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At least 469 records · Page 26
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Conjugated Metal–Organic Macrocycles: Synthesis, Characterization, and Electrical Conductivity

The dimensional reduction of solids into smaller fragments provides a route to achieve new physical properties and gain deeper insight into the extended parent structures. Here, we report the synthesis of CuTOTP-OR (TOTP n – = 2,3,6,7-tetraoxidotriphenylene), a family of copper-based macrocycles that resemble truncated fragments of the conductive 2D metal–organic framework Cu 3 (HHTP) 2 (HHTP = 2,3,6,7,10,11-hexahydroxytriphenylene). The planar metal–organic macrocycles self-assemble into ordered nanotubes with internal diameters of ~2 nm and short interlayer distances of ~3.20 Å. Strong π–π stacking interactions between macrocycles facilitate out-of-plane charge transport, and pressed pellet conductivities as high as 2(1)×10 -3 S cm -1 are observed. Peripheral alkyl functionalization enhances solution processability and enables the fabrication of thin-film field-effect transistor devices. Ambipolar charge transport is observed, suggesting similar behavior may be operative in Cu 3 (HHTP) 2 . By coupling the attractive features of metal–organic frameworks with greater processability, these macrocycles enable facile device integration and a more nuanced understanding of out-of-plane charge transport in 2D conductive metal–organic frameworks.

36 MATERIALS SCIENCE↗
DOE OSTI2019

Magnetic Interactions on Oxide Ferromagnet/Ferromagnetic Intermetallide Interface

The magnetic properties of heterostructures consisting of two films are studied. The upper layer involves rare-earth intermetallic nanostructured superlattices consisting of exchange-coupled layers (TbCo{sub 2}/FeCo){sub n} (TCFC), and the lower layer includes either epitaxial manganite La{sub 0.7}Sr{sub 0.3}MnO{sub 3} (LSMO) with optimum strontium doping or an epitaxial film of an yttrium–iron garnet Y{sub 3}Fe{sub 5}O{sub 12} (YIG) with a Bi additive. TCFC is a ferromagnet having high Curie temperature and provides controllable induced magnetic anisotropy. Experimental studies showed that the interlayer interaction of the TCFC/LSMO heterostructure is antiferromagnetic. There was an increase in the FMR line width in the structures due to the flow of a spin current through the interface between two films. There was electric voltage in the TCFC/YIG heterostructure induced in the TCFC intermetallide film, due to an inverse spin Hall effect under ferromagnetic resonance conditions.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2025

High-field magnetic phase diagrams of the 𝑅⁢Mn 6 ⁢Sn 6 (𝑅=Gd–Tm) kagome metals

𝑅⁢Mn 6 ⁢Sn 6 (𝑅=Y, Gd–Lu) kagome metals are promising materials hosting flat electronic bands and Dirac points that interact with magnetism. The coupling between the two magnetic 𝑅 and Mn sublattices can drive complex magnetic states with potential consequences for spin and charge transport and other topological properties. Here, in this work, we use a detailed magnetic Hamiltonian to calculate and predict the magnetic phase diagrams for 𝑅⁢Mn 6 ⁢Sn 6 kagome metals within the mean-field approximation. These calculations reveal a variety of collinear, noncollinear, and noncoplanar phases that arise from competition between various interlayer magnetic exchange interactions and magnetic anisotropies of the 𝑅 and Mn ions. We enumerate these phases and their magnetic space groups for future analysis of their impact on topological and trivial bands near the Fermi surface.

kagome metal↗
DOE OSTI2015

Intercalation of organic molecules in 2D copper (II) nitroprusside: Intermolecular interactions and magnetic properties

This contribution discusses the intercalation of imidazole and its 2-ethyl derivative, and pyridine in 2D copper nitroprusside. In the interlayer region, neighboring molecules remain interacting throu gh their dipole and quadrupole moments, which supports the solid 3D crystal structure. The crystal structure of this series of intercalation compounds was solved and refined from powder X-ray diffraction patterns complemented with spectroscopic information. The intermolecular interactions were studied from the refined crystal structures and low temperature magnetic measurements. Due to strong attractive forces between neighboring molecules, the resulting π–π cloud overlapping enables the ferromagnetic coupling between metal centers on neighboring layers, which was actually observed for the solids containing imidazole and pyridine as intercalated molecules. For these two solids, the magnetic data were properly described with a model of six neighbors. For the solid containing 2-ethylimidazole and for 2D copper nitroprusside, a model of four neighbors in a plane is sufficient to obtain a reliable data fitting. - Highlights: • Intercalation of organic molecules in 2D copper (II) nitroprusside. • Molecular properties of intercalation compounds of 2D copper (II) nitroprusside. • Magnetic properties of hybrid inorganic–organic solids. • Hybrid inorganic–organic 3D framework.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2015

