Small Wave Vectors Research Articles

Temperature and inhomogeneous background affect plasmons in four-layer graphene structures

We employ the random-phase approximation to investigate the effects of temperature and the inhomogeneity of background dielectric on the collective excitations and respective broadening functions in 4-MLG structures. Computations present that the systems have four plasmon modes, corresponding to one in-phase and three out-of-phase oscillations of charged particles. We obtain that plasmon frequency and respective broadening functions behave as increasing functions of temperature with sufficiently large wave vectors. Dissimilarly, in small wave vector regions, the increase in temperature slightly decreases plasmon energy, but further increases in temperature increase this parameter. In addition, as the separation increases, both plasmon frequency and broadening functions significantly reduce, and the inhomogeneity of the dielectric background strongly decreases plasmon energy and its loss. We observe that both temperature and the environment's inhomogeneity should be considered in calculations.

Morphology-independent general-purpose optical surface tractor beam

Optical tractor beams capable of pulling particles backward have garnered significant and increasing interest. Traditional optical tractor beams are limited to free space beams with small forward wavevectors, enabling them to pull selected particles. Here, we present a comprehensive theory for the optical force exerted by a surface wave using analytical and numerical calculations, revealing the relationship between the canonical momentum and optical forces. Based on this theory, we demonstrate a general purpose optical surface tractor beam that can pull any passive particle, regardless of size, composition, or geometry. The tractor beam utilizes a surface wave with negative canonical momentum characterized by a single well-defined negative Bloch k vector. The tractor beam relies on a mechanism where the negative incident force always surpasses the recoil force. As such, the tractor beam, when excited on the surface of a double-negative index metamaterial, can pull particles with different morphologies.

Doping dependence and multichannel mediators of superconductivity: calculations for a cuprate model

We study two aspects of the superconductivity in a cuprate model system, its doping dependence and the influence of competing pairing mediators. We first include electron–phonon interactions beyond Migdal’s approximation and solve self-consistently, as a function of doping and for an isotropic electron–phonon coupling, the full-bandwidth, anisotropic vertex-corrected Eliashberg equations under a non-interacting state approximation for the vertex correction. Our results show that such pairing interaction supports the experimentally observed dx2−y2 -wave symmetry of the superconducting gap, but only in a narrow doping interval of the hole-doped system. Depending on the coupling strength, we obtain realistic values for the gap magnitude and superconducting critical temperature Tc close to optimal doping, rendering the electron–phonon mechanism an important candidate for mediating superconductivity in this model system. Second, for a doping near optimal hole doping, we study multichannel superconductivity, by including both vertex-corrected electron–phonon interaction and spin and charge fluctuations as pairing mechanisms. We find that both mechanisms cooperate to support an unconventional d-wave symmetry of the order parameter, yet the electron–phonon interaction is mainly responsible for the Cooper pairing and high critical temperature Tc . Spin fluctuations are found to have a suppressing effect on the gap magnitude and critical temperature due to their repulsive interaction at small coupling wave vectors.

Topological ordering during flexible to rigid transitions in disordered networks

This contribution focuses on the structural origin of flexible to rigid transitions and the possible underlying intermediate phase which have been reported to occur in a variety of network glasses such as chalcogenides or modified oxides. Here, using molecular dynamics simulations of densified glass-forming liquids, 2SiO 2 -Na 2 O, which are known to display a numerical reversibility window as a signature of an intermediate phase, we focus on structural functions emphasizing topological ordering using the Bhatia–Thornton formalism. Results not only reveal that densified silicates display topological ordering on lengthscales of about 25 Å, but also display obvious threshold behaviors close to the isostatic condition when the network undergoes a flexible to rigid transition. The mechanical constraint count of the atomic network structure reveals that a typical lengthscale characterizing the decay of topological correlations emerges for stressed rigid systems at ≃3.5 Å, whereas small wavevector oscillations are found to be minimal when the isostatic condition is merely satisfied. An additional analysis building on diffusivity and liquid entropy suggests that the locus of flexible to rigid transitions has also connections with water-like anomalies of densified tetrahedral liquids.

