Lattice Modes Research Articles

Polarizability, plasmons and damping in pseudospin-1 gapped materials with a flat band

The subject of our present investigation is the collective electronic properties of various types of pseudospin-1 Dirac-cone materials with a flat band and finite bandgaps in their low-energy spectra. Specifically, we have calculated the dynamical polarization, plasmon dispersions, as well as their decay rates due to Landau damping and presented the closed-form analytical expressions for the wave function overlaps for both the gapped dice lattice and the Lieb lattice. The gapped dice lattice is a special case of the more generalα-T3model such that its band structure is symmetric and the flat band remains dispersionless. On the other hand, the Lieb lattice has a flat band which appears at the lowest point of its conduction band. Our results for these two materials exhibit unique features in the plasmon spectra and their damping regions, which have never been previously reported. For example, the particle-hole modes of a Lieb lattice appear as finite-size regions, while the plasmon modes exist only in areas with small wave numbers but an extended range of frequencies.

Photocontrol of ferroelectricity in multiferroic BiFeO3 via structural modification coupled with photocarrier

Ultrafast control of ferroelectricity and magnetism by light is essential for future development in multiple functioning devices. Here, we demonstrate that the intense and ultrafast photo-modulation of the electric dipole can be realized by photocarrier injection into a multiferroic BiFeO3 thin film using optical pump-probe and second harmonic generation measurements. Results of ultrafast electron diffraction with <100 fs time resolution and theoretical study reveal that the localized photocarrier strongly couples with the lattice structure and becomes the origin for the observed sudden change in the electric dipole. In addition, the subsequent structural dynamics involve a strong oscillation with a frequency of ~3.3 THz despite a poor structural symmetry change. Based on a theoretical calculation, this oscillation can be attributed to an unexpectedly softened new phonon mode generated by mixing essential two phonon modes governing the multiferroic (ferroelectric and antiferromagnetic) nature of BiFeO3 in the ground state due to strong coupling with a localized photocarrier. The comprehensive study shows that injection of the localized photocarrier strongly coupled with the lattice vibration mode can simultaneously realize the ultrafast switching of electric dipoles and magnetic interaction at once, even at room temperature, without modifying the long-range lattice structure.

Equilibrium oxygen isotope fractionation in Mg(OH)2-Ca(OH)2-H2O: Implication from in situ high-temperature and high-pressure vibrational spectra

Abstract Equilibrium oxygen isotope fractionations have been extensively studied between H2O and minerals (like brucite-type hydroxides) in isotope geochemistry. In this study, pure 18O-enriched hydroxides were synthesized through reactions between M3N2 (M = Mg and Ca) powders and H218O water. In situ high-temperature (T) and high-pressure (P) Raman and Fourier transform infrared (FTIR) spectra were systematically collected for these phases. The observed 18O-16O effect on the frequency shifts aligns with the theoretical model, and has little impact on the anharmonic O-H potential well. The calculated intrinsic anharmonic parameters (ai) for both lattice and OH-stretching modes are essentially identical between M(16OH)2 and M(18OH)2, satisfying the classical limit for the Helmholtz free energy at extremely high temperature. Based on the measured vibrational data, the equilibrium oxygen isotope fractionation β(T,P) factors were modeled for both hydroxides. Both the intrinsic and external anharmonic contributions are smaller than the experimental uncertainties, and this model is also validated by ab initio calculation. Next, the 103·lnα(T) profiles were computed between brucite/portlandite and H2O, which are consistent with the reported oxygen isotope exchange measurements above 200 °C. Additionally, the discrepancy between this equilibrium model and the precipitation experiment below 120 °C also provides useful information for investigating the mechanism of kinetic isotope fractionation. The predicted 103·lnαbrucite-portlandite(T) curve also agrees well with points inferred from the 18O-16O exchange measurements, while the pressure effect can be ignored for 18O-16O fractionations. Therefore, vibrational spectroscopic measurements, including both Raman and infrared spectroscopies, have valuable applications in studying equilibrium non-metallic isotope fractionations in minerals.

