Multiple-scattering Formalism Research Articles

Octahedral Tilting in Homologous Perovskite Series CaMoO3-SrMoO3-BaMoO3 Probed by Temperature-Dependent EXAFS Spectroscopy

Local distortions in perovskites can be induced by cation displacements and/or by the tilting and rotating of cation-anion octahedra. Both phenomena have been subject to intense investigations over many years. However, there are still controversies in the results obtained from experimental techniques that are sensitive to long-range order (X-ray, neutron, or electron diffraction) and those sensitive to short-range order (X-ray absorption spectroscopy). In this study, we probed the details of the local environment in AMoO3 perovskites (A = Ca, Sr, Ba) using extended X-ray absorption fine structure (EXAFS) in a wide temperature range (10-300 K). An advanced analysis of the EXAFS spectra within the multiple-scattering formalism using the reverse Monte Carlo method enhanced by an evolutionary algorithm allowed us (i) to extract detailed information on metal-oxygen and metal-metal radial distribution functions, and metal-oxygen-metal and oxygen-metal-oxygen bond angle distribution functions, and (ii) to perform polyhedral analysis. The obtained results demonstrate the strong sensitivity of the EXAFS spectra to the tilting of [MoO6] octahedra induced by the differences in the sizes of alkaline earth metal cations (Ca2+, Sr2+, and Ba2+).

Quantifying the breakdown of the rotating-wave approximation in single-photon superradiance

We study quantitatively the breakdown of the rotating-wave approximation (RWA) when calculating collective light emission by quantum emitters, in particular in the weak-excitation limit. Our starting point is a known multiple-scattering formalism where the full light–matter interaction leads to induced inter-emitter interactions described by the classical Green function of inhomogeneous dielectric media. When making the RWA in the light–matter interaction, however, these induced interactions differ from the classical Green function, and for free space we find a reduction of the interatomic interaction strength by up to a factor of two. By contrast, for the corresponding scalar model the relative RWA error for the inter-emitter interaction even diverges in the near field. For two identical emitters, the errors due to the RWA in collective light emission will show up in the emission spectrum, but not in the sub- and superradiant decay rates. In case of two non-identical emitters, also the collective emission rates will differ by making the RWA. For three or more identical emitters, the RWA errors in the interatomic interaction in general affect both the collective emission spectra and the collective decay rates. Ring configurations with discrete rotational symmetry are an interesting exception. Interestingly, the maximal errors in the collective decay rates due to making the RWA occur for finite emitter separations.

Multiple-scattering approach for multi-spin chiral magnetic interactions: application to the one- and two-dimensional Rashba electron gas

Various multi-spin magnetic exchange interactions (MEI) of chiral nature have been recently unveiled. Owing to their potential impact on the realisation of twisted spin-textures, their future implication in spintronics or quantum computing is very promising. Here, I address the long-range behavior of multi-spin MEI on the basis of a multiple-scattering formalism implementable in Green functions based methods such as the Korringa–Kohn–Rostoker (KKR) Green function framework. I consider the impact of spin–orbit coupling (SOC) as described in the one- (1D) and two-dimensional (2D) Rashba model, from which the analytical forms of the four- and six-spin interactions are extracted and compared to the well known bilinear isotropic, anisotropic and Dzyaloshinskii–Moriya interactions (DMI). Similarly to the DMI between two sites i and j, there is a four-spin chiral vector perpendicular to the bond connecting the two sites. The oscillatory behavior of the MEI and their decay as function of interatomic distances are analysed and quantified for the Rashba surfaces states characterizing Au surfaces. The interplay of beating effects and strength of SOC gives rise to a wide parameter space where chiral MEI are more prominent than the isotropic ones. The multi-spin interactions for a plaquette of N magnetic moments decay like simplifying to for equidistant atoms, where d is the dimension of the mediating electrons, qF the Fermi wave vector, L the perimeter of the plaquette while P is the product of interatomic distances. This recovers the behavior of the bilinear MEI, , and shows that increasing the perimeter of the plaquette weakens the MEI. More important, the power-law pertaining to the distance-dependent 1D MEI is insensitive to the number of atoms in the plaquette in contrast to the linear dependence associated with the 2D MEI. Furthermore, the N-dependence of qF offers the possibility of tuning the interactions amplitude by engineering the electronic occupation.

Strong electromagnetic coupling in dimers of topological-insulator nanoparticles and quantum emitters

In this work, we theoretically investigate the optical properties of a topological-insulator nanoparticle--quantum emitter dimer interacting in the strong-coupling regime. The calculations are based on a recently developed semianalytical technique based on a multiple-scattering polaritonic-operator formalism in conjunction with an electromagnetic coupled dipole method. We calculate the light spectrum of the above dimer and report the emergence of a mode that stems from the coupling of the surface topological particle polariton of the topological insulator with the resonance state of the quantum emitter.

