Higher-order Multipole Moments Research Articles

Transport of Spin Magnetic Multipole Moments Carried by Bloch Quasiparticles.

Magnetic ordering beyond the standard dipolar order has attracted significant attention in recent years, but it remains an open question how to effectively manipulate such nontrivial order parameters using external perturbations such as electric currents or fields. In particular, it is desirable to have a conceptual tool similar to nonequilibrium spin currents in spintronics to describe the creation and transport of multipole moments. In this context, we present a theory for Cartesian spin magnetic multipole moments of Bloch quasiparticles and their transport based on a general gauge-invariant formula obtained using the wave packet approach. As a concrete example, we point out that the low-energy Hamiltonian of phosphorene subject to a perpendicular electric field has a valley structure that hosts magnetic octupole moments. The magnetic octupole moments can be exhibited by an in-plane electric current and lead to accumulation of staggered spin densities at the corners of a rectangular sample. Our Letter paves the way for systematically seeking and utilizing quasiparticles with higher-order magnetic multipole moments in crystal materials towards the emergence of multipoletronics.

Strongly coupled surface plasmon resonance modes at both FF and SH in clusters of symmetrically distributed metallic nanospheres

Plasmonic nanoclusters play an important role in the rapid development of application of nanophotonics. In this article both the fundamental-frequency (FF) and second-harmonic (SH) responses of the complex nanoclusters (tetramer, hexamer, and octamer), constructed by coupled spherical plasmonic nanoparticles, are theoretically investigated. By using the multiple scattering algorithm, we present the comprehensive numerical analysis of the physical mechanisms pertaining to the linear and nonlinear coupled-plasmon modes, including ‘hot spot’ modes (HSMs) and ‘whispering-gallery’ modes (WGMs). Different from the symmetric coupling of plasmonic eigenmodes excited by the nanodimer, our analysis reveals that such coupled modes from the nanomultimers are the result of the ‘hybridization’ of symmetric and asymmetric coupling between adjacent dipole or higher-order multipole moments. Also, the remarkable enhancement as large as 3–4 orders of magnitude is achieved for the SH intensity when employing the plasmonic HSMs or WGMs at the FF. Interestingly, the nonlinear plasmonic HSMs and WGMs (the maximum Q up to 4800) can also be obtained by elaborately designing the system geometry. In addition, the resonant wavelengths of such coupled-plasmon modes can be linearly modulated within a broad range. These numerical results have potential applications in surface optical microscopy, plasmonic sensor and nanolaser.

Control and measurement of electric dipole moments in levitated optomechanics

Levitated optomechanical systems are rapidly becoming leading tools for precision sensing, enabling a high level of control over the sensor's center of mass motion, rotation and electric charge state. Higher-order multipole moments in the charge distribution, however, remain a major source of backgrounds. By applying controlled precessive torques to the dipole moment of a levitated microsphere in vacuum, we demonstrate cancellation of dipole-induced backgrounds by 2 orders of magnitude. We measure the dipole moments of ng-mass spheres and determine their scaling with sphere size, finding that the dominant torques arise from induced dipole moments related to dielectric-loss properties of the SiO$_2$ spheres. Control of multipole moments in the charge distribution of levitated sensors is a key requirement to sufficiently reduce background sources in future applications.

Quadrupole-mediated dielectric response and the charge-asymmetric solvation of ions in water.

Treating water as a linearly responding dielectric continuum on molecular length scales allows very simple estimates of the solvation structure and thermodynamics for charged and polar solutes. While this approach can successfully account for basic length and energy scales of ion solvation, computer simulations indicate not only its quantitative inaccuracies but also its inability to capture some basic and important aspects of microscopic polarization response. Here, we consider one such shortcoming, a failure to distinguish the solvation thermodynamics of cations from that of otherwise-identical anions, and we pursue a simple, physically inspired modification of the dielectric continuum model to address it. The adaptation is motivated by analyzing the orientational response of an isolated water molecule whose dipole is rigidly constrained. Its free energy suggests a Hamiltonian for dipole fluctuations that accounts implicitly for the influence of higher-order multipole moments while respecting constraints of molecular geometry. We propose a field theory with the suggested form, whose nonlinear response breaks the charge symmetry of ion solvation. An approximate variational solution of this theory, with a single adjustable parameter, yields solvation free energies that agree closely with simulation results over a considerable range of solute size and charge.

