Quadrupolar State Research Articles

Probing octupolar hidden order via Janus impurities

Quantum materials with non-Kramers doublets are a fascinating venue to realize multipolar hidden orders. Impurity probes which break point group symmetries, such as implanted muons or substitutional impurities, split the non-Kramers degeneracy and exhibit a Janus-faced influence in such systems: they can destroy the very order they seek to probe. Here, we explore this duality in cubic osmate double perovskites which are candidates for exotic d-orbital octupolar order competing with quadrupolar states. Using ab initio computations, Landau theory, and Monte Carlo simulations, we show that Janus impurities induce local strain fields, nucleating quadrupolar puddles and suppressing the octupolar Tc. At the same time, strains mix the non-Kramers doublet with an excited magnetic triplet, creating parasitic dipole moments which directly expose the hidden octupolar order parameter. Our work unravels this Janus duality in recent impurity nuclear magnetic resonance (NMR) experiments, with important implications for uncovering hidden order in diverse multipolar materials.

Orientational Wetting and Topological Transitions in Confined Solutions of Semiflexible Polymers

Despite their considerable practical and biological applications, the link between molecular properties, assembly conditions and self-organized structure in confined polymer solutions remains elusive. Here, we explore the lyotropic nematic ordering of semi-flexible chains in spherical confinement for multiple contour lengths across a wide regime of concentrations. We uncover an original crossover from two distinct quadrupolar states, both characterized by regular tetrahedral patterns of surface topological defects, to either longitudinal, latitudinal or spontaneously-twisted bipolar structures with increasing densities. These transitions, along with the intermediary arrangements that they involve, are attributed to the combination of orientational wetting with subtle variations in their liquid-crystal (LC) elastic anisotropies. Our molecular simulations are corroborated by density functional calculations, and are quantified through the introduction of several order parameters as well as an unsupervised learning scheme for the localization of topological defects. Our results agree quantitatively with the predictions of continuum nematic elasticity theories, and evidence the extent to which the folding of macromolecules and the self-assembly of low-molecular-weight LCs may be guided by the same, universal principles.

Broken-axisymmetry state and magnetic state diagram of spin-1 condensate through the prism of quadrupole degrees of freedom

We theoretically study a weakly interacting gas of spin-1 atoms with Bose–Einstein condensate in external magnetic field within the Bogoliubov approach. To this end, in contrast to previous studies, we employ the general Hamiltonian, which includes both spin and quadrupole exchange interactions as well as the couplings of the spin and quadrupole moment with the external magnetic field (the linear and quadratic Zeeman terms). The latter is responsible for the emergence of the broken-axisymmetry state. We also reexamine ferromagnetic, quadrupolar, and paramagnetic states employing the proposed Hamiltonian. For all magnetic states, we find the relevant thermodynamic characteristics such as magnetization, quadrupole moment, thermodynamic potential. We also obtain three-branch excitation spectrum of the broken-axisymmetry state. We show that this state can be prepared at three different regimes of applied magnetic field. Finally, we present the magnetic state diagrams for each regime of realizing the broken-axisymmetry state.

Small mode volume topological photonic states in one-dimensional lattices with dipole-quadrupole interactions

We study the topological photonic states in one-dimensional lattices analog to the Su-Schrieffer-Heeger model beyond the dipole approximation. The electromagnetic resonances of the lattices supported by near-field interactions between the plasmonic nanoparticles are studied analytically with coupled dipole-quadrupole method. The topological phase transition in the bipartite lattices is determined by the change of Zak phase. Our results reveal the contribution of quadrupole moments to the near-field interactions and the band topology. It is found that the topological edge states in nontrivial lattices have both dipolar and quadrupolar nature. The quadrupolar edge states are not only orthogonal to the dipolar edge states, but also spatially localized at different sublattices. Furthermore, the quadrupolar topological edge states, which coexist at the same energy with the quadrupolar flat band have shorter localization length and hence smaller mode volume than the conventional dipolar edge states. The findings deepen our understanding in topological systems that involve higher-order multipoles, or in analogy to the wave functions in quantum systems with higher-orbital angular momentum, and may be useful in designing topological systems for confining light robustly and enhancing light-matter interactions.