Cyclic and helical symmetry-informed machine learned force fields: Application to lattice vibrations in carbon nanotubes

We present a formalism for developing cyclic and helical symmetry-informed machine learned force fields (MLFFs). In particular, employing the smooth overlap of atomic positions descriptors with the polynomial kernel method, we derive cyclic and helical symmetry-adapted expressions for the energy, atomic forces, and phonons, i.e., lattice vibration frequencies and modes. We use this formulation to construct a symmetry-informed MLFF for carbon nanotubes (CNTs), where the model is trained through Bayesian linear regression, with the data generated from ab initio density functional theory (DFT) calculations performed during on-the-fly symmetry-informed MLFF molecular dynamics simulations of representative CNTs. We demonstrate the accuracy of the MLFF model by comparisons with DFT calculations for the energies and forces, and density functional perturbation theory calculations for the phonons, while considering CNTs not used in the training. In particular, we obtain a root mean square error of 1.4×10−4 Ha/atom, 4.7×10−4 Ha/Bohr, and 4.8 cm−1 in the energy, forces, and phonon frequencies, respectively, which are well within the accuracy targeted in ab initio calculations. We apply this framework to study phonons in CNTs of various diameters and chiralities, where we identify the torsional rigid body mode that is unique to cylindrical structures and establish laws for variation of the phonon frequencies associated with the ring modes and radial breathing modes. Overall, the proposed formalism provides an avenue for studying nanostructures with cyclic and helical symmetry at ab initio accuracy, while providing orders-of-magnitude speedup relative to such methods.

Phase-transition of hydrophobic dipeptide l-phenylalanyl-l-alanine under high pressure via Raman spectroscopy

The study conducted on l-Phenylalanyl-l-Alanine (C12H16N2O3) dehydrated crystals under high-pressure conditions up to 7.0 GPa using Raman spectroscopy revealed significant modifications in both lattice and internal modes. Particularly, alterations were observed in modes associated with carbonyl and NH2 functionalities around 1600 cm−1. The Raman spectra exhibited distinct changes in modes related to torsions and stretching of the ring, suggesting a potential conformational change in specific pressure intervals: 2.6–3.0 GPa, and 5.0–5.1 GPa. Furthermore, notable changes between 0.4 and 1.0 GPa hinted at a structural transformation in the crystal. Additionally, Scanning Electron Microscopy-Field Emission Gun (SEM-FEG) was employed to elucidate the crystal pattern of Phe-Ala·2H2O. The ambient study, incorporating calculations, infrared, and Raman spectroscopy, contributed to a comprehensive understanding of vibrational mode assignments. This research sheds light on the behavior of l-Phenylalanyl-l-Alanine dehydrated crystals under varying pressure conditions, offering valuable insights for medicinal and pharmacological applications.

Sr4Os3O12 – A Layered Osmate(V,VI) that is Magnetic Close to Room Temperature

AbstractBlack crystals of the mixed‐valence osmate(V,VI) Sr4Os3O12 were grown via a gas phase reaction in an evacuated silica tube. The material is attracted to a permanent magnet at room temperature (295±5 K) but loses this property when heated or cooled. In this temperature interval, soft magnetic behavior with vanishing coercivity is observed, but the saturation magnetization is only 0.05 μB per formula unit. Resistivity measurements show that Sr4Os3O12 is a semiconductor with a small band gap of about 0.26 eV at room temperature. X‐ray diffraction on a single‐crystal revealed a rhombohedral structure with the space group R m and lattice parameters ar=554.64(2) pm and cr=2700.1(1) pm at 300(1) K. The compound crystallizes in the La4Ti3O12 structure type and is isostructural to Sr4CoRe2O12. The structure is a rhombohedral stack of layered blocks, each of which can be considered as a section of three layers of the cubic perovskite structure cut perpendicular to one of its threefold axes. The Os–O−Os bond angle of about 175° favors superexchange that leads to antiferromagnetic coupling between the osmium atoms with 5d3 and 5d2 configurations. Sr4Os3O12 exhibits strong lattice dynamics. One aspect is the antiferro‐rotative lattice modes of the corner‐sharing [OsO6] octahedra, which freeze upon cooling. At 100 K, an ordered, yet twinned triclinic superstructure is formed. Strong spin‐orbit coupling and other effects cause deformations of the [OsO6] octahedra that differ significantly at 300 K and 100 K, suggesting a change in the electronic configuration. Competing ground states could also explain the temperature‐dependent band gap and the magnetic fluctuations manifested in the magnetization peak at room temperature.

