Quadrupolar Symmetry Research Articles

The Diverse Electrochemistry and Photophysics of Pyrrolopyrroles

Pyrrole is among the most popular molecular scaffolds for biology. Tetrapyrroles, such as porphyrins, corrins and their derivatives, are the quintessential redox centers and chromophores exhibiting a wide range of electrochemical and optical characteristics. Similarly, pyrrolopyrroles, built on condensed five-member rings with nitrogens as heteroatoms, offer scaffolds for organic chromophores with diversity of redox and photophysical properties. For example, pyrrolo[3,2-b]pyrroles are stable electron-rich UV absorbers with quadrupole symmetry (Acc. Chem. Res. 2017, 50, 2334-2345). They can act as immensely potent electron donors and attaching electron-accepting moieties to them leads to the emergence of a myriad of optical phenomena, such as excited-state symmetry breaking (Commun. Chem. 2020, 3, 190) and generating white fluorescence by tuning donor-acceptor electronic coupling (Chem. Sci. 2023). Attaching carbonyls to the pyrrolopyrrole rings drastically changes their electronic properties, making them pronouncedly electron deficient and shifting their absorption to the visible spectral region. For example, 2,5-dihydropyrrolo[3,4-c]pyrrole-1,4-diones, or diketopyrrolopyrroles (DPPs) for short, are excellent electron acceptors and photooxidants (Adv. Opt. Matter. 2015, 3, 2018-320). Their reduction potentials are susceptible to localized electric fields, which has allowed demonstrating dipole-induced rectification of photoinduced hole transfer (Angew. Chem. Int. Ed. 2018, 57, 12365-12369). This field susceptibility extends to the optical properties of DPPs, providing an extra dimension in their utility for photonics and optoelectronics. DPPs, and pyrrolopyrroles in general, are built on small bicyclic scaffolds, i.e., considerably smaller than those of other multi-pyrrole chromophores. The small size enhances the susceptibility of their redox properties to solvation and makes them attractive photoprobes. Therefore, this class of compounds have become indispensable agents for electrochemical and photonic science and engineering.

Phonon-mediated spin transport in quantum paraelectric metals

The concept of ferroelectricity is now often extended to include continuous inversion symmetry-breaking transitions in various metals and doped semiconductors. Paraelectric metals near ferroelectric quantum criticality, which we term ‘quantum paraelectric metals,’ possess soft transverse optical phonons which can have Rashba-type coupling to itinerant electrons in the presence of spin-orbit coupling. We find through the Kubo formula calculation that such Rashba electron-phonon coupling has a profound impact on electron spin transport. While the spin Hall effect arising from non-trivial electronic band structures has been studied extensively, we find here the presence of the Rashba electron-phonon coupling can give rise to spin current, including spin Hall current, in response to an inhomogeneous electric field even with a completely trivial band structure. Furthermore, this spin conductivity displays unconventional characteristics, such as quadrupolar symmetry associated with the wave vector of the electric field and a thermal activation behavior characterized by scaling laws dependent on the phonon frequency to temperature ratio. These findings shed light on exotic electronic transport phenomena originating from ferroelectric quantum criticality, highlighting the intricate interplay of charge and spin degrees of freedom.

Nanoscale Porosity in Microellipsoids Cloaks Interparticle Capillary Attraction at Fluid Interfaces.