Theory of double-resonance alignment magnetometers based on atomic high-order multipole moments using effective master equations

We present a theoretical study of double-resonance alignment magnetometers using linearly polarized light, in which the effect of atomic high-order multipole moments is considered. Starting from the effective master equation of our system obtained by eliminating the excited state adiabatically, we derive the full evolution equations of the atomic multipole moments. The analytic solutions of resonance signals involving the four-order multipole moments effect are obtained by using the perturbation approach. We present that the four-order multipole moments effect is negligible in the weak laser field, and the results reduce to that obtained by a three-step approach. However, the role of four-order multipole moments coupled by two-order tensor moments is more significant with the increasing Rabi frequency of light, which cannot be ignored. Meanwhile, the analytic expressions of relaxation processes are also studied, which are a linear combination of the laser-induced equivalent relaxation rate Γ L and the spin-exchange collision rate Γ g . The expected domain of validity of the three-step approach on light power is roughly given by Γ L < 1 2 Γ g . In addition, the steady-state results of resonance signals are presented in a strong radio-frequency magnetic field; in that case, the physical mechanism of the splitting of resonance signals is discussed. These results are valid for arbitrary light power and for an arbitrarily oriented static magnetic field.

Higher-order topological insulators in synthetic dimensions

Conventional topological insulators support boundary states with dimension one lower than that of the bulk system that hosts them, and these states are topologically protected due to quantized bulk dipole moments. Recently, higher-order topological insulators have been proposed as a way of realizing topological states with dimensions two or more lower than that of the bulk due to the quantization of bulk quadrupole or octupole moments. However, all these proposals as well as experimental realizations have been restricted to real-space dimensions. Here, we construct photonic higher-order topological insulators (PHOTIs) in synthetic dimensions. We show the emergence of a quadrupole PHOTI supporting topologically protected corner modes in an array of modulated photonic molecules with a synthetic frequency dimension, where each photonic molecule comprises two coupled rings. By changing the phase difference of the modulation between adjacent coupled photonic molecules, we predict a dynamical topological phase transition in the PHOTI. Furthermore, we show that the concept of synthetic dimensions can be exploited to realize even higher-order multipole moments such as a fourth-order hexadecapole (16-pole) insulator supporting 0D corner modes in a 4D hypercubic synthetic lattice that cannot be realized in real-space lattices.

Effects of higher-order multipoles of the lunar disturbing potential on elongated orbits in cislunar space

For an Earth satellite in cislunar space, the effects of the third or higher-order harmonics in the solar disturbing function are negligible. For lunar perturbations, however, these terms become increasingly important as the semimajor axis increases. We investigate the effects of these higher-order multipole moments on circular, moderate, and highly elliptical orbits, where the semimajor axis is a relatively large fraction (~20%) of the Moon’s one. We specifically characterize the regions of cislunar space where the octupole-order approximation, often used in celestial and astrophysical dynamics for studying the stability and fates of hierarchical planetary systems, is actually a valid truncation of the gravitational interactions.

Demonstration of a quantized acoustic octupole topological insulator

Recently introduced quantized multipole topological insulators (QMTIs) reveal new types of gapped boundary states, which themselves represent lower-dimensional topological phases and host symmetry protected zero-dimensional corner states. Inspired by these predictions, tremendous efforts have been devoted to the experimental observation of quantized quadrupole topological phase. However, due to stringent requirements of anti-commuting reflection symmetries, it is challenging to achieve higher-order quantized multipole moments, such as octupole moments, in a three-dimensional structure. Here, we overcome this challenge, and experimentally realize the acoustic analogue of a quantized octupole topological insulator using negatively coupled resonators. We confirm by first-principle studies that our design possesses a quantized octupole topological phase, and experimentally demonstrate spectroscopic evidence of a hierarchy of boundary modes, observing 3rd order topological corner states. Furthermore, we reveal topological phase transitions from higher- to lower-order multipole moments. Our work offers a pathway to explore higher-order topological states in 3D classical platforms.

