routing reveals precisely how different modeled brain regions shape the semantic and spatial attributes of the reconstructed image. Extensive experiments validate MoRE-Brain’s high reconstruction fidelity, with bottleneck analyses further demonstrating its effective utilization of fMRI signals, distinguishing genuine neural decoding from over-reliance on generative priors. Consequently, MoRE-Brain marks a substantial advance towards more generalizable and interpretable fMRI-based visual decoding.

Wei, Yuxiang [Georgia Institute of Technology]↗
DOE OSTI2021

Spin pinning effect to reconstructed oxyhydroxide layer on ferromagnetic oxides for enhanced water oxidation

Producing hydrogen by water electrolysis suffers from the kinetic barriers in the oxygen evolution reaction (OER) that limits the overall efficiency. With spin-dependent kinetics in OER, to manipulate the spin ordering of ferromagnetic OER catalysts (e.g., by magnetization) can reduce the kinetic barrier. However, most active OER catalysts are not ferromagnetic, which makes the spin manipulation challenging. In this work, we report a strategy with spin pinning effect to make the spins in paramagnetic oxyhydroxides more aligned for higher intrinsic OER activity. The spin pinning effect is established in oxideFM/oxyhydroxide interface which is realized by a controlled surface reconstruction of ferromagnetic oxides. Under spin pinning, simple magnetization further increases the spin alignment and thus the OER activity, which validates the spin effect in rate-limiting OER step. The spin polarization in OER highly relies on oxyl radicals (O∙) created by 1 st dehydrogenation to reduce the barrier for subsequent O-O coupling.

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

Iterative redox activation promotes interfacial synergy in an Ag/Cu x O catalyst for oxygen reduction

In this study, an iterative electrochemical activation process is demonstrated to maximize the interface between Ag and Cu x O. Morphological reconstruction and phase transformation of Cu x O occurs through the iterative electrochemical redox reaction, as indicated by energy-dispersive spectroscopy and X-ray photoelectron spectroscopy. The activated Ag/Cu x O/C catalysts exhibits enhanced oxygen reduction reaction performance, with an onset potential of 0.86 V vs. the reversible hydrogen electrode, a Tafel slope of 46mV dec -1 , and a high stability as compared to Ag/C. A mechanistic study using density functional theory shows that the weakened binding energy of the OH intermediate, originating from the charge transfer from Ag to Cu x O, improves the ORR activity at the interface sites of the Ag/Cu x O electrocatalysts. Ag/Cu x O shows a higher limiting potential of 0.14V for interface sites than isolated Ag nanoparticles. The interfacial charge transfer between Ag and CuO is verified experimentally.

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

Bicrystallography-informed Frenkel–Kontorova model for interlayer dislocations in strained 2D heterostructures

In recent years, van der Waals (vdW) heterostructures and homostructures, which consist of stacks of two-dimensional (2D) materials, have risen to prominence due to their association with exotic quantum phenomena originating from correlated electronic states harbored by them. Atomistic scale relaxation effects play an extremely important role in the electronic scale quantum physics of these systems, providing means of manipulation of these materials and allowing them to be tailored for emergent technologies. We investigate such structural relaxation effects in this work using atomistic and mesoscale models, within the context of twisted bilayer graphene — a well-known heterostructure system that features moiré patterns arising from the lattices of the two graphene layers. For small twist angles, atomic relaxation effects in this system are associated with the natural emergence of interface dislocations or strain solitons, which result from the cyclic nature of the generalized stacking fault energy (GSFE), that measures the interface energy based on the relative movement of the two layers. Here, in this work, we first demonstrate using atomistic simulations that atomic reconstruction in bilayer graphene under a large twist also results from interface dislocations, although the Burgers vectors of such dislocations are considerably smaller than those observed in small-twist systems. To reveal the translational invariance of the heterointerface responsible for the formation of such dislocations, we derive the translational symmetry of the GSFE of a 2D heterostructure using the notions of coincident site lattices (CSLs) and displacement shift complete lattices (DSCLs). The workhorse for this exercise is a recently developed Smith normal form bicrystallography framework. Next, we construct a bicrystallography-informed and frame-invariant Frenkel–Kontorova model, which can predict the formation of strain solitons in arbitrary 2D heterostructures, and apply it to study a heterostrained, large-twist bilayer graphene system. Our mesoscale model is found to produce results consistent with atomistic simulations. We anticipate that the model will be invaluable in predicting structural relaxation and for providing insights into various heterostructure systems, especially in cases where the fundamental unit cell is large and therefore, atomistic simulations are computationally expensive.

2D heterostructures↗