Systematics of plexciton formation in linear chains of quantum emitters and metal nanoparticles

We present systematic numerical calculations of plexcitonic properties of a linear chain comprised of quantum emitters - metal nanoparticle dimers interacting in the strong coupling regime. The calculations are based on a recently developed semi-analytical technique based on a multiple-scattering polaritonic-operator formalism in conjunction with an electromagnetic coupled dipole method. Based on this method, we calculate the two main features corresponding to the formation of plexcitonic chain modes: the primary plexcitonic resonance as well as the corresponding Rabi splitting associated with the generation of an avoided-crossing area. We apply an exponential model to the numerical results obtained via the above technique to describe the plexciton redshift induced with increasing chain length. We also identify an asymptotic plexciton frequency at a chain length of approximately 20 dimers. A model Hamiltonian is employed to assess the energy splitting defined by the avoided crossing area of the main plexciton resonance which is found to scale as where N is the number of dimers in the chain.

Charge polarization near dielectric interfaces and the multiple-scattering formalism.

Interfacial charge polarization is ubiquitous in systems with sharp dielectric contrast. Fully resolving the interfacial charges often relies on demanding numerical algorithms to solve the boundary value problem. The recent development of an analytical multiple-scattering formalism to solve the interfacial charge polarization problem for particles carrying monopolar, dipolar, and multipolar charges is reviewed. Every term produced in this formalism has a simple interpretation, and terms for spherical particles can be rapidly evaluated using an image-line construction. Several practical applications of this formalism are illustrated. A dielectric virial expansion for polarizable particles based on this formalism is also described. The origins of singular polarization charges for particles in close contact are explained and evaluated for both dielectric and conducting spheres.

A multiple-scattering polaritonic-operator method for hybrid arrays of metal nanoparticles and quantum emitters

We present a new technique for the study of hybrid collections of quantum emitters (atoms, molecules, quantum dots) with nanoparticles. The technique is based on a multiple-scattering polaritonic-operator formalism in conjunction with an electromagnetic coupled dipole method. Apart from collections of quantum emitters and nanoparticles, the method can equally treat the interaction of a collection of quantum emitters with a single nano-object of arbitrary shape in which case the nano-object is treated as a finite three-dimensional lattice of point scatterers. We have applied our method to the case of linear array (chain) of dimers of quantum emitters and metallic nanoparticles wherein the corresponding (geometrical and physical) parameters of the dimers are chosen so as the interaction between the emitter and the nanoparticle lies in the strong-coupling regime in order to enable the formation of plexciton states in the dimer. In particular, for a linear chain of dimers, we show that the corresponding light spectra reveal a multitude of plexciton modes resulting from the hybridization of the plexciton resonances of each individual dimer in a manner similar to the tight-binding description of electrons in solids.

Optical transmission theory for metal-insulator-metal periodic nanostructures

Abstract A semi-analytical formalism for the optical properties of a metal-insulator-metal periodic nanostructure using coupled-mode theory is presented. This structure consists in a dielectric layer in between two metallic layers with periodic one-dimensional nanoslit corrugation. The model is developed using multiple-scattering formalism, which defines transmission and reflection coefficients for each of the interface as a semi-infinite medium. Total transmission is then calculated using a summation of the multiple paths of light inside the structure. This method allows finding an exact solution for the transmission problem in every dimension regime, as long as a sufficient number of diffraction orders and guided modes are considered for the structure. The resonant modes of the structure are found to be related to the metallic slab only and to a combination of both the metallic slab and dielectric layer. This model also allows describing the resonant behavior of the system in the limit of a small dielectric layer, for which discontinuities in the dispersion curves are found. These discontinuities result from the out-of-phase interference of the different diffraction orders of the system, which account for field interaction for both inner interfaces of the structure.

First Principles Calculations of Palladium Nanoparticle XANES Spectra

X-ray absorption spectroscopy is a common technique for in situ studies of catalysts. The interpretation of the near edge structure is, however, often hampered by lack of information of how structural and electronic contributions affect the spectra. Here, first principles calculations were used to explore effects of particle size, structural motif and oxidation state on the X-ray absorption near edge structure (XANES) for palladium nanoparticles (PdNP). A range of PdNP were structurally optimized within the density function theory and Pd K edge XANES spectra were calculated using the real-space multiple-scattering formalism. The results show that the Pd-Pd distances are compressed for small NP which yields shifts in the XANES peak positions as compared to bulk Pd. Moreover, the amplitude of the fine structure oscillations is found to increase with the average coordination number. The spectra are only to a minor extent influenced by the structural motif of the PdNP. Oxidation of the Pd surface increases the intensity in the XANES spectrum between the first and the second absorption feature, which correspond to the initial development of a whiteline peak. It is found that a strong whiteline peak only is developed for Pd-atoms with complete oxidation, which corresponds to coordination to four oxygen atoms.