Suppression of high-order multipole moments in a resonant periodic dipole chain

In this work we study the properties of optical states in transverse subdiffractional dipolar chains of periodically spaced scatterers. We demonstrate that in this system there are states with low values of emission rates, and we explain this as a reduction of different multipolar contributions up to high values of orbital angular momentum. We also show that the emission rate for these states decreases as ∼ N −6.76 with the number of scatterers.

Concentration dependent energy levels shifts in donor-acceptor mixtures due to intermolecular electrostatic interaction

Recent progress in the improvement of organic solar cells lead to a power conversion efficiency to over 16%. One of the key factors for this improvement is a more favorable energy level alignment between donor and acceptor materials, which demonstrates that the properties of interfaces between donor and acceptor regions are of paramount importance. Recent investigations showed a significant dependence of the energy levels of organic semiconductors upon admixture of different materials, but its origin is presently not well understood. Here, we use multiscale simulation protocols to investigate the molecular origin of the mixing induced energy level shifts and show that electrostatic properties, in particular higher-order multipole moments and polarizability determine the strength of the effect. The findings of this study may guide future material-design efforts in order to improve device performance by systematic modification of molecular properties.

Rocksalt or cesium chloride: Investigating the relative stability of the cesium halide structures with random phase approximation based methods

The ground state structural and energetic properties for rocksalt and cesium chloride phases of the cesium halides were explored using the random phase approximation (RPA) and beyond-RPA methods to benchmark the nonempirical SCAN meta-GGA and its empirical dispersion corrections. The importance of nonadditivity and higher-order multipole moments of dispersion in these systems is discussed. RPA generally predicts the equilibrium volume for these halides within 2.4% of the experimental value, while beyond-RPA methods utilizing the renormalized adiabatic LDA (rALDA) exchange-correlation kernel are typically within 1.8%. The zero-point vibrational energy is small and shows that the stability of these halides is purely due to electronic correlation effects. The rAPBE kernel as a correction to RPA overestimates the equilibrium volume and could not predict the correct phase ordering in the case of cesium chloride, while the rALDA kernel consistently predicted results in agreement with the experiment for all of the halides. However, due to its reasonable accuracy with lower computational cost, SCAN+rVV10 proved to be a good alternative to the RPA-like methods for describing the properties of these ionic solids.

Hydrodynamics of micro-swimmers in films

One of the principal mechanisms by which surfaces and interfaces affect microbial life is by perturbing the hydrodynamic flows generated by swimming. By summing a recursive series of image systems, we derive a numerically tractable approximation to the three-dimensional flow fields of a stokeslet (point force) within a viscous film between a parallel no-slip surface and a no-shear interface and, from this Green’s function, we compute the flows produced by a force- and torque-free micro-swimmer. We also extend the exact solution of Liron & Mochon (J. Engng Maths, vol. 10 (4), 1976, pp. 287–303) to the film geometry, which demonstrates that the image series gives a satisfactory approximation to the swimmer flow fields if the film is sufficiently thick compared to the swimmer size, and we derive the swimmer flows in the thin-film limit. Concentrating on the thick-film case, we find that the dipole moment induces a bias towards swimmer accumulation at the no-slip wall rather than the water–air interface, but that higher-order multipole moments can oppose this. Based on the analytic predictions, we propose an experimental method to find the multipole coefficient that induces circular swimming trajectories, allowing one to analytically determine the swimmer’s three-dimensional position under a microscope.