Magnetization switching of a metallic nanomagnet via current-induced surface spin-polarization of an underlying topological insulator

We consider a thermally stable, metallic nanoscale ferromagnet (FM) subject to spin-polarized current injection and exchange coupling from the spin-helically locked surface states of a topological insulator (TI) to evaluate possible non-volatile memory applications. We consider parallel transport in the TI and the metallic FM, and focus on the efficiency of magnetization switching as a function of transport between the TI and the FM. Transport is modeled as diffusive in the TI beneath the FM, consistent with the mobility in the TI at room temperature, and in the FM, which essentially serves as a constant potential region albeit spin-dependent except in the low conductivity, diffusive limit. Thus, it can be captured by drift-diffusion simulation, which allows for ready interpretation of the results. We calculate switching time and energy consumed per write operation using self-consistent transport, spin-transfer-torque (STT), and magnetization dynamics calculations. Calculated switching energies and times compare favorably to conventional spin-torque memory schemes for substantial interlayer conductivity. Nevertheless, we find that shunting of current from the TI to a metallic nanomagnet can substantially limit efficiency. Exacerbating the problem, STT from the TI effectively increases the TI resistivity. We show that for optimum performance, the sheet resistivity of the FM layer should be comparable to or larger than that of the TI surface layer. Thus, the effective conductivity of the FM layer becomes a critical design consideration for TI-based non-volatile memory.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2015

Low damage etching method of low-k material with a neutral beam for interlayer dielectric of semiconductor device

To reduce the cross-talk between nanoscale devices, low-k materials such as methyl silsesquioxane (MSQ), which is damaged easily during plasma etching, are introduced as an intermetallic dielectric material in addition to the use of copper as the conducting material for the reduction of parasitic resistance and capacitance. In this study, beam techniques such as neutral/ion beams were used in the etching of MSQ and the effect of these beam techniques on the reduction of the degradation of the MSQ were investigated. When MSQ was etched using the same CF{sub 4} etch gas at the similar etch rate as that used for conventional MSQ etching using inductively coupled plasmas (ICPs), the neutral/ion beam etching showed lower F contents and lower penetration depth of F, indicating decreased degradation by fluorination of MSQ during etching using the beam techniques. Especially, the neutral beam etching technique showed the lowest F contamination and the lower penetration depth of F among the etch methods. When the dielectric constant was measured after the etching of the same depth, the MSQ etched with the neutral beam showed the lowest change of the dielectric constant, while that etched using the ICP showed the highest change of dielectric constant. The lower degradation, that is, the lower chemical modification of MSQ material with the beam technique is believed to be related to the decreased concentration of radical species in the processing chamber reacting with the MSQ surface, while the lowest degradation using the neutral beam is believed to be due to the lower reaction rate of the reactive neutral compared to reactive ions.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Reaction Current Heterogeneity at the Interface between a Lithium Electrode and Polymer/Ceramic Composite Electrolytes

Although lithium metal anodes are expected to increase the energy density of next-generation batteries, dendrite growth during charge remains a major bottleneck preventing widespread implementation. Composite solid electrolytes with ceramic particles embedded in a polymer matrix have the potential to prevent dendrites owing to the higher mechanical stiffness while also possessing the flexibility to maintain contact with the electrode. However, microscopically, the different mechanical and electrochemical properties of the polymer and ceramic domains can cause inhomogeneous charge transfer at the Li/electrolyte interface, which can lead to nonuniform Li deposition and propagation of dendrites. Here, we computationally examine the coupled electrochemical, transport, and mechanical processes at the interface to determine the propensity for dendrite formation and possible approaches to mitigate this issue. Predictions of two possible microstructures at the interface, namely, (i) where both the polymer and ceramic come in contact with Li metal and (ii) when only the polymer comes in contact with Li metal, suggest that the former has a greater tendency for nonuniform plating. In addition, predictions suggest that minimizing the interfacial resistance between polymers and ceramics and incorporating interlayers between the electrode and electrolyte help mitigate current heterogeneity. In conclusion, these predictions provide guidance for experimental approaches to prevent dendrites in composite electrolytes.