Engineering Fano resonances in plasmonic metasurfaces for colorimetric sensing and structural colors

In this paper, we present the design and fabrication of a plasmonic metasurface based on titanium dioxide (TiO2) nanowire arrays integrated with plasmonic layers. The structure is engineered to produce Fano resonances within the visible spectrum, resulting from the coupling of localized surface plasmon resonances, lattice modes, and nanowire's optical modes. Experimentally, we show that by tuning the geometrical features of the metasurface, such as the length, diameter, and period of the nanowires, a high-quality factor single peak can be achieved in the reflection spectra, resulting in vivid structural colors in bright field. To our knowledge, this is the first demonstration of such vivid colors with nanowire arrays in bright field reflections. When characterized by refractive index fluids around the refractive index of water, the plasmonic metasurface also showed great potential for biochemical colorimetric sensing. The best design demonstrated a bulk sensitivity of 183 nm/RIU with high Q resonance features and linear changes in color values using image processing.

Pressure-Induced Structural Phase Transitions and Photoluminescence Properties of Micro/Nanocrystals HoF3.

HoF3 crystals of varying sizes and morphologies were synthesized by controlling the amount of water. As the water content gradually decreased, the size of the crystals reduced, transforming from microcrystals to approximately 100 nm nanocrystals with unique morphologies. At room temperature, the pressure-induced phase transitions, and photoluminescence (PL) properties of HoF3 micro/nanocrystals are studied using in situ high-pressure PL technique. The PL spectra show that the HoF3 micro/nanocrystals exhibit two structural phase transformations at 5 (6 GPa for NCs) and 12 GPa. Nanoparticles have higher fluorescence intensity, which initially increases and then decreases with changes in pressure. Based on first-principles calculations, HoF3 transforms from an orthorhombic structure to a hexagonal structure during the phase transition, with the coordination number of holmium atoms increasing from 9 to 11. The high-pressure Raman spectra on lattice modes also confirmed the existence of the two phase transitions. This work not only provides precise structural changes but also facilitates the understanding of two typical structures of rare-earth trifluoride (REF3), which may play an important role in the application of the RE family.

Evaluation of multi-phased heterostructures in Fe-Cr-based alloys through TEM observation combined with a newly developed LRLM model

The characteristics of the multi-phased oxide-TiN-TiC-(δ-Fe) heterostructures in Fe-Cr-based alloys are essential for TiN refinement and resultant grain refinement. While the refining phenomena of TiN and as-cast grains in Fe-Cr-based alloys were well reported, the detailed refining mechanisms for TiN and δ-Fe grains remain to be further elucidated. In order to evaluate the oxide-TiN-TiC-(δ-Fe) heterostructures, three foils for transmission electron microscope (TEM) examination were prepared, denoted as the I0, R1, and MR1 samples, respectively. Here, the atomic lattice matching modes and orientation relationships (ORs) across the (Mg and /or RE bearing oxide)-TiN-TiC-(δ-Fe) heterostructures were revealed. Based on the results, the simulated multilayer /3D atomic matching models for the interfaces of each heterostructure were established, revealing the actual atomic-scale structures of the heterostructures and their formation processes originating from the oxides. Furthermore, a newly developed long-range lattice matching (LRLM) model was established to provide a new method of the OR verifications. In summary, this study does provide new insights into interfacial engineering and new ideals on refining TiN and as-cast grains in industrial production of Fe-Cr-based alloys.

Elucidating the Limit of Lithium Difluorophosphate Electrolyte Additive for High‐Voltage Li/Mn‐Rich Layered Oxide || Graphite Li Ion Batteries

Li/Mn‐rich layered oxide (LMR) cathode active materials offer remarkably high specific discharge capacity (&gt;250 mAh g−1) from both cationic and anionic redox. The latter necessitates harsh charging conditions to high cathode potentials (&gt;4.5 V vs Li|Li+), which is accompanied by lattice oxygen release, phase transformation, voltage fade, and transition metal (TM) dissolution. In cells with graphite anode, TM dissolution is particularly detrimental as it initiates electrode crosstalk. Lithium difluorophosphate (LiDFP) is known for its pivotal role in suppressing electrode crosstalk through TM scavenging. In LMR || graphite cells charged to an upper cutoff voltage (UCV) of 4.5 V, effective TM scavenging effects of LiDFP are observed. In contrast, for an UCV of 4.7 V, the scavenging effects are limited due to more severe TM dissolution compared an UCV of 4.5 V. Given the saturation in solubility of the TM scavenging agents, which are LiDFP decomposition products, e.g., PO43− and PO3F2−, higher concentrations of the LiDFP as “precursor” cannot enhance the amount of scavenging species, they rather start to precipitate and damage the anode.