Effect of higher-order multipole moments on the Stark line shape

Spectral line shapes are sensitive to plasma conditions and are often used to diagnose electron density of laboratory plasmas as well as astrophysical plasmas. Stark line-shape models take into account the perturbation of the radiator's energy structure due to the Coulomb interaction with the surrounding charged particles. Solving this Coulomb interaction is challenging and is commonly approximated via a multipole expansion. However, most models include only up to the second term of the expansion (the dipole term). While there have been studies on the higher-order terms due to one of the species (i.e., either ions or electrons), there is no model that includes the terms beyond dipole from both species. Here, we investigate the importance of the higher-order multipole terms from both species on the $\mathrm{H}\ensuremath{\beta}$ line shape. First, we find that it is important to include higher-order terms consistently from both ions and electrons to reproduce measured line-shape asymmetry. Next, we find that the line shape calculated with the dipole-only approximation becomes inaccurate as density increases. It is necessary to include up to the third (quadrupole) term to compute the line shape accurately within 2%. Since most existing models include only up to the dipole terms, the densities inferred with such models are in question. We find that the model without the quadrupole term slightly underestimates the density, and the discrepancy becomes as large as 12% at high densities. While the case of study is limited to $\mathrm{H}\ensuremath{\beta}$, we expect similar impact on other lines.

Dynamics of spherical distributions of charge with small internal dipolar motion.

This paper extends the Lorentz-Abraham model of an electron (i.e., the equations of motion for a small spherical shell of charge, which is rigid in its proper frame) to treat a small, spherically symmetric charge distribution, allowing for small internal dipolar motion. This is done by dividing the distribution into thin spherical shells (in the continuum limit), and tracking the interactions between shells. Dipolar motion of each constituent spherical shell is allowed along the net dipole moment, but higher-order multipole moments are ignored. The amplitude of dipolar motion of each spherical shell is assumed to be linearly proportional to the net dipole moment. Under these assumptions, low-velocity equations of motion are determined for both the center-of-mass motion and net dipolar motion of the distribution. This is then generalized to arbitrary (relativistic) center-of-mass velocity and acceleration, assuming the motion of individual shells is completely in phase or out of phase with the net dipole moment.

Leaky domino-modes in regular arrays of substantially thick metal nanostrips

In previous works, an efficient light trapping performed by arrays of metal nanoantennas whose building block was a slightly tapered (trapezoidal) substantially thick nanostrip was revealed. This light trapping implied a broad spectrum of solar light concentrated in a subwavelength depth of the semiconductor substrate. This is a very advantageous feature allowing our structure to enhance thin-film solar cells. However, the physics of the broadband resonant absorption in the substrate was not investigated. In the present paper, we show that our arrays support so-called leaky domino-modes, responsible for such the light trapping. These modes are multipole oscillations of the array of substantially thick nanostrips. In this work we have thoroughly studied these leaky modes relating them to resonances of high-order multipole moments and to broadband light-trapping effect.

Collective aspects deduced from time-dependent microscopic mean-field with pairing: Application to the fission process

Given a set of collective variables, a method is proposed to obtain the associated conjugated collective momenta and masses starting from a microscopic time-dependent mean-field theory. The construction of pairs of conjugated variables is the first step to bridge microscopic and macroscopic approaches. The method is versatile and can be applied to study a large class of nuclear processes. An illustration is given here with the fission of $^{258}\mathrm{Fm}$. Using the quadrupole moment and eventually higher-order multipole moments, the associated collective masses are estimated along the microscopic mean-field evolution. When more than one collective variable is considered, it is shown that the off-diagonal matrix elements of the inertia play a crucial role. Using the information on the quadrupole moment and associated momentum, the collective evolution is studied. It is shown that dynamical effects beyond the adiabatic limit are important. Nuclei formed after fission tend to stick together for a longer time leading to a dynamical scission point at a larger distance between nuclei compared to the one anticipated from the adiabatic energy landscape. The effective nucleus-nucleus potential felt by the emitted nuclei is finally extracted.

Electronic Energy Transfer in Polarizable Heterogeneous Environments: A Systematic Investigation of Different Quantum Chemical Approaches.

