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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 289 records · Page 16
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Origin of insulating and nonferromagnetic SrRuO 3 monolayers

The electro-magnetic properties of ultrathin epitaxial ruthenate films have long been the subject of debate. Here we combine experimental with theoretical investigations of (SrTiO 3 ) 5 -(SrRuO 3 ) n -(SrTiO 3 ) 5 (STO 5 -SRO n -STO 5 ) heterostructures with n = 1 and 2 unit cells, including extensive atomic-resolution scanning-transmission-electron-microscopy imaging, electron-energy-loss-spectroscopy chemical mapping, as well as transport and magneto-transport measurements. The experimental data demonstrate that the STO 5 -SRO 2 -STO 5 heterostructure is nearly stoichiometric, metallic, and ferromagnetic with T C ~ 128 K, even though it lacks the characteristic bulk-SRO octahedral tilts and matches the cubic STO structure. In contrast, the STO 5 -SRO 1 -STO 5 heterostructure features Ru-Ti intermixing in the RuO 2 layer, also without octahedral tilts, but is accompanied by a loss of metallicity and ferromagnetism. Density-functional-theory calculations show that stoichiometric n = 1 and n = 2 heterostructures are metallic and ferromagnetic with no octahedral tilts, while non-stoichiometry in the Ru sublattice in the n = 1 case opens an energy gap and induces antiferromagnetic ordering. Furthermore, the results indicate that the observed non-stoichiometry is the cause of the observed loss of metallicity and ferromagnetism in the n = 1 case.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2024

Nanocompression of 20 nm Silver Nanoparticles: In situ Aberration‐Corrected TEM and Atomistic Simulations

Single‐crystalline nanoparticles play an increasingly important role in a wide variety of fields including pharmaceuticals, advanced materials, catalysts for fuel cells, energy materials, as well as environmental detection and monitoring. Yet, the deformation mechanisms of very small nanoparticles are still poorly understood, in particular the role played by single dislocations and their interaction with surfaces. Here, in this work, silver nanoparticles with particularly small dimensions (≈20 nanometers in diameter) are compressed in situ in an aberration‐corrected transmission electron microscopy (TEM) and molecular dynamics (MD) simulations. During compression, the emergence of both dislocations and nanotwins are observed. However, these defects prove to be unstable and disappear upon removal of the indenter. Atomistic simulations confirm the role played by image stresses associated with the nearby surfaces and the reduction in dislocation line length as it approaches the free surface, thereby supporting the experimental observations. These results provide justification for the frequent observation of the absence of dislocations in nanoparticles of a few nanometers in size during in situ experiments, even after significant deformation. This phenomenon contributes to the self‐healing of samples through dislocation ejection toward the surfaces.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2020

Superconducting pairing mechanism in CeCoIn 5 revisited

Spectroscopic-imaging scanning-tunneling microscopy (SI-STM) measurements have previously been applied to the study of the heavy-fermion system CeCoIn 5 to examine the superconducting gap structure and band dispersions via quasiparticle intereference. Here we directly measure the dispersing electron bands with angle-resolved-photoelectron spectroscopy (ARPES) and compare with first principles electronic structure calculations. By auto-correllating the ARPES-resolved bands with themselves we can measure the potential q-vectors and discern exactly which bands the STM is measuring. We find that the STM results are dominated by scattering associated with a cloverleaf shaped band centered at the zone corners. This same band is also a viable candidate to host the superconducting gap. Overall, the electronic structure calculations indicate that this region of the Fermi surface involves significant contributions from the Co d-electrons, an indication that the superconductivity in these materials is more 3-dimensional than that found in the related unconventional superconductors, the cuprates and the pnictides.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2020