Real-space multiple-scattering Hubbard model calculations for d- and f-state materials.

Calculations are presented of the electronic structure and X-ray spectra of materials with correlated d- and f-electron states based on the Hubbard model, a real-space multiple-scattering formalism and a rotationally invariant local density approximation. Values of the Hubbard parameter are calculated ab initio using the constrained random-phase approximation. The combination of the real-space Green's function with Hubbard model corrections provides an efficient approach to describe localized correlated electron states in these systems, and their effect on core-level X-ray spectra. Results are presented for the projected density of states and X-ray absorption spectra for transition metal- and lanthanide-oxides. Results are found to be in good agreement with experiment.

Three-body effects in Casimir-Polder repulsion

In this paper we study an archetypical scenario in which repulsive Casimir-Polder forces between an atom or molecule and two macroscopic bodies can be achieved. This is an extension of previous studies of the interaction between a polarizable atom and a wedge, in which repulsion occurs if the atom is sufficiently anisotropic and close enough to the symmetry plane of the wedge. A similar repulsion occurs if such an atom passes a thin cylinder or a wire. An obvious extension is to compute the interaction between such an atom and two facing wedges, which includes as a special case the interaction of an atom with a conducting screen possessing a slit, or between two parallel wires. To this end we further extend the electromagnetic multiple-scattering formalism for three-body interactions. To test this machinery we reinvestigate the interaction of a polarizable atom between two parallel conducting plates. In that case, three-body effects are shown to be small and are dominated by three- and four-scattering terms. The atom-wedge calculation is illustrated by an analogous scalar situation, described in the Appendix. The wedge-wedge-atom geometry is difficult to analyze because this is a scale-free problem. However, it is not so hard to investigate the three-body corrections to the interaction between an anisotropic atom or nanoparticle and a pair of parallel conducting cylinders and show that the three-body effects are very small and do not affect the Casimir-Polder repulsion at large distances between the cylinders. Finally, we consider whether such highly anisotropic atoms needed for repulsion are practically realizable. Since this appears rather difficult to accomplish, it may be more feasible to observe such effects with highly anisotropic nanoparticles.

On the theory of the optical Bloch oscillations

The light Bloch oscillations in the array of optical waveguides are investigated based on the electrodynamics of continual approach. The array possesses a step-like refractive index profile. Usually, these oscillations are described in a phenomenological manner. However, the parameters entering the phenomenological equations are obtained either from additional numerical simulations or from experiments. The approach proposed here is based on multiple-scattering formalism. This approach allows us to justify the phenomenological description. The phenomenological approach is valid only if the interaction between the waveguides is weak and the nearest neighbor approximation is applicable. To describe the path of light, we calculate the local isofrequency curve. It is shown that the path represents Bloch oscillations. The results obtained are found to correlate with the experiments available.

Highly Sensitive Plasmonic Sensor Based on Fano Resonance from Silver Nanoparticle Heterodimer Array on a Thin Silver Film

We investigate the optical spectrum of a multilayer metallic slab using multiple-scattering formalism. A thin silver film is attached to a periodic array of heterodimers consisting of two vertically spaced silver nanoparticles of different radii. Depending on the radius of nanoparticles, heterodimer array presents a simple nanoscale geometry which gives rise to remarkable plasmonic properties of multipolar resonances. Due to the coherent interference of the localized nanoparticle plasmons (discrete mode) and surface plasmon polaritons of metallic film (continuous mode), the reflection spectrum represents a sharp asymmetric Fano resonance dip, which is strongly sensitive to the refractive index of the surrounding embedded dielectric host. The physical features contribute to a highly efficient plasmonic sensor for refractive index sensing with sensitivity of ∼1.5 × 10−3 RIU/nm.

Spin relaxation and the Elliott-Yafet parameter in W(001) ultrathin films: Surface states, anisotropy, and oscillation effects

Using first-principles methods based on density-functional theory we investigate the spin relaxation in W(001) ultrathin films. Within the framework of the Elliott-Yafet theory we calculate the spin mixing of the Bloch states and we explicitly consider spin-flip scattering off self-adatoms. We find an oscillatory behavior of the spin-mixing parameter and relaxation rate as a function of the film thickness, which we trace back tosurface-state properties. We also analyze the Rashba effect experienced by the surface states and discuss its influence on the spin relaxation. Finally we calculate the anisotropy of the spin-relaxation rate with respect to the polarization direction of the excited spin population relative to the crystallographic axes of thefilm. We find that the spin-relaxation rate can increase by as much as 47% when the spin polarization is directed out of plane, compared to the case when it is in plane. Our calculations are based on the multiple-scattering formalism of the Korringa-Kohn-Rostoker Green-function method.