Optically driven plasmons in graphene/hBN van der Waals heterostructures: simulating s-SNOM measurements

Abstract Converting transverse photons into longitudinal two-dimensional plasmon-–polaritons (2D-PP) and vice versa presents a significant challenge within the fields of photonics and plasmonics. Therefore, understanding the mechanism which increases the photon – 2D-PP conversion efficiency could significantly contribute to those efforts. In this study, we theoretically examine how efficiently incident radiation, when scattered by a silver spherical nanoparticle (Ag-NP), can be transformed into 2D-PP within van der Waals (vdW) heterostructures composed of hexagonal boron nitride and graphene (hBN/Gr composites). We show that the Dirac plasmon (DP) excitation efficiency depends on the Ag-NP radius as R 3, and decreases exponentially with Ag-NP height h, so that for a certain Ag-NP geometry up to 25 % of the incident electrical field is channeled into the DP. We demonstrate that the linear plasmons (LPs) excitation efficiency can be manipulated by changing the graphene–graphene distance Δ (or hBN thickness) or by changing the number of graphene layers N. By increasing Δ and/or N the LPs move towards smaller wave vectors Q and become accessible by the Ag-NP dipole field, so that for N ≥ 5 the excitation of more than one LP is possible. These results are supported by recent scattering-type scanning near-field optical microscopy (s-SNOM) measurements. Furthermore, we show that Ag-NPs with specific parameters preferentially hybridizes with DPs of a particular wavelength λ D , facilitating selective excitation of DPs. The obtained tuning possibilities could have a significant impact on applied plasmonics, photonics or optoelectronics.

The Shocks in Josephson Transmission Line Revisited

We continue our previous studies of the shocks in the lossy Josephson transmission line (JTL). The article consists of two parts. In the first part, we analyze the scattering of the “sound” (small amplitude small wave vector harmonic wave) on the shock wave and calculate the reflection and the transmission coefficients. In the second part, we show that the kinks, which we previously studied only in the lossless JTL, exist also in the lossy JTL and study the similarities and the dissimilarities between the shocks and the kinks there. We find that the nonlinear equation describing the weak kinks and the weak shocks can be integrated (in particular cases) in terms of elementary functions. We also show that the profile of the shock in the lossy JTL demonstrates oscillatory behavior with leading peaks resembling solitary waves if the losses are weak.

Symmetry-selective quasiparticle scattering and electric field tunability of the ZrSiS surface electronic structure

Three-dimensional Dirac semimetals with square-net non-symmorphic symmetry, such as ternary ZrXY (X = Si, Ge; Y = S, Se, Te) compounds, have attracted significant attention owing to the presence of topological nodal lines, loops, or networks in their bulk. Orbital symmetry plays a profound role in such materials as the different branches of the nodal dispersion can be distinguished by their distinct orbital symmetry eigenvalues. The presence of different eigenvalues suggests that scattering between states of different orbital symmetry may be strongly suppressed. Indeed, in ZrSiS, there has been no clear experimental evidence of quasiparticle scattering reported between states of different symmetry eigenvalues at small wave vector q⃗. Here we show, using quasiparticle interference, that atomic step-edges in the ZrSiS surface facilitate quasiparticle scattering between states of different symmetry eigenvalues. This symmetry eigenvalue mixing quasiparticle scattering is the first to be reported for ZrSiS and contrasts quasiparticle scattering with no mixing of symmetry eigenvalues, where the latter occurs with scatterers preserving the glide mirror symmetry of the crystal lattice, e.g. native point defects in ZrSiS. Finally, we show that the electronic structure of the ZrSiS surface, including its unique floating band surface state, can be tuned by a vertical electric field locally applied by the tip of a scanning tunneling microscope (STM), enabling control of a spin–orbit induced avoided crossing near the Fermi level by as much as 300%.

Germanium-based nearly hyperuniform nanoarchitectures by ion beam impact

We address the fabrication of nano-architectures by impacting thin layers of amorphous Ge deposited on SiO2 with a Ga+ ion beam and investigate the structural and optical properties of the resulting patterns. By adjusting beam current and scanning parameters, different classes of nano-architectures can be formed, from elongated and periodic structures to disordered ones with a footprint of a few tens of nm. The latter disordered case features a significant suppression of large length scale fluctuations that are conventionally observed in ordered systems and exhibits a nearly hyperuniform character, as shown by the analysis of the spectral density at small wave vectors. It deviates from conventional random fields as accounted for by the analysis of Minkowski functionals. A proof of concept for potential applications is given by showing peculiar reflection properties of the resulting nano-structured films that exhibit colorization and enhanced light absorption with respect to the flat Ge layer counterpart (up to one order of magnitude at some wavelength). This fabrication method for disordered hyperuniform structures does not depend on the beam size. Being ion beam technology widely adopted in semiconductor foundries over 200 mm wafers, our work provides a viable pathway for obtaining disordered, nearly-hyperuniform materials by self-assembly with a footprint of tens of nanometers for electronic and photonic devices, energy storage and sensing.

Correlations of tensor field components in isotropic systems with an application to stress correlations in elastic bodies.