MOCVD Growth and Characterization of Wide Bandgap ZnGeN 2 Thin Films

ZnGeN 2 is a wide bandgap material having less than 0.1% lattice mismatch with GaN and bandgap within few percent of that of GaN. Based on the first principle calculations, the valence band of ZnGeN 2 is situated ~1.4 eV above that of GaN at the heterointerface. Such a staggered band alignment between two closely lattice matched materials has already been demonstrated promising for novel optoelectronic device designs, for example, high efficiency blue and green light emitting diodes. However, the research on ZnGeN 2 is yet to pass the inceptive period. We report on the growth of single crystalline ZnGeN 2 films using metalorganic chemical vapor deposition and investigation on the crystalline, optical, electrical properties. Diethylzinc (DEZn), germane (GeH 4 ) and ammonia were used as the precursors for Zn, Ge and N, respectively. Films were grown on GaN and sapphire substrates. The Zn/Ge atomic ratio in the films determined from energy dispersive X-ray spectroscopy was found to decrease with increase in growth temperature but to increase with increase in pressure and DEZn/GeH 4 molar flow rate ratio. The X-ray diffraction (XRD) 2θ-ω spectra of the single crystalline ZnGeN 2 films resembled those of orthorhombic (perfectly ordered cations) or distorted wurtzite (disordered cations) polymorphs. High resolution scanning transmission electron microscopy imaging was used to further investigate the crystalline quality and crystalline structure of the films. The single crystalline films on c-sapphire or GaN substrates were found to have planar surface from scanning electron micrographs while those on r-sapphire substrate had stepped surface. No near band edge peak but a broad peak at ~2.05 eV was observed in the photoluminescence (PL) spectra, which was attributed to the transitions involving deep level defects. The PL excitation spectra peaked around 3.4 eV, which is due to the enhanced absorption of photons having energy close to the band gap. The as grown films were found to be n-type with 10 18 – 10 19 cm -3 carrier densities and mobility up to 17 cm 2 /V·s. In the end, the advancement made in this work regarding the growth of ZnGeN 2 thin films is a footstep towards the understanding of the material itself and in turn, towards the implementation of ZnGeN 2 based novel device designs.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2022

Magnetic circuit for Abrikosov vortices: Vortex motion in a periodic labyrinth of magnetic T and I-shaped elements under a superconducting film

Here we explore tailored labyrinth-like vortex motion in a niobium film placed on top of periodic arrays of T and I -shaped permalloy elements by imaging the vortex distribution in magnetic fields applied perpendicular to the superconducting layer under different in-plane polarizations of the TI structure. At low temperatures, we observe pronounced meandering of vortex motion around the TI elements. Remarkably, vortices can easily penetrate the sample along the TI columns even though the average vortex pinning in the patterned area is larger than in a bare niobium film. Accordingly, at temperatures close to the superconducting transition temperature, T c , the voltagecurrent curves in the patterned area show an earlier departure from the zero-resistivity state at small currents, followed by slower growth with increasing current as compared to the un-patterned film. We present a model based on magnetostatic interactions between magnetic charges at the edges of the polarized TI-elements and single magnetic charges of induced vortices to account for this behavior. We expect that similar magnetic structures imposing labyrinth-like vortex motion could be used for collective entanglement of vortices envisioned in quantum circuit operations.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2022

Visualizing the unusual spectral weight transfer in DyBa2Cu3O7–δ thin film

Abstract We report a Spectroscopic Imaging Scanning Tunneling Microscopy (SI-STM) study of a DyBa 2 Cu 3 O 7-δ (DBCO) thin film ( T c ~ 79 K) synthesized by the molecular beam epitaxy (MBE). We observed an unusual transfer of spectral weight in the local density of states (LDOS) spectra occurring only within the superconducting gap. By a systematic control of the tip-sample distance and the junction resistance, we demonstrate that the spectral weight transfer can be switched at a nano-meter length scale. These results suggest that an interaction between the STM tip and the sample alters the electronic configurations in the film. This probably originates from a combination of an intrinsic band bending at the interface between the surface and the bulk, and a tip-induced band bending. These results may open a new avenue for band engineering and applications of thin films of high- T c cuprates.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2024

Massive all-atom analysis of 2D materials with quantum properties (Final report)

Improvements in microscopy have enabled the acquisition of data at a scale that is difficult to process manually, making automated machine learning approaches to analyzing experimental images essential. In this project, we developed and applied machine learning (ML) workflows for atomic resolution scanning transmission electron microscopy (STEM) images. This development included improving both methodology as well as generating user-friendly codes. We developed machine learning architectures which, after training, automatically identify the location and types of defects throughout a material. We used these data to produce class-averaged images of 2D atomic coordinates with up to 0.3 pm precision, uncovering the structure and oscillations of long-range strain fields around point defects in WSe 2-2x Te 2x . We also resolved a long-standing problem in this field in the training of ML models, a lack of labeled experimental data, by developing a cycle-GAN that transformed simulated-generated labeled data into labeled data indistinguishable from experiment and therefore suitable for training. This removed the remaining parts of the ML data processing workflow where human intervention was still critical and therefore a bottleneck to working at scale. Codes have been developed and released for this full machine learning workflow. ML approaches to partially automate STEM acquisition were also developed. Finally we applied ML and other advanced data processing methods to several materials science problems in two-dimensional materials, including studying the evolution of hyperuniformity with defect concentration in WSe2, understanding phase transformations in transition metal dichalcogenides during in-situ heating in the STEM, and exploring how 2D interfaces transform from twisted into aligned structures.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2020