Anisotropic particles pinned at fluid interfaces tend toward disordered multiparticle configurations due to large, orientationally dependent, capillary forces, which is a significant barrier to exploiting these particles to create functional self-assembled materials. Therefore, current interfacial assembly methods typically focus on isotropic spheres, which have minimal capillary attraction and no dependence on orientation in the plane of the interface. In order to create long-range ordered structures with complex configurations via interfacially trapped anisotropic particles, control over the interparticle interaction energy via external fields and/or particle engineering is necessary. Here, we synthesize colloidal ellipsoids with nanoscale porosity and show that their interparticle capillary attraction at a water-air interface is reduced by an order of magnitude compared to their smooth counterparts. This is accomplished by comparing the behavior of smooth, rough, and porous ellipsoids at a water-air interface. By monitoring the dynamics of two particles approaching one another, we show that the porous particles exhibit a much shorter-range capillary interaction potential, with scaling intriguingly different than theory describing the behavior of smooth ellipsoids. Further, interferometry measurements of the fluid deformation surrounding a single particle shows that the interface around porous ellipsoids does not possess the characteristic quadrupolar symmetry of smooth ellipsoids, and quantitatively confirms the decrease in capillary interaction energy. By engineering nanostructured surface features in this fashion, the interfacial capillary interactions between particles may be controlled, informing an approach for the self-assembly of complex two-dimensional microstructures composed of anisotropic particles.

Direct observation of quadrupolar strain fields surrounding Eshelby inclusions in metallic glasses.

For decades, scanning/transmission electron microscopy (S/TEM) techniques have been employed to analyze shear bands in metallic glasses and understand their formation in order to improve the mechanical properties of metallic glasses. However, due to a lack of direct information in reciprocal space, conventional S/TEM cannot characterize the local strain and atomic structure of amorphous materials, which are key to describe the deformation of glasses. For this work, we applied 4-dimensional STEM to map and directly correlate the local strain and the atomic structure at the nanometer scale in deformed metallic glasses. We observe residual strain fields with quadrupolar symmetry concentrated at dilated Eshelby inclusions. The strain fields percolate in a vortex-like manner building up the shear band. This provides a new understanding of the formation of shear bands in metallic glass. This article is protected by copyright. All rights reserved.

The magic of biaryl linkers: the electronic coupling through them defines the propensity for excited-state symmetry breaking in quadrupolar acceptor-donor-acceptor fluorophores.

Charge transfer (CT) is key for molecular photonics, governing the optical properties of chromophores comprising electron-rich and electron-deficient components. In photoexcited dyes with an acceptor-donor-acceptor or donor-acceptor-donor architecture, CT breaks their quadrupolar symmetry and yields dipolar structures manifesting pronounced solvatochromism. Herein, we explore the effects of electronic coupling through biaryl linkers on the excited-state symmetry breaking of such hybrid dyes composed of an electron-rich core, i.e., 1,4-dihydropyrrolo[3,2-b]pyrrole (DHPP), and pyrene substituents that can act as electron acceptors. Experimental and theoretical studies reveal that strengthening the donor-acceptor electronic coupling decreases the CT rates and the propensity for symmetry breaking. We ascribe this unexpected result to effects of electronic coupling on the CT thermodynamics, which in its turn affects the CT kinetics. In cases of intermediate electronic coupling, the pyrene-DHPP conjugates produce fluorescence spectra, spreading over the whole visible range, that in addition to the broad CT emission, show bands from the radiative deactivation of the locally excited states of the donor and the acceptors. Because the radiative deactivation of the low-lying CT states is distinctly slow, fluorescence from upper locally excited states emerge leading to the observed anti-Kasha behaviour. As a result, these dyes exhibit white fluorescence. In addition to demonstrating the multifaceted nature of the effects of electronic coupling on CT dynamics, these chromophores can act as broad-band light sources with practical importance for imaging and photonics.

Pinning effect on the correlations of nonaffine displacement in metallic glasses

We mimic the structural heterogeneity of inclusions in nanoscale by pinning a portion of atoms in CuZr metallic glasses (MGs) on molecular dynamics simulations with shear deformation. Results show yielding of the MGs transits from a system-spanning shear band (SB) to a localized plastic flow with pinning, due to the constrained length scale for the organization of the plastic events imposed by pinning. Spatial correlation of the nonaffine displacement exhibits a quadrupolar symmetry that shrinks with pinning, giving two characteristic lengths in the maximum and minimum directions that are both constrained by the static length for the pinned atoms. The two characteristic lengths signify the anisotropic nature of the plastic regions, which diminishes with pinning. These results shed light on the microscopic mechanism of tailoring the mechanical properties by tuning the static structure in MGs.