New metamaterial mathematical modeling of acoustic topological insulators via tunable underwater local resonance

This study presents a new type of active underwater local resonance metamaterial mathematical model for topologically protected acoustic wave propagation. The underwater acoustic metamaterial consists of arrays of core cylinders coated with soft shells periodically located in a water environment. An efficient but simple computational model is established to analytically predict the system band behavior. Compared to a system with only Bragg scatters, two double Dirac cones (DDCs) are observed in the dispersion curve due to the local resonance mechanism. The result obtained from numerical analysis shows great consistency with analytical prediction. By tuning structural parameters, the four-fold degeneracy is realized at the center of the irreducible Brillouin zone, i.e., the Γ point. It leads to the generation of two dipolar states and two quadrupolar states. Motivated by the theoretical prediction, locations of the cylinders are tuned and the closing-reopening phenomenon of bandgaps in both higher frequency region and lower region is observed with topologically protected phase transition. Besides, it is found that two frequency domains for topologically protected interface modes (TPIMs) occur. It provides potentials for two passive working frequency ranges without structural reconstruction or active tuning of the system. The effects of temperature on TPIM behavior are also demonstrated. Both working frequencies of TPIMs can be easily tuned to different ranges without influencing the quality of TPIMs. Besides, robustness and defect-immune properties of the topologically protected wave propagation are exhibited. With temperature control, this smart system can be performed as an acoustic metamaterial switch device.

Elastic study of electric quadrupolar correlation in the paramagnetic state of the frustrated quantum magnet Tb2+δTi2−δO7

The electric quadrupolar state in the frustrated quantum magnet ${\mathrm{Tb}}_{2+\ensuremath{\delta}}{\mathrm{Ti}}_{2\ensuremath{-}\ensuremath{\delta}}{\mathrm{O}}_{7}$ has been studied by means of ultrasonic and magnetostriction measurements. A single crystal showed an elastic anomaly around 0.4 K, manifesting a long-range quadrupole ordering. By investigating the anisotropy of the magnetoelastic responses, we found a crossover temperature for the strongly correlated quadrupole state, below which the experimental data of the elastic constant and magnetostriction become qualitatively different from their calculations based on a single-ion model. We suppose that relatively high onset temperature of the quadrupole correlation compared with the transition temperature is ascribed to the geometrical frustration effect, and this correlated state seems to be responsible for the unusual properties in the paramagnetic state of ${\mathrm{Tb}}_{2}{\mathrm{Ti}}_{2}{\mathrm{O}}_{7}$.

Quadrupolar Ultrafast Charge Transfer in Diaminoazobenzene-Bridged Perylenediimide Triads.

Strong push-pull interactions between electron donor, diaminoazobenzene (azo), and an electron acceptor, perylenediimide (PDI), entities in the newly synthesized A-D-A type triads (A=electron acceptor and D=electron donor) and the corresponding A-D dyads are shown to reveal wide-band absorption covering the entire visible spectrum. Electrochemical studies revealed the facile reduction of PDI and relatively easier oxidation of diaminoazobenzene in the dyads and triads. Charge transfer reversal using fluorescence-spectroelectrochemistry wherein the PDI fluorescence recovery upon one-electron oxidation, deterring the charge-transfer interactions, was possible to accomplish. The charge transfer state density difference and the frontier orbitals from the DFT calculations established the electron-deficient PDI to be an electron acceptor and diaminoazobenzene to be an electron donor resulting in energetically closely positioned PDIδ- -Azoδ+ -PDIδ- quadrupolar charge-transfer states in the case of triads and Azoδ+ -PDIδ- dipolar charge-transfer states in the case of dyads. Subsequent femtosecond transient absorption spectral studies unequivocally proved the occurrence of excited-state charge transfer in these dyads and triads in benzonitrile wherein the calculated forward charge transfer rate constants, kf , were limited to instrument response factor, meaning >1012 s-1 revealing the occurrence of ultrafast photo-events. The charge recombination rate constant, kr , was found to depend on the type of donor-acceptor conjugates, that is, it was possible to establish faster kr in the case of triads (∼1011 s-1 ) compared to dyads (∼1010 s-1 ). Modulating both ground and excited-state properties of PDI with the help of strong quadrupolar and dipolar charge transfer and witnessing ultrafast charge transfer events in the studied triads and dyads is borne out from the present study.