Correlation functions of components of second-order tensor fields in isotropic systems can be reduced to an isotropic fourth-order tensor field characterized by a few invariant correlation functions (ICFs). It is emphasized that components of this field depend in general on the coordinates of the field vector variable and thus on the orientation of the coordinate system. These angular dependencies are distinct from those of ordinary anisotropic systems. As a simple example of the procedure to obtain the ICFs we discuss correlations of time-averaged stresses in isotropic glasses where only one ICF in reciprocal space becomes a finite constant e for large sampling times and small wave vectors. It is shown that e is set by the typical size of the frozen-in stress components normal to the wave vectors, i.e., it is caused by the symmetry breaking of the stress for each independent configuration. Using the presented general mathematical formalism for isotropic tensor fields this finding explains in turn the observed long-range stress correlations in real space. Under additional but rather general assumptions e is shown to be given by a thermodynamic quantity, the equilibrium Young modulus E. We thus relate for certain isotropic amorphous bodies the existence of finite Young or shear moduli to the symmetry breaking of a stress component in reciprocal space.

Microscopic dynamics of liquid gallium

The coherent collective dynamics of liquid Gallium for the small wave vector range (3.25 nm−1 ≤ k ≤ 12.5 nm−1) at 315 K which is close to its melting point have been studied using modified microscopic theory. The computed results for the energy dependent spectra for the dynamical structure factor of the liquid Gallium sample show the variation quite close to the corresponding accurate experimental values obtained using coherent inelastic X-ray scattering. The characteristics of simple liquid metals are exhibited in the different graphs plotted.

Collective excitations of a general spin-3/2 Fermi gas

Collective excitation modes in a general 3D homogenous spin-3/2 Fermi gas with spin-dependent contact interactions are investigated by two-particle Green’s functions and diagram techniques. Energy spectra for two branches of charge-density waves and three branches of transverse spin-density waves are obtained within the random-phase approximation. All spectra are gapless and linear in the small wave vector q, with their slopes dependent on the interaction parameters. It is also found that the spin-mixing interaction has effects on the transverse spin-density waves, but not on the charge-density modes. When the system satisfies SU(4) symmetry, the two charge-density modes become degenerate and two of the three transverse spin-density modes are degenerate, too. Furthermore, static spin susceptibilities are discussed in detail. It is found that susceptibilities increase with the enhancement of all interaction parameters, and become divergent at certain points. This phenomenon is analogous to the Stoner transition in spin-1/2 fermion gas.

Sound attenuation in two-dimensional glasses at finite temperatures.

The thermal conductivity of glasses exhibits an unusual temperature dependence compared to their crystalline counterparts. Sound attenuation due to disorder in glasses was proposed to be important in rationalizing this special behavior. Simulation studies suggest that in the harmonic approximation, the sound attenuation follows Rayleigh scattering scaling at small wave vector in both two-dimensional (2D) and 3D glasses. The influence of the anharmonicity on sound attenuation has very recently been investigated numerically, but only in 3D glasses. Hence, it remains unknown in simulations how sound attenuation changes with the wave vector in 2D glasses when the anharmonicity comes into play. Here, we address this issue by performing computer simulations in low-temperature 2D glasses over a large range of glass stabilities. We find that the way the anharmonicity affects sound attenuation in 2D glasses is the same as that in 3D, thus revealing that numerically the influence of the anharmonicity on sound attenuation does not rely on the spatial dimension.

Frustrated antiferromagnetic triangular lattice with Dzyaloshinskii–Moriya interaction: Ground states, spin waves, skyrmion crystal, phase transition

We study in this article a triangular lattice with Heisenberg spins interacting with each other via an antiferromagnetic exchange interaction J and a Dzyaloshinskii–Moriya (DM) interaction D, between nearest-neighbors (NN). We consider two cases: the first case in which the DM vector D is perpendicular to the lattice plane and the second case where it lies in the plane. A magnetic field H is applied perpendicular to the spin plane in both cases. The ground state (GS) of this system is calculated by minimizing the energy using the very fast steepest-descent method in the two cases. In the case of perpendicular D with H=0, the GS is periodic. We analytically determine the GS configuration which is characterized by two well-defined angles. We calculate the spin-wave spectrum in this case which shows that for small wave vectors the spin waves are forbidden in the system. When H≠0, the GS in the perpendicular D case shows no skyrmions. However, in the case of in-plane D with H≠0, we find a crystal of skyrmions at T=0 composed of three interpenetrating skyrmion sublattice crystals, in agreement with low-T spin textures found in earlier works. We show by Monte Carlo simulations that this skyrmion crystal is stable at finite temperatures below a critical temperature.