Anisotropic correlations of plasticity on the yielding of metallic glasses.

We report computer simulations on the shear deformation of CuZr metallic glasses at zero and room temperatures. Shear bands emerge in athermal alloys at strain γ_{c}, with a finite-size effect found. The correlation of nonaffine displacement exhibits an exponential decay even after yielding in thermal alloys, but transits to a power law at γ>γ_{c} in athermal ones. The algebraic exponent is around -1 for the decay inside shear bands, consistent with the theoretical prediction in random elastic media. We quantify the anisotropic correlation with harmonic projection, finding the spectrum is weak in the exponential-decay regime, while it displays a strong polar and quadrupolar symmetry in the power-law regime. The nonvanishing quadrupolar symmetry at long distance signifies the nonlocality of plastic correlation in the athermal alloys. In contrast, the plastic correlation was found to be isotropic and localized at the yielding in the thermal alloys without shear bands.

Spatial correlation of irreversible displacement in oscillatory-sheared metallic glasses

We report computer simulations on the oscillatory of CuZr metallic glasses at zero temperature with different shear amplitudes. In small system a homogenous shear deformation is found, while in large system an inhomogeneous shear deformation is found with a shear band formed. Concomitantly, spatial correlation of irreversible displacement exhibits an isotropic and exponential decay in the case of homogeneous deformation, whereas a mixed power-law and exponential decay in the case of anisotropic and inhomogeneous deformation. By projecting the azimuthal-dependent correlation function onto the spherical harmonics, we found a strong polar symmetry that accounts for the emerged shear band, and a weaker quadrupolar symmetry that accounts for the elastic filed generated by Eshelby inclusions. By this, we conclude that the anisotropy and decaying formula of the plastic correlation are dominated by the homogeneity or inhomogeneity for the deformation in the metallic glasses.

Exotic shape symmetries around the fourfold octupole magic number N=136 : Formulation of experimental identification criteria

We employ a realistic nuclear mean-field theory using the phenomenological, Woods-Saxon Hamiltonian with newly adjusted parameters containing no parametric correlations; originally present correlations are removed employing the Monte Carlo approach. We find very large neutron shell gaps at $N=136$ for all the four octupole deformations ${\ensuremath{\alpha}}_{3\ensuremath{\mu}=0,1,2,3}$. These shell gaps generate well-pronounced double potential-energy minima in the standard multipole $({\ensuremath{\alpha}}_{20},{\ensuremath{\alpha}}_{22},{\ensuremath{\alpha}}_{3\ensuremath{\mu}},{\ensuremath{\alpha}}_{40})$ representation, often at ${\ensuremath{\alpha}}_{20}=0$, which in turn generate exotic symmetries ${C}_{2v}$, ${D}_{2d}$, ${T}_{d}$, and ${D}_{3h}$, discussed in detail. The main goal of the article is to formulate spectroscopic criteria for experimental identification. Calculations employing macroscopic-microscopic method are performed for nuclei with $Z\ensuremath{\ge}82$ and $N\ensuremath{\ge}126$ in multidimensional deformation spaces to analyze the expected exotic symmetries and octupole shape instabilities in the mass table ``northeast'' of the doubly magic $^{208}\mathrm{Pb}$ nucleus. Whereas the proton-unperturbed properties of neutron-generated octupole shell effects are illustrated in detail for exotic ${}_{Z=82}{\mathrm{Pb}}_{N>126}$ nuclei, our discussion is extended into even-even $Z>82$ nuclei approaching the less exotic $Z/N$ ratios, to encourage experiments which could identify the predicted exotic symmetries. In addition to the tetrahedral point group symmetry, ${T}_{d}$, of which experimental evidence has recently been published, we present ${D}_{2d}$ symmetry resulting from a superposition of axially symmetric quadrupole and tetrahedral symmetries and two new point group symmetries, ${D}_{3h}$ and ${C}_{2v}$, associated with the octupole ${\ensuremath{\alpha}}_{33}$ and ${\ensuremath{\alpha}}_{31}$ energy minima, respectively. The multidimensional $n>2$ deformation spaces are treated as usual by projecting the total potential energies onto the $n=2$ subspace. Using the representation theory of point groups we formulate quantum mechanical criteria for experimental identification of exotic symmetries through analysis of the specific properties of the collective rotational bands generated by the symmetries. The resulting band structures happen to be markedly distinct from the structure of the bands generated by ellipsoidal symmetry quantum rotors; those various rotational properties are discussed in detail.