Excited-State Symmetry Breaking in a Multiple Multipolar Chromophore Probed by Single-Molecule Fluorescence Imaging and Spectroscopy.

Excited-state symmetry breaking (ESB) has attracted much attention because it is often observed in symmetric multipolar chromophores designed as two-photon absorption/emission materials. Herein, we report an ensemble and single-molecule fluorescence imaging and spectroscopy investigation of ESB in hexakis[4-(p-dioctylaminostyryl)phenylethynyl]benzene(DB6), a two-photon absorber possessing a C6-symmetric π-D6 structure (π = hexaethynylbenzene, D = (p-dioctylaminostyryl)phenyl group) consisting of three equivalent D-π-D moieties. Ensemble and single-molecule measurements and theoretical calculations revealed that DB6 undergoes a photoabsorption process with two orthogonal transition dipole moments, whereas it fluoresces with a single transition dipole moment after one- or two-step ESB upon photoexcitation, depending on the environmental polarity. In nonpolar solvents and polymer films, one of the three D-π-D sites becomes planar, and the excited state is localized on this moiety: a [Dδ+-πδ--Dδ+]* quadrupolar state is formed. In polar solvents, the symmetry is further broken within the planarized D-π-D moiety, and the excited state is localized on one of the two D-π sites; i.e., a D-[πδ--Dδ+]* dipolar state is generated. Hence, DB6 can behave like a multichromophore with multiple emission sites in the molecule, which was demonstrated by stepwise photobleaching under photon antibunching conditions.

Ultrafast Nonradiative Decay of a Dipolar Plasmon-like State in Naphthalene.

Motivated by the uncertainty in our understanding of ultrafast plasmon decay mechanisms, we examine the effect of nuclear vibrations on the dynamical behavior of the strong plasmon-like dipole response of naphthalene, known as the β peak. The real-time time-dependent density functional (RT-TDDFT) method coupled with Ehrenfest molecular dynamics is used to describe the interconnected nuclear and electronic motion. Several vibrational modes promote drastic plasmon decay in naphthalene. The most astonishing finding of this study is that activation of one particular vibrational mode (corresponding to the B1u representation in D2h point group symmetry) leads to a continuous drop of the dipole response corresponding to the β peak into a totally symmetric, dark, quadrupolar electronic state. A second B1u mode provokes the sharp plasmon-like peak to split due to the breaking of structural symmetry. Nonadiabatic coupling between a B2g vibrational mode and the β peak (a B1u electronic state) gives rise to a B3u vibronic state, which can be identified as one of the p-band peaks that reside close in energy to the β peak energy. Overall, strong nonadiabatic coupling initiates plasmon decay into nearby electronic states in acenes, most importantly into dark states. These findings expand our knowledge about possible plasmon decay processes and pave the way for achieving high optical performance in acene-based materials such as graphene.