25 ENERGY STORAGE↗
DOE OSTI2022

Trigonal symmetry breaking and its electronic effects in the two-dimensional dihalides MX 2 and trihalides MX 3

We study the consequences of the approximately trigonal (D 3d ) point symmetry of the transition metal (M) site in two-dimensional van der Waals MX 2 dihalides and MX 3 trihalides. The trigonal symmetry leads to a 2-2-1 orbital splitting of the transition metal d shell, which is best represented by d orbitals that describe the trigonal rather than Oh symmetry. The ligand-ligand bond length differences (rather than metal-ligand) take the role of a Jahn-Teller-like mode and in combination with interlayer distances and dimensionality effects tune the crystal field splittings and bandwidths. These effects, in turn, are amplified by electronic correlation effects—leading to crystal field splittings of the order of 0.1–1 eV between the singlet and the lowest orbital doublet—as opposed to the often assumed degenerate 3 t 2g states. Our calculations explain why most of the materials in this family are insulating, and why these considerations have to be taken into account in realistic models of them. Further, orbital order coupled to various lower symmetry lattice modes may lift the remaining orbital degeneracies, and we explain how these may support unique electronic states using ZrI 2 and CuCl 2 as examples, and offer a brief overview of possible electronic configurations in this class of materials. By building and analyzing Wannier models adapted to the appropriate symmetry we examine how the interplay among trigonal symmetry, electronic correlation effects, and – d orbital charge transfer leads to insulating, orbitally polarized magnetic and/or orbital-selective Mott states, and we provide a simple framework and numerical tool for others. Our paper establishes a rigorous framework to understand, control, and tune the electronic states in low-dimensional correlated halides. Furthermore, our analysis shows that trigonal symmetry and its breaking is a key feature of the two-dimensional halides that needs to be accounted for in search of novel electronic states in materials ranging from CrI 3 to α–RuCl 3 .

2-dimensional systems↗
DOE OSTI2017

Calorimetric Study of Alkali Metal Ion (K + , Na + , Li + ) Exchange in a Clay-Like MXene

Intercalation of ions in layered materials has been explored to improve the rate capability in Li-ion batteries and supercapacitors. This work investigates the energetics of alkali ion exchange in a clay-like MXene, Ti 3 C 2 T x , where T x stands for anionic surface moieties, by immersion calorimetry in aqueous solutions. The measured immersion enthalpies of clay-like Ti 3 C 2 T x , ΔH imm , at 25 °C in 1 M KCl, 1 M NaCl, 1 M LiCl, and nanopure water are -9.19 (±0.56), -5.90 (±0.31), -1.31 (±0.20), and -1.29 (±0.13) kJ/mol of MXene, respectively. Inductively coupled plasma mass spectrometry is used to obtain the concentrations of alkali ions in the solid and aqueous phases. Using these concentrations, the enthalpies of exchange of alkali metal ions (Li+, Na+, and K+) are calculated; ΔHex in 1 M KCl, 1 M NaCl, 1 M LiCl, and nanopure water are -9.3 (±2.2), 21.0 (±0.9), -1.3 (±0.2), and 302.4 (±0.6) kJ/mol of MXene, respectively. Both immersion and exchange enthalpies are most exothermic for potassium. This suggests that K+ ions interact more strongly with anions present in the interlayers of this MXene than Na + and Li + ions. Water vapor adsorption calorimetry indicates very weak interaction of water with the MXene, while immersion calorimetry suggests a weakly hydrophilic nature of the MXene surface.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2017

Epitaxial Templating of Two-Dimensional Metal Chloride Nanocrystals on Monolayer Molybdenum Disulfide