Capillary force on an 'inert' colloid: a physical analogy to dielectrophoresis.

“Inert” colloids are μm-scale particles that create no distortion when trapped at a planar fluid–fluid interface. When placed in a curved interface, however, such colloids can create interfacial distortions of quadrupolar symmetry – so-called “induced capillary quadrupoles.” The present work explores the analogy between capillary quadrupoles and electric dipoles, and the forces exerted on them by a symmetry-breaking gradient. In doing so, we weigh in on an outstanding debate as to whether a curvature gradient can induce a capillary force on an inert colloid. We argue that this force exists, for the opposite would imply that all dielectrophoretic forces vanish in two dimensions (2D). We justify our claim by solving 2D Laplace problems of electrostatics and capillary statics involving a single particle placed within a large circular shell with an imposed gradient. We show that the static boundary condition on the outer shell must be considered when applying the principle of virtual work to compute the force on the particle, as verified by a direct calculation of this force through integration of the particle stresses. Our investigation highlights some of the subtleties that emerge in virtual work calculations of capillary statics and electrostatics, thereby clarifying and extending previous results in the field. The broader implication of our results is that inert particles – including particles with planar, pinned contact lines and equilibrium contact angles – interact through interparticle capillary forces that scale quadratically with the deviatoric curvature of the host interface, contrary to recent claims made in the literature.

Gravitomagnetic resonance in the field of a gravitational wave

Using the construction of the Fermi frame, the field of a gravitational wave can be described in terms of gravito-electromagnetic fields that are transverse to the propagation direction and orthogonal to each other. In particular, the gravito-magnetic field acts on spinning particles and we show that, due to the action of the gravitational wave field, a new phenomenon, that we call gravito-magnetic resonance, may appear. We give both a classical and a quantum description of this phenomenon and suggest that it can be used as the basis for a new type of gravitational wave detectors. Our results highlight the effectiveness of collective spin excitations, e.g. spin waves in magnetized materials, in detecting high frequency gravitational waves. Here we suggest that, when gravitational waves induce a precession of the electron spin, power is released in the ferromagnetic resonant mode endowed with quadrupole symmetry of a magnetized sphere. This offers a possible path to the detection of the gravito-magnetic effects of a gravitational wave.

Solar Quadrupole in Tensor Description

The cyclic variations in the quadrupole component of the solar magnetic field is studied in tensor description. The results are consistent with the classical description of the quadrupole using spherical functions, and the mathematical apparatus of tensor algebra allows one to compare the observed changes in the magnetic quadrupole and the changes predicted by the dynamo theories. In conclusion, the quadrupole properties can be adequately described by solar dynamo models that assume deviations from the dipole symmetry without the independent excitation of the quadrupole symmetry modes.

Two-symmetry Penning-Ioffe trap for antihydrogen cooling and spectroscopy

High-accuracy spectroscopic comparisons of trapped antihydrogen atoms (H¯) and hydrogen atoms (H) promise to stringently test the fundamental CPT symmetry invariance of the standard model of particle physics. ATRAP’s nested Penning-Ioffe trap was developed for such studies. The first of its unique features is that its magnetic Ioffe trap for H¯atoms can be switched between quadrupole and octupole symmetries. The second is that it allows laser and microwave access perpendicular to the central axis of the traps.