Metastability, tetragonality and quadrupolar glass states in cubic stabilized zirconia

AbstractFor cubic lime‐stabilized and yttria‐stabilized zirconia ceramic alloys the temperatures at which the onset of metastability and a sharp reduction in ionic conductivity occur are observed to coincide, appearing at approximately 1000°C and 650°C respectively. This behavior is attributed to the development of quadrupolar (orientational) glass states in each alloy below its transition temperature. We suggest that several other unexplained phenomena including tetragonal distortion in these cubic phases may also be understood by reference to the alloys' crystalline structures, which differ slightly. At equilibrium, each possesses a random two‐component crystalline constitution, one component of which is a low‐symmetry quadrupole intergrown with the other and capable of switching its unique axis in a small number of different directions. The quadrupoles interact, thereby imparting a disordered stress on the other component in the lattice. Such a structure is identifiable as a quadrupolar glass, the elastic analog of a spin glass.

Quadrupolar Cyclopenta[Hi]Aceanthrylene-Based Electron Donor-Acceptor-Donor Conjugates: Charge Transfer Versuscharge Separation

Cyclopenta[hi]aceanthrylene (CPA) has been functionalized at two of its positions with electronically-inert trimethylsilylethynyl (1), as well as electron donating 4-ethynyl-N,N-dimethylaniline (2), ethynyl Zn(II)phthalocyanine (3), and ethynyl Zn(II)porphyrin (4) units. Consistent with X-ray crystal structures of 2 and 4, analyses of absorption and fluorescence of 2-4 prompt to strong electronic communication between CPA and the peripheral units, affording quadrupolar electron donor-acceptor-donor charge transfer conjugates. By virtue of their quadrupolar/dipolar charge transfer characters in the excited state, 2-4 exhibit fluorosolvatochromism. Transient absorption spectroscopy confirmed delocalized quadrupolar ground states and formation of weakly solvent stabilized quadrupolar singlet excited states. The latter transform into strongly stabilized dipolar excited states before deactivating to the ground state in 2 and give rise to a fully charge separated state in 3 and 4.

Kagome model for a Z2 quantum spin liquid

We present a study of a simple model antiferromagnet consisting of a sum of nearest neighbor SO($N$) singlet projectors on the Kagome lattice. Our model shares some features with the popular $S=1/2$ Kagome antiferromagnet but is specifically designed to be free of the sign-problem of quantum Monte Carlo. In our numerical analysis, we find as a function of $N$ a quadrupolar magnetic state and a wide range of a quantum spin liquid. A solvable large-$N$ generalization suggests that the quantum spin liquid in our original model is a gapped ${\mathbb Z}_2$ topological phase. Supporting this assertion, a numerical study of the entanglement entropy in the sign free model shows a quantized topological contribution.

The origin of parity changes in the solar cycle

ABSTRACT Although sunspots have been systematically observed on the Sun’s surface over the last four centuries, their magnetic properties have been revealed and documented only since the early 1900s. Sunspots typically appear in pairs of opposite magnetic polarities which have a systematic orientation. This polarity orientation is opposite across the equator – a trend that has persisted over the last century. Taken together with the configuration of the global poloidal field of the Sun – this phenomena is consistent with the dipolar parity state of an underlying magnetohydrodynamic dynamo. Although transient hemispheric asymmetry in sunspot emergence is observed, a global parity shift has never been observed. We simulate hemispheric asymmetry through introduction of random fluctuations in a computational dynamo model of the solar cycle and demonstrate that changes in parity are indeed possible in long-term simulations covering thousands of years. Quadrupolar modes are found to exist over significant fraction of the simulated time. In particular, we find that a parity shift in the underlying nature of the sunspot cycle is more likely to occur when sunspot activity dominates in any one hemisphere for a time which is significantly longer than the cycle period. We establish causal pathways connecting hemispheric asymmetry to parity flips mediated via a decoupling of the dynamo cycle period across the two solar hemispheres. Our findings indicate that the solar cycle may have resided in quadrupolar parity states in the past, and provides a possible pathway for predicting parity flips in the future.

Quadrupolar Cyclopenta[hi]aceanthrylene-Based Electron Donor-Acceptor-Donor Conjugates: Charge Transfer versus Charge Separation.