Ultralong mean free path phonons in HKUST-1 and their scattering by water adsorbates

Metal-organic frameworks (MOFs) have shown big potential in energy storage and thermal management, which are closely related to their thermal properties. It has been believed for some time that the vibrational mean free path in MOFs is relatively small and the resulting thermal conductivity has weak size dependence. By studying one of the typical MOFs, i.e., ${\mathrm{Cu}}_{3}{(\mathrm{BTC})}_{2}$ where BTC is benzene-1,3,5-tricarboxylate, also referred to as HKUST-1, we computationally prove that the mean free path of these small wave vectors or equivalently low-frequency vibrations in HKUST-1 can be as large as \ensuremath{\sim}120 nm and the corresponding thermal conductivity is strongly size dependent, which is attributed to its good crystallinity. We further find that these long mean free path phonons are strongly scattered by the adsorbed water molecules and the thermal conductivity is decreased by \ensuremath{\sim}51.3% when the water molecules are adsorbed. Consequently, the thermal conductivity of HKUST-1 with water molecules is weakly size dependent. Two pathways for the thermal energy exchange, e.g., the phonons and the water molecules, exist in HKUST-1 with water molecules. The thermal conductivity of the adsorbed HKUST-1 is found to decrease and then increase with the quantity of the adsorbates owing to the competition between the two thermal pathways. Our study here provides a fundamental understanding on the thermal transport mechanisms in the metal-organic framework with consideration of adsorbates, which offers useful guidance for thermal management design in these thermal-related applications such as adsorption-driven heat pumps.

Active-gel theory for multicellular migration of polar cells in the extra-cellular matrix

We formulate an active-gel theory for multicellular migration in the extra-cellular matrix (ECM). The cells are modeled as an active, polar solvent, and the ECM as a viscoelastic solid. Our theory enables to analyze the dynamic reciprocity between the migrating cells and their environment in terms of distinct relative forces and alignment mechanisms. We analyze the linear stability of polar cells migrating homogeneously in the ECM. Our theory predicts that, as a consequence of cell-matrix alignment, contractile cells migrate homogeneously for small wave vectors, while sufficiently extensile cells migrate in domains. Homogeneous cell migration of both extensile and contractile cells may be unstable for larger wave vectors, due to active forces and the alignment of cells with their concentration gradient. These mechanisms are stabilized by cellular alignment to the migration flow and matrix stiffness. They are expected to be suppressed entirely for rigid matrices with elastic moduli of order 10 kPa. Our theory should be useful in analyzing multicellular migration and ECM patterning at the mesoscopic scale.

Surface criticality of the antiferromagnetic Potts model

We study the three-state antiferromagnetic Potts model on the simple-cubic lattice, paying attention to the surface critical behaviors. When the nearest neighboring interactions of the surface is tuned, we obtain a phase diagram similar to the XY model, owing to the emergent O(2) symmetry of the bulk critical point. For the ordinary transition, we get $y_{h1}=0.780(3)$, $\eta_\parallel=1.44(1)$, and $\eta_\perp=0.736(6)$; for the special transition, we get $y_s=0.59(1)$, $y_{h1}=1.693(2)$, $\eta_\parallel=-0.391(4)$, and $\eta_\perp=-0.179(5)$; in the extraordinary-log phase, the surface correlation function $C_\parallel(r)$ decays logarithmically, with decaying exponent $q=0.60(2)$, however, the correlation $C_\perp(r)$ still decays algebraically, with critical exponent $\eta_\perp=-0.442(5)$. If the ferromagnetic next nearest neighboring surface interactions are added, we find two transition points, the first one is a special point between the ordinary phase and the extraordinary-log phase, the second one is a transition between the extraordinary-log phase and the $Z_6$ symmetry-breaking phase, with critical exponent $y_{\rm s}=0.41(2)$. The scaling behaviors of the second transition is very interesting, the surface spin correlation function $C_\parallel(r)$ and the surface squared staggered magnetization at this point decays logarithmically, with exponent $q=0.37(1)$; however, the surface structure factor with the smallest wave vector and the correlation function $C_\perp(r)$ satisfy power-law decaying, with critical exponents $\eta_\parallel=-0.69(1)$ and $\eta_\perp=-0.37(1)$, respectively.