We demonstrate the formation of ionic metal chloride (CuCl) two-dimensional (2D) nanocrystals epitaxially templated on the surface of monolayer molybdenum disulfide (MoS 2 ). These 2D CuCl nanocrystals are single atomic planes from a nonlayered bulk CuCl structure. They are stabilized as a 2D monolayer on the surface of the MoS 2 through interactions with the uniform periodic surface of the MoS 2 . The heterostructure 2D system is studied at the atomic level using aberration-corrected transmission electron microscopy at 80 kV. Dynamics of discrete rotations of the CuCl nanocrystals are observed, maintaining two types of preferential alignments to the MoS 2 lattice, confirming that the strong interlayer interactions drive the stable CuCl structure. Strain maps are produced from displacement maps and used to track real-time variations of local atomic bonding and defect production. Density functional theory calculations interpret the formation of two types of energetically advantageous commensurate superlattices via strong chemical bonds at interfaces and predict their corresponding electronic structures. These results show how vertical heterostructured 2D nanoscale systems can be formed beyond the simple assembly of preformed layered materials and provide indications about how different 2D components and their interfacial coupling mode could influence the overall property of the heterostructures.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Incommensurate charge-stripe correlations in the kagome superconductor CsV 3 Sb 5–x Sn x

The class of AV 3 Sb 5 (A=K, Rb, Cs) kagome metals hosts unconventional charge density wave states seemingly intertwined with their low temperature superconducting phases. The nature of the coupling between these two states and the potential presence of nearby, competing charge instabilities however remain open questions. This phenomenology is strikingly highlighted by the formation of two ‘domes’ in the superconducting transition temperature upon hole-doping CsV 3 Sb 5 . Here we track the evolution of charge correlations upon the suppression of long-range charge density wave order in the first dome and into the second of the hole-doped kagome superconductor CsV 3 Sb 5–x Sn x . Initially, hole-doping drives interlayer charge correlations to become short-ranged with their periodicity diminished along the interlayer direction. Beyond the peak of the first superconducting dome, the parent charge density wave state vanishes and incommensurate, quasi-1D charge correlations are stabilized in its place. These competing, unidirectional charge correlations demonstrate an inherent electronic rotational symmetry breaking in CsV 3 Sb 5 , and reveal a complex landscape of charge correlations within its electronic phase diagram. Our data suggest an inherent 2k ƒ charge instability and competing charge orders in the AV 3 Sb 5 class of kagome superconductors.

36 MATERIALS SCIENCE↗
DOE OSTI2017

Long-range stripe nanodomains in epitaxial (110) BiFeO 3 thin films on (100) NdGaO 3 substrate

Here, we report the observation of ferroelectric and ferroelastic nanodomains in (110)-oriented BiFeO 3 (BFO) thin films epitaxially grown on low symmetric (100) NdGaO 3 (NGO) substrate. We observed long range ordering of ferroelectric 109° stripe nanodomains separated by periodic vertical domain walls in as-grown 130 nm thick BFO films. The effect of La 0.67 Sr 0.33 CoO 3 (LSCO) conducting interlayer on domain configurations in BFO/NGO film was also observed with relatively short range-ordering of stripe domains due to the modified electrostatic boundary conditions in BFO/LSCO/NGO film. Additional studies on B-site doping of Nb ions in BFO films showed change in the domain structures due to doping induced change in lattice anisotropy while maintaining the stripe domain morphology with 109° domain wall. Finally, this long-range array of ferroelectric and ferroelastic domains can be useful for optoelectronic devices and ferroelastic templates for strain coupled artificial magnetoelectric heterostructures.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Epitaxy, exfoliation, and strain-induced magnetism in rippled Heusler membranes

Single-crystalline membranes of functional materials enable the tuning of properties via extreme strain states; however, conventional routes for producing membranes require the use of sacrificial layers and chemical etchants, which can both damage the membrane and limit the ability to make them ultrathin. Here we demonstrate the epitaxial growth of the cubic Heusler compound GdPtSb on graphene-terminated Al 2 O 3 substrates. Despite the presence of the graphene interlayer, the Heusler films have epitaxial registry to the underlying sapphire, as revealed by x-ray diffraction, reflection high energy electron diffraction, and transmission electron microscopy. The weak Van der Waals interactions of graphene enable mechanical exfoliation to yield free-standing GdPtSb membranes, which form ripples when transferred to a flexible polymer handle. Whereas unstrained GdPtSb is antiferromagnetic, measurements on rippled membranes show a spontaneous magnetic moment at room temperature, with a saturation magnetization of 5.2 bohr magneton per Gd. First-principles calculations show that the coupling to homogeneous strain is too small to induce ferromagnetism, suggesting a dominant role for strain gradients. Our membranes provide a novel platform for tuning the magnetic properties of intermetallic compounds via strain (piezomagnetism and magnetostriction) and strain gradients (flexomagnetism).