Adaptive Machine Learning for Bragg Coherent Diffraction Imaging (BCDI) of 3D Electron Density Maps with Application to La 2-x Ba x CuO 4 (LBCO) High Temperature Superconductor Studies [PowerPoint]

Understanding mesoscale heterogeneity is important for evaluating fatigue and failure of structural materials and for manufacturing processes. Data-driven tools can facilitate in guiding effort investment (measurements and computations) at various stages of the materials development. Our 3D reconstruction approach is to find a set of coefficients which define a bounding surface of the electron density. Data for training the 3D CNN was generated by sampling coefficients from uniform distributions. Test vs. prediction values are shown for the 28 even-valued coefficients for 1000 test structures, with the best and worst performers highlighted. The adaptive part of this work utilized a model independent extremum seeking (ES). The predictions of the CNN were used as the starting point for the ES algorithm. The convergence of the ES algorithm for 3 different structures is illustrated, and the robustness of the adaptive ML approach was demonstrated on experimentally measured 3D crystal from high energy diffraction microscopy. Reconstruction of a non-uniform density volume with different levels of Poisson noise is also shown. Preliminary attempts at reconstructing measured La 2-x Ba x CuO 4 diffraction patterns have so far failed.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2021

Structure and energetics of the elbows in the Au(111) herringbone reconstruction

We study the structure of the threading edge dislocations, or “elbows,” which are an essential component of the well-known herringbone reconstruction of the (111) surface of Au. Previous work had shown that these dislocations can be stabilized by long-range elastic relaxations into the bulk. However, the validity of the harmonic spring model that had been used to estimate the energies of the dislocations is uncertain. To enable a more refined model of the dislocation energetics, we have imaged the atomic structure of these dislocations using scanning tunneling microscopy. We find that the harmonic spring model does not adequately reproduce the observed structure. We are able to reproduce the structure, however, with a two-dimensional Frenkel-Kontorova (FK) model that uses a pairwise Morse potential to describe the interactions between the top layer Au atoms on a rigid substrate. The parameters of the potential were obtained by fitting the energy of uniaxially compressed phases, or “stripes”, computed with density functional theory, as a function of surface Au density. Within this model, the formation of the threading dislocations remains unfavorable. However, the large forces on the substrate atoms near the threading-dislocation cores, render the assumption of a completely rigid substrate questionable. Indeed, if the FK parameters are modified to account for the relaxation of just one more atomic layer, threading dislocations can, in principle, become favorable, even without bulk elastic relaxations. Additional evidence for a small elbow energy is that our computed change in the Au(111) surface stress tensor caused by the (√ 3 × 22) reconstruction is considerably smaller than previous estimates.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2022

Origin of structural degradation in Li-rich layered oxide cathode

Li- and Mn-rich (LMR) cathode materials that utilize both cation and anion redox can yield substantial increases in battery energy density 1,2,3 . However, although voltage decay issues cause continuous energy loss and impede commercialization, the prerequisite driving force for this phenomenon remains a mystery 3,4,5,6 In this work, with in situ nanoscale sensitive coherent X-ray diffraction imaging techniques, we reveal that nanostrain and lattice displacement accumulate continuously during operation of the cell. Evidence shows that this effect is the driving force for both structure degradation and oxygen loss, which trigger the well-known rapid voltage decay in LMR cathodes. By carrying out micro- to macro-length characterizations that span atomic structure, the primary particle, multiparticle and electrode levels, we demonstrate that the heterogeneous nature of LMR cathodes inevitably causes pernicious phase displacement/strain, which cannot be eliminated by conventional doping or coating methods. We therefore propose mesostructural design as a strategy to mitigate lattice displacement and inhomogeneous electrochemical/structural evolutions, thereby achieving stable voltage and capacity profiles. These findings highlight the significance of lattice strain/displacement in causing voltage decay and will inspire a wave of efforts to unlock the potential of the broad-scale commercialization of LMR cathode materials.