Topologically protected bound modes in non-neighboring hexagonal lattices

In the last decade, the study of wave localization and guiding has gained a renewed interest thanks to the introduction of the concept of topological protection. Originally developed in the field of quantum mechanics, topological protection has successively inspired the search for its analogue in other physical domains, including elasticity. In this context, periodic hexagonal lattices have been proposed as ideal candidates to realize these concepts. In this work, we explore the dynamic behavior of discrete hexagonal lattices with third nearest neighbor connections. First, the formation and transition of multiple Dirac cones above a critical value of the relative stiffness between the first and third nearest neighbor connections is derived. Then, the formation of extremely localized modes (i.e., bound modes) at the interface between regions formed by lattices which are inverted copies of each other is demonstrated. Our results show that this localization derives from a type of interface satisfying a point reflection symmetry for which the considered chain decouples into two identical copies at the high symmetry point of the Brillouin zone. Our findings open novel avenues for topological waveguiding and confinement with potential applications in surface acoustic wave devices.

Effects of acoustic shock waves on the structural and optical properties of cadmium borate

Cadmium borate (CdB₂O₄), an inorganic compound combining transition metals and non-metals, has a broad range of optical applications. In this study, CdB₂O₄ was subjected to acoustic transient pressure using a semi-automatic Reddy tube, with shock pulses applied at counts of 100, 200, 300, and 400 at a Mach number of 1.5, corresponding to a transient pressure of 0.59 MPa and a temperature of 520 K. Control and shock-treated samples were analyzed using XRD, Raman, FTIR, SEM, UV-DRS, and photoluminescence spectroscopy to investigate shock wave effects. The XRD analysis revealed peak disappearance, the formation of new peaks, increased crystallinity, and instability in crystallite size. Raman spectroscopy showed peak disappearance, shifts, and broadening of lattice modes. SEM indicated increased particle size and agglomeration under shock conditions, consistent with changes in crystallinity. UV-DRS analysis shows a slight change in their band gap. Photoluminescence exhibited fluctuating trends in luminescent properties after the shock treatment. The findings reveal that CdB₂O₄'s structural and optical properties are sensitive to acoustic pressure, suggesting its potential for tailored optical behavior in specific applications. These results enhance our understanding of how acoustic pressure affects CdB₂O₄ and open new possibilities for optimizing its use in high-pressure applications.

3-Electrode Setup for the Operando Detection of Side Reactions in Li-Ion Batteries: The Quantification of Released Lattice Oxygen and Transition Metal Ions from NCA

Detecting parasitic side reactions is paramount for developing stable cathode active materials (CAMs) for Li-ion batteries. This study presents a method for the quantification of released lattice oxygen and transition metal ions (TMII+ ions). It is based on a 3-electrode cell design employing a Vulcan carbon-based sense electrode (SE) that is held at a controlled voltage against a partially delithiated lithium iron phosphate (LFP) counter electrode (CE). At this SE, reductive currents can be measured while polarizing a CAM working electrode (WE), here a LiNi0.80Co0.15Al0.05O2 (NCA), against the same LFP CE. In voltammetric scans, we show how the SE potential can be selected to specifically detect a given side reaction during CAM charge/discharge, allowing, e.g., to discriminate between lattice oxygen and dissolved TMs. Furthermore, it is shown via online electrochemical mass spectrometry (OEMS) that O2 reduction in the here-used LP47 electrolyte consumes ∼2.3 electrons/O2. Using this value, the lattice oxygen release deduced from the 3-electrode setup upon charging of the NCA WE is in good agreement with OEMS measurements up to NCA potentials >4.65 VLi. At higher potentials, the contributions from the reduction of TMII+ ions can be quantified by comparing the integrated SE current with the O2 evolution from OEMS.