Critical Casimir interaction between colloidal Janus-type particles in two spatial dimensions

We study colloidal particles with chemically inhomogeneous surfaces suspended in a critical binary liquid mixture. The inhomogeneous particle surface is composed of patches with alternating adsorption preferences for the two components of the binary solvent. By describing the binary liquid mixture at its consolute point in terms of the critical Ising model we exploit its conformal invariance in two spatial dimension. This allows us to determine exactly the universal profiles of the order parameter, the energy density, and the stress tensor as well as some of their correlation functions around a single particle for various shapes and configurations of the surface patches. The formalism encompasses several interesting configurations, including Janus particles of circular and needle shapes with dipolar symmetry and a circular particle with quadrupolar symmetry. From these single-particle properties we construct the so-called small particle operator expansion (SPOE), which enables us to obtain asymptotically exact expressions for the position- and orientation-dependent critical Casimir interactions of the particles with distant objects, such as another particle or the confining walls of a half plane, strip, or wedge, with various boundary conditions for the order parameter. In several cases we compare the interactions at large distances with the ones at close distance (but still large on the molecular scale). We also compare our analytical results for two Janus particles with recent simulation data.

Cyclic variations in the main components of the solar large-scale magnetic field

ABSTRACT We consider variations of the dipole and quadrupole components of the solar large-scale magnetic field. Both axial and equatorial dipoles exhibit a systematic decrease during the past four cycles, in accordance with the general decrease of solar activity. The transition of the pole of a dipole from the polar region to the midlatitudes occurs rather quickly, so that the longitude of the pole changes little. With time, however, this inclined dipole region shifts to larger longitudes, which suggests an acceleration of dipole rotation. The mean rotation rate exceeds the Carrington velocity by 0.6 per cent. The behaviour of a quadrupole differs dramatically. Its decrease over the last four cycles was much smaller than that of the dipole moment. The ratio of the quadrupole and dipole moments has increased for four cycles more than twice, in contrast to sunspot numbers, which displayed a twofold decrease for the same time interval. Regarding quadrupole rotation, the mean longitude of the poles of one sign decreased by 600° over four cycles, which suggests that the mean rotation rate was lower than the Carrington velocity by 0.28 per cent. We do not, however, see any conclusive evidence that, in the period under discussion, a mode of quadrupole symmetry was excited in the Sun along with the dipole mode.

Effects of Intrinsic Local Fields on Molecular Fluorescence and Energy Transfer: Dipole Mechanisms and Surface Potentials.

A general theory is developed to identify the influence of local dipole fields on fluorescence and intermolecular electronic excitation transfer. The analysis, based on electrodynamical principles, identifies the fundamental quantum mechanisms and delivers full analytical results. The aim is to afford new physical insights, assisting the interpretation of measurements on the specific effects of local molecular dipoles on direct fluorescence and on fluorescence resonance energy transfer. Dipole field effects, which include those originating from intrinsically polar chromophores and surface field gradients, also prove to be manifest in electronic transitions of quadrupole symmetry character. The results have particular significance for fluorescence studies of cell membrane biophysics.

A physical approach to modelling large-scale galactic magnetic fields

Context.A convenient representation of the structure of the large-scale galactic magnetic field is required for the interpretation of polarization data in the sub-mm and radio ranges, in both the Milky Way and external galaxies.Aims.We develop a simple and flexible approach to construct parametrised models of the large-scale magnetic field of the Milky Way and other disc galaxies, based on physically justifiable models of magnetic field structure. The resulting models are designed to be optimised against available observational data.Methods.Representations for the large-scale magnetic fields in the flared disc and spherical halo of a disc galaxy were obtained in the form of series expansions whose coefficients can be calculated from observable or theoretically known galactic properties. The functional basis for the expansions is derived as eigenfunctions of the mean-field dynamo equation or of the vectorial magnetic diffusion equation.Results.The solutions presented are axially symmetric but the approach can be extended straightforwardly to non-axisymmetric cases. The magnetic fields are solenoidal by construction, can be helical, and are parametrised in terms of observable properties of the host object, such as the rotation curve and the shape of the gaseous disc. The magnetic field in the disc can have a prescribed number of field reversals at any specified radii. Both the disc and halo magnetic fields can separately have either dipolar or quadrupolar symmetry. The model is implemented as a publicly available software packageGALMAGwhich allows, in particular, the computation of the synchrotron emission and Faraday rotation produced by the model’s magnetic field.Conclusions.The model can be used in interpretations of observations of magnetic fields in the Milky Way and other spiral galaxies, in particular as a prior in Bayesian analyses. It can also be used for a simple simulation of a time-dependent magnetic field generated by dynamo action.