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Multiband superconductivity in strongly hybridized 1 T ' - WTe 2 / NbSe 2 heterostructures

The interplay of topology and superconductivity has become a subject of intense research in condensed-matter physics for the pursuit of topologically nontrivial forms of superconducting pairing. An intrinsically normal-conducting material can inherit superconductivity via electrical contact to a parent superconductor via the proximity effect, usually understood as Andreev reflection at the interface between the distinct electronic structures of two separate conductors. However, at high interface transparency, strong coupling inevitably leads to changes in the band structure, locally, owing to hybridization of electronic states. Here, we investigate such strongly proximity-coupled heterostructures of monolayer $1T$' - $\mathrm{WTe_2}$ grown on NbSe 2 by van der Waals epitaxy. The superconducting local density of states, resolved in scanning tunneling spectroscopy down to 500 mK, reflects a hybrid electronic structure well described by a multiband framework based on the McMillan equations which captures the multiband superconductivity inherent to the NbSe 2 substrate and that is induced by proximity to $\mathrm{WTe_2}$ self-consistently. Our material-specific tight-binding model captures the hybridized heterostructure quantitatively and confirms that strong interlayer hopping gives rise to a semimetallic density of states in the two-dimensional $\mathrm{WTe_2}$ bulk, even for nominally band-insulating crystals. The model further accurately predicts the measured order parameter Δ ≅ 0.6 meV induced in the $\mathrm{WTe_2}$ monolayer bulk, stable beyond a 2 T magnetic field. So we believe that our detailed multiband analysis of the hybrid electronic structure provides a useful tool for sensitive spatial mapping of induced order parameters in proximitized atomically thin topological materials.

36 MATERIALS SCIENCE↗
DOE OSTI2026

In Situ Insights into Enhanced Cooperative Ligand Exchange Kinetics via Solvent-Induced Restacking in a 2D Metal–Organic Framework

Understanding the reaction kinetics at catalytically active sites is crucial for integrating catalytic two-dimensional (2D) materials into industrial processes. This study focuses on in situ observation of ligand exchange kinetics and solvent-assisted structural restacking transition in the 2D paddle wheel-based MOF [Cu 2 (dttc) 2 ] n (DUT-134(Cu), dttc = dithieno[3,2-b:2′,3′- d]thiophene-2,6-dicarboxylate). The ligand exchange process, involving the replacement of dimethylformamide (DMF) with nitriles such as acetonitrile (ACN), pentanenitrile, and heptanenitrile, was investigated using advanced in situ characterization techniques with high temporal resolution, including powder X-ray diffraction and Raman spectroscopy. The larger analytes exhibited reduced exchange rates, consistent with enhanced steric hindrance and greater diffusion constraints. Interestingly, the study revealed that the exchange of DMF with ACN induces a structural transition to higher symmetry within few seconds, a transition from AB to AA stacking mode of the layers, and a widening of the interlayer distance. Crucially, this structural transition dramatically accelerates the solvent exchange process through cooperative effects, offering critical advantages for catalytic applications. Notably, the reverse exchange from ACN to DMF proceeds more slowly and does not reverse the structural changes, but a new phase is formed with preserved AA stacking. By isotope labeling of linker molecules in combination with two complementary theoretical vibrational simulation methods, the precise assignment of Raman bands and the vibrational modes associated with the ligand exchange process could be achieved. These pioneering insights into the dynamic behavior of 2D MOFs, coupled with ligand exchange, establish a highly promising and transformative approach to achieving enhanced tunability and responsiveness in future catalytic applications.