Moiré photonic superlattice-induced transparency at commensurate angle in a terahertz metasurface composed of triple layer square lattices

The control of the speed of terahertz waves is always a challenge since the bandgap of most optical materials is much larger beyond meV with subtle nonlinear susceptibility. Moiré metasurfaces are shown to exhibit wide tunable optical properties and extraordinary physical phenomena at specific commensurate angles. These can be achieved by a careful design of the metasurface to manipulate terahertz slow light. Herein, we demonstrate a triple layer Moiré metasurface with a distinct electromagnetically induced transparency (EIT) phenomenon at commensurate angles. The proposed metasurface is composed of an intrinsic square lattice embedded into another Moiré photonic superlattice made of twisted square lattice at commensurate angles of 10.39° and 7.63°. The coupling between adjacent meta-atoms on the combined metasurface leads to destructive interference of dual trapped lattice modes, which results in a transparency window at the terahertz band. A maximum group delay of 9.76 ps is found at the transparent window of 0.84 THz when the commensurate angle is 10.39°. When the commensurate angle reduces to 7.63°, the transparency window shifts to 0.57 THz with a 5.96 ps group delay. The coupled Lorentz oscillator model indicates that the nonlinear optical susceptibility at transparency windows is above zero. Our results create an approach to tune the EIT as well as slow light in the terahertz band. Our device can have potential applications in terahertz signal processing and storage.

Raman spectroscopic insights into the pressure-induced phase transition in natural elbaite

Tourmaline [XY₃Z₆(T₆O₁₈)(BO₃)₃V₃W] is a potential carrier for water and boron cycles in the Earth's interior. Its high-pressure structural behavior has been extensively investigated by single-crystal or powder X-ray diffraction. Here, we collected Raman spectroscopy data of natural elbaite with two different compositions (Fe-poor elbaite and Fe-rich elbaite) up to 35.1 GPa to complementarily characterize the structural modifications proposed by previous studies. Our results reveal two clear discontinuous changes in high-pressure Raman spectra of both samples. The first change occurred at around 15 GPa, characterized by changes in Raman peak intensity, and the pressure dependence of the frequencies of several lattice vibration modes and hydroxyl stretching vibrations. The second change emerged at around 26 GPa and was marked by the systematic appearance of new Raman peaks. Based on previous X-ray diffraction studies, the change at around 26 GPa is likely caused by a phase transition from rhombohedral R3m to rhombohedral R3, whereas the change at around 15 GPa is likely caused by a change in compression mechanism. Furthermore, the WOH stretching vibrations at 3691 cm−1 in Fe-rich elbaite exhibited a negative pressure coefficient, contrasting with the positive pressure coefficient observed in Fe-poor elbaite, suggesting a significant influence of chemical composition on the evolution of stretching vibration in WOH groups under high pressure. After release of pressure, the spectra return to their initial state, indicating the reversibility of all observed changes.

Realization of hydrogenation-induced superconductivity in two-dimensional Ti2N MXene.

Two-dimensional (2D) MXene superconductors have been currently attracting considerable interest due to their unique electronic properties and diverse applicability. Utilizing first-principles computational methods, we have designed two distinct configurations of hydrogenated 2D Ti2N MXene materials, namely Ti2NH2 and Ti2NH4, and have conducted an exhaustive analysis of their structural stability, electronic characteristics, and superconductivity. Hydrogenation endows monolayer Ti2N with inherent metallic characteristics, as evidenced by an elevated density of states (DOS) at the Fermi level (Ef). Notably, Ti2NH4 exhibits a superconducting critical temperature (Tc) of 15.8 K, which is predominantly ascribed to the electronic contributions stemming from the Ti 3d orbitals. Analysis of phonon dispersion underscores the pivotal role that diverse lattice vibrational modes play in electron-phonon coupling (EPC), particularly the significance of low-frequency vibrations for facilitating electron pairing and the emergence of superconductivity. Furthermore, strain engineering can effectively modulate the superconducting properties of Ti2NH4, with a 2% tensile strain enhancing the EPC strength (λ) to 0.857 and increasing Tc to 18.7 K. This research elucidates the superconducting mechanisms of hydrogenated Ti2N structures, offering valuable insights for the development of novel 2D superconducting materials.