Three-dimensional photonic band gap cavity with finite support: Enhanced energy density and optical absorption

We study numerically the transport and storage of light in a 3D photonic band gap crystal doped by a single embedded resonant cavity. The crystal has finite support since it is surrounded by vacuum, as in experiments. Therefore, we employ the finite element method to model the diamond-like inverse woodpile crystal that consists of two orthogonal arrays of pores in a high-index dielectric such as silicon and that has experimentally been realized by CMOS-compatible methods. A point defect that functions as the resonant cavity is formed in the proximal region of two selected orthogonal pores with a radius smaller than the ones in the bulk of the crystal. We present a field-field cross-correlation method to identify resonances in the finite-support crystal with defect states that appear in the 3D photonic band gap of the infinite crystal. Out of 5 observed angle-independent cavity resonances, one is s-polarized and 4 are p-polarized for light incident in the X or Z directions. It is remarkable that quality factors up to Q = 1000 appear in such thin structures (3 unit cells). We find that the optical energy density is remarkably enhanced at the cavity resonances by up to 2400x the incident energy density in vacuum or up to 1200x the energy density of the equivalent effective medium. We find that an inverse woodpile photonic band gap cavity with a suitably adapted lattice parameter reveals substantial absorption in the visible range. Below the 3D photonic band gap, Fano resonances arise due to interference between the discrete fundamental cavity mode and the continuum light scattered by the photonic crystal. We argue that the five eigenstates of our 3D photonic band gap cavity have quadrupolar symmetry, in analogy to d-like orbitals of transition metals. We conclude that inverse woodpile cavities offer interesting perspectives for applications in optical sensing and photovoltaics.

Superflares on Giant Stars

The Kepler mission identified huge flares on various stars including some of solar type. These events are substantially more energetic than solar flares, and so they are referred to as superflares. Even a small probability of such a superflare on the Sun would be a menace to modern society. A flare comparable in energy with that of superflares was observed on 24th and 25th September on the binary HK Lac. Unlike the Kepler stars, there are observations of differential rotation for HK Lac. This differential rotation appears to be anti-solar. For anti-solar differential rotation, dynamo models can give magnetic activity waves of dipole symmetry as well as quasi-stationary magnetic configurations with quadrupole symmetry. The magnetic energy of such stationary configurations is usually about two orders of magnitude higher than that associated with activity waves. We believe that this mechanism could provide sufficient energy to produce superflares on late type stars, and present some simple models in support of this idea.

Torus Dynamo Model for Study of Magnetic Fields in the Outer Rings of Galaxies

At present, there is essentially no doubt that magnetic fields of a few μG exist in some spiral galaxies. The fields are produced by a dynamo mechanism. Because the equations of the dynamo theory are quite complicated, a two-dimensional approximation is often used since the galactic disk is sufficiently thin, so it is possible to replace some partial derivatives with algebraic expressions. Some galaxies have outer rings in which magnetic fields may also exist. The generation of these fields can also be studied using a two-dimensional approximation, but because that approximation was not developed for rings, but for thin disks, in this case it only yields qualitative results. Therefore, a torus dynamo model is used to study this process. This model is used to analyze possible scenarios for the evolution of magnetic fields in outer rings. It is found that for motions that are not too intense, a field with a quadrupole symmetry is generated. For faster motions a dipole component of the field may develop, which is fundamentally impossible in the two-dimensional approximation.