Solution to the two-body Smoluchowski equation with shear flow for charge-stabilized colloids at low to moderate Péclet numbers

We developed an analytical theoretical method to determine the microscopical structure of weakly to moderately sheared colloidal suspensions in dilute conditions. The microstructure is described by the static structure factor, obtained by solving the stationary two-body Smoluchowski advection-diffusion equation. The singularly perturbed PDE problem is solved by performing an angular averaging over the extensional and compressing sectors and by the rigorous application of boundary-layer theory (intermediate asymptotics). This allows us to expand the solution to a higher order in P\'eclet with respect to previous methods. The scheme is independent of the type of interaction potential. We apply it to the example of charge-stabilized colloidal particles interacting via the repulsive Yukawa potential and study the distortion of the structure factor. It is predicted that the distortion is larger at small wavevectors $k$ and its dependence on $Pe$ is a simple power law. At increasing $Pe$, the main peak of the structure factor displays a broadening and shift towards lower $k$ in the extensional sectors, which indicates shear-induced spreading out of particle correlations and neighbor particles locally being dragged away from the reference one. In the compressing sectors, instead, a narrowing and shift towards high $k$ is predicted, reflecting shear-induced ordering near contact and concomitant depletion in the medium-range. An overall narrowing of the peak is also predicted for the structure factor averaged over the whole solid angle. Calculations are also performed for hard spheres, showing good overall agreement with experimental data. It is also shown that the shear-induced structure factor distortion is orders of magnitude larger for the Yukawa repulsion than for the hard spheres.

Evaluation strategy towards an accurate determination of viscosity and interfacial tension by surface light scattering in presence of line-broadening effects

HypothesisThe accurate determination of viscosity and interfacial tension by surface light scattering (SLS) represents a challenging task, especially in the range of small wave vectors. Here, measurements are subjected to line-broadening effects, which are often not adequately described by empirical fitting routines in literature. ExperimentsFor tackling this limitation, a novel evaluation strategy relying on a Monte-Carlo-based optimization is suggested in the present study. Without making prior assumptions about the underlying distribution of wave vectors, the method allows to decompose the measured SLS signal into a superposition of individual contributions represented by damped oscillations. The resulting amplitude distribution for damping and frequency is used to estimate the central wave vector, all of which is required to solve the dispersion relation for hydrodynamic surface fluctuations in its exact form. FindingsBy applying the evaluation strategy to SLS signals recorded in reflection direction for the reference fluid toluene, it is demonstrated that the presented concept provides a route towards an accurate determination of viscosity and surface tension in the range of small wave vectors. Hence, the strategy is considered to extend the application range of SLS in connection with opaque and non-transparent fluids for which small wave vectors often need to be probed experimentally.

Microscopic analysis of sound attenuation in low-temperature amorphous solids reveals quantitative importance of non-affine effects.

Sound attenuation in low-temperature amorphous solids originates from their disordered structure. However, its detailed mechanism is still being debated. Here, we analyze sound attenuation starting directly from the microscopic equations of motion. We derive an exact expression for the zero-temperature sound damping coefficient. We verify that the sound damping coefficients calculated from our expression agree very well with results from independent simulations of sound attenuation. Small wavevector analysis of our expression shows that sound attenuation is primarily determined by the non-affine displacements' contribution to the sound wave propagation coefficient coming from the frequency shell of the sound wave. Our expression involves only quantities that pertain to solids' static configurations. It can be used to evaluate the low-temperature sound damping coefficients without directly simulating sound attenuation.

High spin-wave asymmetry and emergence of radial standing modes in thick ferromagnetic nanotubes

Magnetochiral properties are enriched in curved magnetic nanostructures, in which dipole-dipole and exchange couplings are their physical sources. In such systems, direct implications are evidenced in the magnetization dynamics, where a noticeable frequency shift appears between two counterpropagating spin waves. In this paper, the spin-wave asymmetry induced by the curvature is theoretically studied in thick ferromagnetic nanotubes with a vortex ground state. The spin-wave spectra are obtained using semianalytical calculations and the dynamical matrix method for thin and thick nanotubes. Under the thickness increase, radial standing spin waves are observed at low frequencies, while the nonreciprocal properties are improved. Such standing waves exhibit a nonreciprocal spin-wave dispersion, but it is not as prominent as the asymmetry of the low-frequency in-phase modes. In the limit of small wave vectors, analytical expressions are reported for the spin-wave dispersion, where the resonance frequency, the frequency shift of two counterpropagating waves, and the critical field that destabilizes the vortex state are determined. The obtained frequency shift allows us to estimate the influence of thickness and curvature on the nonreciprocity of the spin waves. These results constitute a significant advance in the fundamental understanding of the spin-wave dynamics of ferromagnetic nanotubes, predicting new phenomena and providing expressions that are easy to interpret and that allow us, therefore, to promote the study of magnetization dynamics in curved structures.