Revealing discontinuous and continuous quantum phase transitions in shaken optical lattices

We perform the cluster mean-field with density matrix renormalization (CMFT+DMRG) calculation on the two-band extended Bose–Hubbard model to uncover the physics behind the discontinuous transitions observed in the one-dimensional shaken optical lattice with hybridized two lowest Bloch bands. We determine the superfluid, Mott insulator, and staggered superfluid phases associated with this model using the appropriate order parameters. We obtained the phase diagrams for two values of shaking amplitudes and illustrated the phases and nature of phase transitions. The transition from Mott insulator and superfluid to staggered superfluid is discontinuous for small shaking amplitudes. We analyse how the shaking frequency controls the effective chemical potential in the model and, consequently, the ground state energy that drives the discontinuous transition. Finally, we compare our results with those of earlier works.

Bio-Inspired Curved-Elliptical Lattice Structures for Enhanced Mechanical Performance and Deformation Stability.

Lattice structures, characterized by their lightweight nature, high specific mechanical properties, and high design flexibility, have found widespread applications in fields such as aerospace and automotive engineering. However, the lightweight design of lattice structures often presents a trade-off between strength and stiffness. To tackle this issue, a bio-inspired curved-elliptical (BCE) lattice is proposed to enhance the mechanical performance and deformation stability of three-dimensional lattice structures. BCE lattice specimens with different parameters were fabricated using selective laser melting (SLM) technology, followed by quasi-static compression tests. Finite element (FE) numerical simulations were also carried out for validation. The results demonstrate that the proposed BCE lattice structures exhibit stronger mechanical performance and more stable deformation modes that can be adjusted through parameter tuning. Specifically, by adjusting the design parameters, the BCE lattice structure can exhibit a bending-dominated delocalized deformation mode, avoiding catastrophic collapse during deformation. The specific energy absorption (SEA) can reach 24.6 J/g at a relative density of only 8%, with enhancements of 48.5% and 297.6% compared with the traditional energy-absorbing lattices Octet and body-center cubic (BCC), respectively. Moreover, the crushing force efficiency (CFE) of the BCE lattice structure surpasses those of Octet and BCC by 34.9% and 15.8%, respectively. Through a parametric study of the influence of the number of peaks N and the curve amplitude A on the compression performance of the BCE lattice structure, the compression deformation mechanism is further analyzed. The results indicate that the curve amplitude A and the number of peaks N have significant impacts on the deformation mode of the BCE lattice. By adjusting the parameters N and A, a structure with a combination of high energy absorption, high stiffness, and strong fracture resistance can be obtained, integrating the advantages of tensile-dominated and bending-dominated lattice structures.

First-principles study of the effect of Dirac phonons on the thermoelectric properties in monolayer Ge2H2

The Dirac phonons have been widely attention due to their unique edge or surface states. However, research on their influence in the realm of thermoelectric transport in semiconductor materials remains limited. Here, we have systematically investigated the geometric structure, stability, electronic, thermal conductivity, and thermoelectric properties of the monolayer Ge2H2 and Ge2 based on density functional theory and the Boltzmann transport equation (BTE). The phonon spectrum of monolayer Ge2H2 exhibits both Hourglass-type and Dirac-type phonon dispersion curves. The band structure of monolayer Ge2H2 reveals a relatively large band gap of 1.02 eV (1.75 eV for HSE), indicating that it is a direct band gap semiconductor. These two features make monolayer Ge2H2 an ideal material for exploring the effect of Dirac phonons on thermoelectric transport properties. In this paper, we determined that the lattice thermal conductivity (κl) in Ge2H2 is 0.59 Wm−1K−1 at 300 K, but undergoes a sharp increase upon removal of H atoms. This is mainly attributed to the disappearance of the Dirac phonons and the change of lattice vibration modes by removing the H atoms. While also exhibiting high carrier mobilities (134.86 cm2/Vs for holes) and extended scattering time (4.22 × 10−14 s for holes), indicative of excellent thermoelectric performance. With increasing temperature, the ZTmax of p-type doping reaches 0.63 at 700 K in Ge2H2. Remarkably, at 300K, the Hourglass-type phonon contributes only 5.94 % to κl, while the Dirac phonon contributes 3.44 %. Further analysis reveals that the Dirac phonon within Hourglass-type in monolayer Ge2H2 contributes 2.5 % to the ZTmax at 300K. Our investigation elucidates the impact of Dirac phonons on thermoelectric properties, providing valuable insights for future design and exploration of high-ZT thermoelectric materials.

Purcell effect for high-Q plasmon lattice modes in the coupled dipole approximation

Purcell effect for high-Q plasmon lattice modes in the coupled dipole approximation