25 ENERGY STORAGE↗
DOE OSTI2026

Magnetic flux imaging in a 3D superconductor integrated circuit

We report on imaging magnetic flux distributions in a multilayered superconductor integrated circuit which emerge during magnetization and after field cooling of the circuit in the DC magnetic field. The obtained complicated field maps expose the flux propagation across the patterned superconducting ground planes sandwiching layers with Josephson junction-based logic cells, fine wire grid around the functional units, and multiple superconducting fill structures located in different inner layers. The observed intricate flux distributions are explained by specific patterns of Meissner screening currents and superconducting critical currents in different mutually interacting parts of the integrated circuit. Our results provide important insights into possible ways of improving the protection of superconductor integrated circuits from magnetic fields and their resilience against flux trapping.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2024

Charge state-dependent symmetry breaking of atomic defects in transition metal dichalcogenides

Abstract The functionality of atomic quantum emitters is intrinsically linked to their host lattice coordination. Structural distortions that spontaneously break the lattice symmetry strongly impact their optical emission properties and spin-photon interface. Here we report on the direct imaging of charge state-dependent symmetry breaking of two prototypical atomic quantum emitters in mono- and bilayer MoS 2 by scanning tunneling microscopy (STM) and non-contact atomic force microscopy (nc-AFM). By changing the built-in substrate chemical potential, different charge states of sulfur vacancies (Vac S ) and substitutional rhenium dopants (Re Mo ) can be stabilized. $${\mathrm{Vac}}_{{{{{{{{\rm{S}}}}}}}}}^{-1}$$ Vac S − 1 as well as $${{\mathrm{Re}}}_{{{{{{{{\rm{Mo}}}}}}}}}^{0}$$ Re Mo 0 and $${\mathrm{Re}}_{{\rm{Mo}}}^{-1}$$ Re Mo − 1 exhibit local lattice distortions and symmetry-broken defect orbitals attributed to a Jahn-Teller effect (JTE) and pseudo-JTE, respectively. By mapping the electronic and geometric structure of single point defects, we disentangle the effects of spatial averaging, charge multistability, configurational dynamics, and external perturbations that often mask the presence of local symmetry breaking.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2020

Phase Switching as the Origin of Large Piezoelectric Response in Organic-Inorganic Perovskites: A First-Principles Study

Piezoelectrics are critical functional components of many practical applications such as sensors, ultrasonic transducers, actuators, medical imaging, telecommunications. So far, the best performing piezoelectrics are ferroelectric ceramics, many of which are toxic, heavy, hard, and cost-ineffective. Recently, a groundbreaking discovery of extraordinarily large piezoelectric coefficients in the family of organic-inorganic perovskites gave a hope for a cheaper, environmentally friendly, inexpensive, light-weight and flexible alternative. However, the origin of such response in organic-inorganic ferroelectrics whose spontaneous polarization is an order of magnitude smaller than for inorganic counterparts remains unclear. In this study we employ first-principles simulations to predict that the mechanism associated with large piezoelectric constants is of extrinsic origin and associated with switching between the stable phase and previously overlooked energetically competitive metastable phase that can be stabilized by the external stress. Here, the phase switching changes the polarization direction and, therefore, gives origin to large piezoelectric response, similar to PbZr$_{1-x}$Ti$_x$O$_3$ near morphotropic phase boundary. Existence of such metastable phases is likely to manifest as the dynamical molecular disorder above the Curie temperature and, therefore, could be intrinsic to the entire family of organic-inorganic ferroelectrics with such disorder.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2023

Nonadditive Interactions Unlock Small-Particle Mobility in Binary Colloidal Monolayers

We examine the organization and dynamics of binary colloidal monolayers composed of micron-scale silica particles interspersed with smaller-diameter silica particles that serve as minority component impurities. These binary monolayers are prepared at the surface of ionic liquid droplets over a range of size ratios (σ = 0.16–0.66) and are studied with low-dose minimally perturbative scanning electron microscopy (SEM). The high resolution of SEM imaging provides direct tracking of all particle coordinates over time, enabling a complete description of the microscopic state. In these bidisperse size mixtures, particle interactions are nonadditive because interfacial pinning to the droplet surface causes the equators of differently sized particles to lie in separate planes. By varying the size ratio, we control the extent of nonadditivity in order to achieve phase behavior inaccessible to additive 2D systems. Across the range of size ratios, we tune the system from a mobile small-particle phase (σ < 0.24) to an interstitial solid (0.24 < σ < 0.33) and furthermore to a disordered glass (σ > 0.33). These distinct phase regimes are classified through measurements of hexagonal ordering of the large-particle host lattice and the lattice’s capacity for small-particle transport. Altogether, we explain these structural and dynamic trends by considering the combined influence of interparticle interactions and the colloidal packing geometry. Our measurements are reproduced in molecular dynamics simulations of 2D nonadditive disks, suggesting an efficient method for describing confined systems with reduced dimensionality representations.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Investigation of the cesium activation of Ga⁢N photocathodes by low-energy electron microscopy