Plasmonic coupling from silver nanoparticle dimer array mediating surface plasmon resonant enhancement on the thin silver film

We investigate the optical absorption spectrum of a periodic array of silver nanoparticle dimer on a thin silver film using multiple-scattering formalism. Surface plasmon polariton mediated from silver nanoparticle dimer array is excited and enhanced by about four times compared with that from monomer array. This enhancement results from the coupling between the two nanoparticles’ plasmons of symmetry mode and anti-symmetry mode. We also illustrate the distance-dependent nanoparticle plasmonic coupling modes based on the polarized charge distribution in dimer geometry. The proposed silver nanoparticle dimer array can be used to enhance surface spectroscopy.

Multiple-scattering model for the coherent reflection and transmission of light from a disordered monolayer of particles

Using a multiple-scattering formalism, we derive closed-form expressions for the coherent reflection and transmission coefficients of monochromatic electromagnetic plane waves incident upon a two-dimensional array of randomly located spherical particles. The calculation is performed within the quasi-crystalline approximation, and the statistical correlation among the particles is assumed to be given simply by a correlation hole. In the resulting model, the size of the spheres and the angle of incidence are both unrestricted. The final formulas are relatively simple, making the model suitable for a straightforward interpretation of optical-sensing measurements.

Characterization of lattice defects by x-ray absorption spectroscopy at the Zn K-edge in ferromagnetic, pure ZnO films

Ferromagnetic, pure ZnO films were grown on Al2O3 substrates at various nitrogen pressures (0.01–1.0 mbar) and investigated with x-ray diffraction (XRD) and x-ray absorption spectroscopy. According to XRD data, the crystalline films were composed of crystallites of approximately 50 nm in size, oriented with respect to the substrates, and the lattice spacings show slight deviations with respect to single-crystalline ZnO of wurtzite structure. The parameters determined by XRD agree with those determined by extended x-ray absorption fine structure, except for the sample grown at the lowest N2 pressure of 0.01 mbar, which was attributed to deviations from the ZnO single crystals. The results for the ZnO films grown at 0.1 to 1.0 mbar partial N2 pressure indicate wurtzite unit cells compressed along the c axis. The x-ray absorption near-edge structure (XANES) spectra exhibited a strong dependence on the x-ray polarization and on nitrogen partial pressure, which was explained by the increase in the concentration of defects with nitrogen partial pressure and by interface or grain boundary effects. First-principles calculations using multiple-scattering formalism suggested that the XANES spectra changes were because of increasing Zn vacancy concentration with increasing nitrogen pressure. The results indicated that Zn vacancy defects play a significant role in the ferromagnetism of these films.

Real-space Green’s function approach to resonant inelastic x-ray scattering

We present an ab initio theory of core and valence resonant inelastic x-ray scattering (RIXS) based on a real-space multiple-scattering Green's function formalism and a quasiboson model Hamiltonian. Simplifying assumptions are made that lead to an approximation of the RIXS spectrum in terms of a convolution of an effective x-ray absorption signal with the x-ray emission cross section. Additional many-body corrections are incorporated in terms of an effective energy-dependent spectral function. Example calculations of RIXS are found to give qualitative agreement with experimental data. Our approach also yields simulations of lifetime-broadening suppressed x-ray absorption, as observed in high-energy resolution fluorescence detection experiment. Finally, possible improvements to our approach are briefly discussed.

Casimir energy, dispersion, and the Lifshitz formula

Despite suggestions to the contrary, we show in this paper that the usual dispersive form of the electromagnetic energy must be used to derive the Lifshitz force between parallel dielectric media. This conclusion follows from the general form of the quantum vacuum energy, which is the basis of the multiple-scattering formalism. As an illustration, we explicitly derive the Lifshitz formula for the interaction between parallel dielectric semispaces, including dispersion, starting from the expression for the total energy of the system. The issues of constancy of the energy between parallel plates and of the observability of electrostrictive forces are briefly addressed.

Casimir effect for a semitransparent wedge and an annular piston

We consider the Casimir energy due to a massless scalar field in a geometry of an infinite wedge closed by a Dirichlet circular cylinder, where the wedge is formed by $\delta$-function potentials, so-called semitransparent boundaries. A finite expression for the Casimir energy corresponding to the arc and the presence of both semitransparent potentials is obtained, from which the torque on the sidewalls can be derived. The most interesting part of the calculation is the nontrivial nature of the angular mode functions. Numerical results are obtained which are closely analogous to those recently found for a magnetodielectric wedge, with the same speed of light on both sides of the wedge boundaries. Alternative methods are developed for annular regions with radial semitransparent potentials, based on reduced Green's functions for the angular dependence, which allows calculations using the multiple-scattering formalism. Numerical results corresponding to the torque on the radial plates are likewise computed, which generalize those for the wedge geometry. Generally useful formulas for calculating Casimir energies in separable geometries are derived.