Layers↗
DOE OSTI2025

Boosting the Oxygen Evolution Reaction by Tuning the Interfacial Iron Adsorption on Layered Double Hydroxide

Understanding the interaction between ions in the electrolyte and electrode materials plays an important role in optimizing the water electrolysis performance for hydrogen production. Herein, the synergistic effect of iron (Fe) in the electrolyte and interlayer anions within the layered structure on the oxygen evolution reaction (OER) has been investigated by combining material synthesis with controlled structure, multiple characterization techniques, and first-principles calculations. Nickel aluminum layered double hydroxides (NiAl-LDHs) with different interlayer anions (CO 3 2– , Cl – , and Br – ) show similar oxygen evolution activity in the absence of Fe species in the electrolyte. The addition of Fe into the electrolyte results in improved performance for all of the NiAl-LDHs, following the rank LDH-Br > LDH-Cl > LDH-CO 3 , under all of the conditions with varied concentration of Fe. X-ray absorption spectroscopy and identical location electron microscopy analyses show that the LDH structure remains unchanged after the OER activity test, while in situ stationary probe rotating disk electrode inductively coupled plasma mass spectrometry (SPRDE-ICP-MS) measurements show partial dissolution of the intercalating halide ions during cycling, with less dissolution for Br-intercalated materials. Insights from theoretical calculations demonstrate the thermodynamic preference of Br – to remain intercalated in the presence of Fe, while the stronger adsorption of Fe(OH) 3 species on the LDH-Br sample promotes the OER activity. In conclusion, these results provide mechanistic insights into the rational design of active layered materials with an enhanced OER performance for efficient water electrolysis.

58 GEOSCIENCES↗
DOE OSTI2021

Spin waves and high-frequency response in layered superconductors with helical magnetic structure

Here, we evaluate the spin-wave spectrum and dynamic susceptibility in a layered superconductor with helical interlayer magnetic structure. We especially focus on the structure in which the moments rotate 90 degrees from layer to layer realized in the iron pnictide RbEuFe 4 As 4 . While in nonmagnetic superconductors low-frequency magnetic field decays on the distance of the order of the London penetration depth, spin waves mediate its propagation to much larger distances limited by external dissipation mechanisms. The spin-wave spectrum in superconductors is strongly renormalized due to the long-range electromagnetic interactions between the oscillating magnetic moments. This leads to strong enhancement of the frequency of the mode coupled with uniform field and this enhancement exists only within a narrow range of the c-axis wave vectors of the order of the inverse London penetration depth. The key feature of materials like RbEuFe 4 As 4 is that this uniform mode corresponds to the maximum frequency of the spin-wave spectrum with respect to the c-axis wave vector. As a consequence, the high-frequency surface resistance acquires a very distinct asymmetric feature spreading between the bare and renormalized frequencies. Finally, we also consider excitation of spin waves with the Josephson effect in a tunneling contact between helical-magnetic and conventional superconductors and study the interplay between the spin-wave features and geometrical cavity resonances in the current-voltage characteristics.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2022

Unified ab initio description of Fröhlich electron-phonon interactions in two-dimensional and three-dimensional materials

Ab initio calculations of electron-phonon interactions including the polar Fröhlich coupling have advanced considerably in recent years. The Fröhlich electron-phonon matrix element is by now well understood in the case of bulk three-dimensional (3D) materials. In the case of two-dimensional (2D) materials, the standard procedure to include Fröhlich coupling is to employ Coulomb truncation, so as to eliminate artificial interactions between periodic images of the 2D layer. While these techniques are well established, the transition of the Fröhlich coupling from three to two dimensions has not been investigated. Furthermore, it remains unclear what error one makes when describing 2D systems using the standard bulk formalism in a periodic supercell geometry. In this work, we generalize previous work on the ab initio Fröhlich electron-phonon matrix element in bulk materials by investigating the electrostatic potential of atomic dipoles in a periodic supercell consisting of a 2D material and a continuum dielectric slab. We obtain a unified expression for the matrix element, which reduces to the existing formulas for three-dimensional and 2D systems when the interlayer separation tends to zero or infinity, respectively. This expression enables an accurate description of the Fröhlich matrix element in 2D systems without resorting to Coulomb truncation. We validate our approach by direct ab initio density-functional perturbation theory calculations for monolayer BN and MoS 2 , and we provide a simple expression for the 2D Fröhlich matrix element that can be used in model Hamiltonian approaches. The formalism outlined in this work may find applications in calculations of polarons, quasiparticle renormalization, transport coefficients, and superconductivity, in 2D and quasi-2D materials.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