Theoretical prediction of transport and optical properties of protein-pigment complexes is of significant importance when aiming at understanding the structure-function relationship in such systems. Electronic energy transfer (EET) couplings represent a key property in this respect since such couplings provide important insight into the strength of interaction between photoactive pigments in protein-pigment complexes. Recently, attention has been payed to how the environment modifies or even controls the electronic couplings. To enable such theoretical predictions, a fully polarizable embedding model has been suggested (Curutchet, C., et al. J. Chem. Theory Comput., 2009, 5, 1838-1848). In this work, we further develop this computational model by extending it with an ab initio derived polarizable force field including higher-order multipole moments. We use this extended model to systematically examine three different ways of obtaining EET couplings in a heterogeneous medium ranging from use of the exact transition density to a point-dipole approximation. Several interesting observations are made, for example, the explicit use of transition densities in the calculation of the electronic couplings, and also when including the explicit environment contribution, can be replaced by a much simpler transition point charge description without comprising the quality of the model predictions.

Scattering Dark States in Multiresonant Concentric Plasmonic Nanorings

Plasmonic nanoantennas can feature a sophisticated spectral response that may be the springboard for a plethora of applications. Particularly, spectrally sharp Fano resonances have been at the focus of interest because of their promising applications in sensing. Usually, the observation of Fano resonances requires nanostructures that exhibit multiple plasmonic resonances such as higher-order multipole moments. We show that similar spectral features can be observed with nanoantennas sustaining solely electric-dipolar resonances. The considered nanoantennas consist of multiple concentric gold nanorings separated by thin dielectric spacers. These nanoantennas host multiple resonances with disparate line widths in the visible and near-infrared. We theoretically and experimentally show that the interference of these resonances causes Fano features and scattering dark states. The electric-dipolar character permits the use of a simplified dense-array theory to predict the response of arrays of such nanoantennas ...

Expanding the Scope of Density Derived Electrostatic and Chemical Charge Partitioning to Thousands of Atoms.

The density derived electrostatic and chemical (DDEC/c3) method is implemented into the onetep program to compute net atomic charges (NACs), as well as higher-order atomic multipole moments, of molecules, dense solids, nanoclusters, liquids, and biomolecules using linear-scaling density functional theory (DFT) in a distributed memory parallel computing environment. For a >1000 atom model of the oxygenated myoglobin protein, the DDEC/c3 net charge of the adsorbed oxygen molecule is approximately -1e (in agreement with the Weiss model) using a dynamical mean field theory treatment of the iron atom, but much smaller in magnitude when using the generalized gradient approximation. For GaAs semiconducting nanorods, the system dipole moment using the DDEC/c3 NACs is about 5% higher in magnitude than the dipole computed directly from the quantum mechanical electron density distribution, and the DDEC/c3 NACs reproduce the electrostatic potential to within approximately 0.1 V on the nanorod's solvent-accessible surface. As examples of conducting materials, we study (i) a 55-atom Pt cluster with an adsorbed CO molecule and (ii) the dense solids Mo2C and Pd3V. Our results for solid Mo2C and Pd3V confirm the necessity of a constraint enforcing exponentially decaying electron density in the tails of buried atoms.

An efficient algorithm for multipole energies and derivatives based on spherical harmonics and extensions to particle mesh Ewald.

Next-generation molecular force fields deliver accurate descriptions of non-covalent interactions by employing more elaborate functional forms than their predecessors. Much work has been dedicated to improving the description of the electrostatic potential (ESP) generated by these force fields. A common approach to improving the ESP is by augmenting the point charges on each center with higher-order multipole moments. The resulting anisotropy greatly improves the directionality of the non-covalent bonding, with a concomitant increase in computational cost. In this work, we develop an efficient strategy for enumerating multipole interactions, by casting an efficient spherical harmonic based approach within a particle mesh Ewald (PME) framework. Although the derivation involves lengthy algebra, the final expressions are relatively compact, yielding an approach that can efficiently handle both finite and periodic systems without imposing any approximations beyond PME. Forces and torques are readily obtained, making our method well suited to modern molecular dynamics simulations.