Low-energy electron microscopy (LEEM) was performed on p-Ga⁢N samples during in situ cesium deposition. LEEM images of electron reflectivity recorded as a function of the incident electron energy at different Cs coverages allowed to spatially resolve the evolution of the local work function (WF) during the activation process. While the average WF drops by more than 3 eV, the local WF remains quite uniform across the surface throughout the activation process. Maximum fluctuations of less than 0.2 eV were observed in the WF maps for Cs coverage of a fraction of a monolayer. These fluctuations are mainly related to the surface topography, in particular, to the atomic steps’ structure, which replicates the substrate miscut. Apart from these weak spatial fluctuations, no Cs clusters that would induce strong local WF contrast were observed at the scale of the 20-nm resolution of the measurements. These observations agree with the simple model of semiconductor activation to negative electron affinity that describes the formation of a dipole layer as responsible for the lowering of the WF. Additionally, at complete Cs coverage, the WF becomes fully homogeneous over the surface, smoothing out features originating from defects and topography.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2023

Oscillating paramagnetic Meissner effect and Berezinskii-Kosterlitz-Thouless transition in underdoped Bi2Sr2CaCu2O8+δ

ABSTRACT Superconducting phase transitions in two dimensions lie beyond the description of the Ginzburg-Landau symmetry-breaking paradigm for three-dimensional superconductors. They are Berezinskii-Kosterlitz-Thouless (BKT) transitions of paired-electron condensate driven by the unbinding of topological excitations, i.e. vortices. The recently discovered monolayers of layered high-transition-temperature (${{{T}}}_{{\rm C}}$) cuprate superconductor Bi2Sr2CaCu2O8+δ (Bi2212) meant that this 2D superconductor promised to be ideal for the study of unconventional superconductivity. But inhomogeneity posed challenges for distinguishing BKT physics from charge correlations in this material. Here, we utilize the phase sensitivity of scanning superconducting quantum interference device microscopy susceptometry to image the local magnetic response of underdoped Bi2212 from the monolayer to the bulk throughout its phase transition. The monolayer segregates into domains with independent phases at elevated temperatures below ${{{T}}}_{{\rm C}}$. Within a single domain, we find that the susceptibility oscillates with flux between diamagnetism and paramagnetism in a Fraunhofer-like pattern up to ${{{T}}}_{{\rm C}}$. The finite modulation period, as well as the broadening of the peaks when approaching ${{{T}}}_{{\rm C}}$ from below, suggests well-defined vortices that are increasingly screened by the dissociation of vortex-antivortex plasma through a BKT transition. In the multilayers, the susceptibility oscillation differs in a small temperature regime below ${{{T}}}_{{\rm C}}$, consistent with a dimensional crossover led by interlayer coupling. Serving as strong evidence for BKT transition in the bulk, we observe a sharp jump in phase stiffness and paramagnetism at small fields just below ${{{T}}}_{{\rm C}}$. These results unify the superconducting phase transitions from the monolayer to the bulk underdoped Bi2212, and can be collectively referred to as the BKT transition with interlayer coupling.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2025

Buffer-layer effect on the ferromagnetism of manganite heterojunctions

Identifying and understanding interfacial magnetic structures of transition-metal oxides are of great importance not only for fundamental physics but also for potential device applications. Among them, manganite and ruthenate heterostructures have attracted considerable interest due to their intriguing interfacial properties induced by complex magnetic interactions. Here, we report the observation of dramatic buffer-layer dependence of ferromagnetism in ultrathin (L⁢a 2/3 ⁢C⁢a 1/3 )⁢Mn⁢O 3 (LCMO)-based heterostructures. Though all trilayers are nonmetallic, the SrRu⁢O 3 -buffered LCMO trilayer exhibits enhanced ferromagnetism with the Curie temperature (𝑇 C ∼ 198K) much higher than for CaRu⁢O 3 (𝑇 C ∼ 99K)- and SrTi⁢O 3 (𝑇 C ∼ 42K)-buffered counterparts, as well as the monolithic LCMO films with similar thickness. Combining atomically resolved scanning transmission electron microscopy imaging with electron energy loss spectroscopy mapping, we reveal that asymmetric interfaces exist in the SrRu⁢O 3 buffered trilayer, with one exhibiting 1 unit-cell Sr diffusion into LCMO, which is responsible for the 𝑇 C enhancement. In contrast, charge transfer, which has been proposed previously as a possible mechanism, is excluded in this study. In conclusion, our results may pave a promising road toward effective atomic control of interfacial magnetism.

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↗