Cyclopenta[hi]aceanthrylenes (CPAs) have been functionalized at two of the peripheral positions with electronically inert trimethylsilylethynyl (1), as well as with electron-donating 4-ethynyl-N,N-dimethylaniline (2), ethynyl ZnII phthalocyanine (3), and ethynyl ZnII porphyrin (4) units. Consistent with X-ray crystal structures of 2 and 4, analyses of absorption and fluorescence of 2-4 point to strong electronic communication between the CPA and the peripheral units, affording quadrupolar electron donor-acceptor-donor charge-transfer conjugates. By virtue of their quadrupolar/dipolar charge-transfer characters in the excited state, 2-4 exhibit fluoro-solvatochromism. Transient absorption spectroscopy confirmed delocalized quadrupolar ground states and formation of weakly solvent stabilized quadrupolar singlet excited states. The latter transform into strongly stabilized dipolar excited states before deactivating to the ground state in 2 and give rise to a fully charge separated state in 3 and 4.

Quadrupolar Cyclopenta[hi]aceanthrylene‐Based Electron Donor‐Acceptor‐Donor Conjugates: Charge Transfer versus Charge Separation

AbstractCyclopenta[hi]aceanthrylenes (CPAs) have been functionalized at two of the peripheral positions with electronically inert trimethylsilylethynyl (1), as well as with electron‐donating 4‐ethynyl‐N,N‐dimethylaniline (2), ethynyl ZnIIphthalocyanine (3), and ethynyl ZnIIporphyrin (4) units. Consistent with X‐ray crystal structures of 2 and 4, analyses of absorption and fluorescence of 2–4 point to strong electronic communication between the CPA and the peripheral units, affording quadrupolar electron donor‐acceptor‐donor charge‐transfer conjugates. By virtue of their quadrupolar/dipolar charge‐transfer characters in the excited state, 2–4 exhibit fluoro‐solvatochromism. Transient absorption spectroscopy confirmed delocalized quadrupolar ground states and formation of weakly solvent stabilized quadrupolar singlet excited states. The latter transform into strongly stabilized dipolar excited states before deactivating to the ground state in 2 and give rise to a fully charge separated state in 3 and 4.

Landau theory of multipolar orders in Pr(Y)2X20 Kondo materials ( Y=Ti , V, Rh, Ir; X=Al , Zn)

A series of Pr(TM)$_2$X$_{20}$ (with TM=Ti,V,Rh,Ir and X=Al,Zn) Kondo materials, containing non-Kramers Pr$^{3+}$ $4f^2$ moments on a diamond lattice, have been shown to exhibit intertwined orders such as quadrupolar order and superconductivity. Motivated by these experiments, we propose and study a Landau theory of multipolar order to capture the phase diagram and its field dependence. In zero magnetic field, we show that different quadrupolar states, or the coexistence of quadrupolar and octupolar orderings, may lead to ground states with multiple broken symmetries. Upon heating, such states may undergo two-step thermal transitions into the symmetric paramagnetic phase, with partial restoration of broken symmetries in the intervening phase. For nonzero magnetic field, we show the evolution of these thermal phase transitions strongly depends on the field direction, due to clock anisotropy terms in the free energy. Our findings shed substantial light on experimental results in the Pr(TM)$_2$Al$_{20}$ materials. We propose further experimental tests to distinguish purely quadrupolar orders from coexisting quadrupolar-octupolar orders.

Impacts of Environmental Rigidity on Photophysical Characteristics and Behaviors of a Quadrupolar Chromophore Revealed by Single-Molecule Fluorescence Spectroscopic Study

Multipolar chromophores (e.g., quadrupolar and octupolar molecules) have excellent two-photon absorption properties and exhibit characteristic excited-state relaxation behaviors that involve structural symmetry breaking. Environmental rigidity could provide an appreciable impact on such conformational rearrangement in the excited state; however, details of its effect remain unclear. Herein, we undertake an ensemble and single-molecule spectroscopic investigation into the effects of environmental rigidity on the photophysical characteristics and behaviors of a newly synthesized D−π–A−π–D (donor−π–acceptor−π–donor) quadrupolar chromophore, QC, and its π–A−π analogue, AC, in various solutions and polymers. The fluorescence emission of QC in nonpolar solvents takes place in the symmetric quadrupolar state [Dδ+–π–Aδ−–π–Dδ+]*, whereas the significant fluorescence quenching is observed with increasing solvent polarity, suggesting the gradual stabilization of the nonemissive symmetry-broken dipolar state [Dδ+–π–A...

Light-Forbidden Transitions in Plasmon-Emitter Interactions beyond the Weak Coupling Regime

We investigate the impact of light-forbidden exciton transitions in plasmon-emitter interactions beyond the weak coupling regime. We consider a V-type quantum emitter, with dipolar and quadrupolar excited states, placed at the subnanometric gap of a particle-on-a-mirror metallic cavity. We present a fully analytical description of the near-field population dynamics and far-field scattering spectrum of the hybrid system. Our approach enables us to reveal two realistic system configurations in which the dipole-inactive exciton alters significantly and in completely opposite ways the Purcell enhancement and Rabi splitting phenomenology, effectively enlarging or reducing the emitter lifetime and generating or removing spectral features in the cavity cross section.

Differential Rotation in Solar-like Convective Envelopes: Influence of Overshoot and Magnetism

Abstract We present a set of four global Eulerian/semi-Lagrangian fluid solver (EULAG) hydrodynamical (HD) and magnetohydrodynamical (MHD) simulations of solar convection, two of which are restricted to the nominal convection zone, and the other two include an underlying stably stratified fluid layer. While all four simulations generate reasonably solar-like latitudinal differential rotation profiles where the equatorial region rotates faster than the polar regions, the rotational isocontours vary significantly among them. In particular, the purely HD simulation with a stable layer alone can break the Taylor–Proudman theorem and produce approximately radially oriented rotational isocontours at medium to high latitudes. We trace this effect to the buildup of a significant latitudinal temperature gradient in the stable fluid immediately beneath the convection zone, which imprints itself on the lower convection zone. It develops naturally in our simulations as a consequence of convective overshoot and rotational influence of rotation on convective energy fluxes. This favors the establishment of a thermal wind balance that allows evading the Taylor–Proudman constraint. A much smaller latitudinal temperature gradient develops in the companion MHD simulation that includes a stable fluid layer, reflecting the tapering of deep convective overshoot that occurs at medium to high latitudes, which is caused by the strong magnetic fields that accumulate across the base of the convection zone. The stable fluid layer also has a profound impact on the large-scale magnetic cycles developing in the two MHD simulations. Even though both simulations operate in the same convective parameter regime, the simulation that includes a stable layer eventually loses cyclicity and transits to a non-solar, steady quadrupolar state.

Experimental verification of acoustic pseudospin multipoles in a symmetry-broken snowflakelike topological insulator

Topologically protected wave engineering in artificially structured media resides at the frontier of ongoing metamaterials research, which is inspired by quantum mechanics. Acoustic analogs of electronic topological insulators have recently led to a wealth of new opportunities in manipulating sound propagation by means of robust edge mode excitations through analogies drawn to exotic quantum states. A variety of artificial acoustic systems hosting topological edge states have been proposed analogous to the quantum Hall effect, topological insulators, and Floquet topological insulators in electronic systems. However, those systems were characterized by a fixed geometry and a very narrow frequency response, which severely hinders the exploration and design of useful applications. Here we establish acoustic multipolar pseudospin states as an engineering degree of freedom in time-reversal invariant flow-free phononic crystals and develop reconfigurable topological insulators through rotation of their meta-atoms and reshaping of the metamolecules. Specifically, we show how rotation forms man-made snowflakelike molecules, whose topological phase mimics pseudospin-down (pseudospin-up) dipolar and quadrupolar states, which are responsible for a plethora of robust edge confined properties and topological controlled refraction disobeying Snell's law.