Scattering from topological insulator circular cylinder buried in a semi-infinite medium

The problem of electromagnetic scattering of a plane wave from a topological insulator (TI) cylinder buried beneath a flat interface is undertaken with the method of analysis based on spectral plane wave representation of fields. Saddle point method is employed to evaluate the involved spectral integrals serving as basis functions in the representations of scattered-reflected and scattered-transmitted fields. The distinctions between the scattering pattern for time reversal symmetry TI cylinder and that of time reversal symmetry broken TI cylinder are pronounced. Results are validated through the comparison with the previously available results.     

Engineering Dirac electrons emergent on the surface of a topological insulator

Abstract

The concept of the topological insulator (TI) has introduced a new point of view to condensed-matter physics, relating a priori unrelated subfields such as quantum (spin, anomalous) Hall effects, spin–orbit coupled materials, some classes of nodal superconductors, superfluid ³He, etc. From a technological point of view, TIs are expected to serve as platforms for realizing dissipationless transport in a non-superconducting context. The TI exhibits a gapless surface state with a characteristic conic dispersion (a surface Dirac cone). Here, we review peculiar finite-size effects applicable to such surface states in TI nanostructures. We highlight the specific electronic properties of TI nanowires and nanoparticles, and in this context we contrast the cases of weak and strong TIs. We study the robustness of the surface and the bulk of TIs against disorder, addressing the physics of Dirac and Weyl semimetals as a new research perspective in the field.     

Engineering Dirac electrons emergent on the surface of a topological insulator

The concept of the topological insulator (TI) has introduced a new point of view to condensed-matter physics, relating a priori unrelated subfields such as quantum (spin, anomalous) Hall effects, spin–orbit coupled materials, some classes of nodal superconductors, superfluid ³He, etc. From a technological point of view, TIs are expected to serve as platforms for realizing dissipationless transport in a non-superconducting context. The TI exhibits a gapless surface state with a characteristic conic dispersion (a surface Dirac cone). Here, we review peculiar finite-size effects applicable to such surface states in TI nanostructures. We highlight the specific electronic properties of TI nanowires and nanoparticles, and in this context we contrast the cases of weak and strong TIs. We study the robustness of the surface and the bulk of TIs against disorder, addressing the physics of Dirac and Weyl semimetals as a new research perspective in the field.     

Scattering of electromagnetic spherical waves by a buried spheroidal perfect conductor

We examine the electromagnetic scattering of spherical waves by a buried spheroidal perfect conductor. The proposed analysis is based on the integral equation formalism of the problem and focuses on the establishment of a multiparametric model describing analytically the scattering process under consideration. Both the theoretical and the numerical treatment are presented. The outcome of the analysis is the determination of the scattered field in the observation environment along with its multivariable on several physical and geometric parameters of the system.     

Scattering of s-polarized electromagnetic plane waves from a film with a shallow random rough surface on a perfect conductor

Scattering of s-polarized electromagnetic planes waves from a film, with a shallow random rough one-dimensional surface, bounded by vacuum and a perfect conductor is calculated. An integral equation that relates the amplitude of the scattered field to the incident wave is found by use of the Rayleigh hypothesis. The integral equation is solved numerically and by use of the perturbation theory, up to the fourth order in the surface profile function. In the angular dependence of the incoherent part of the differential reflection coefficient, the backscattering peak and two additional satellite peaks are observed, owing to two guided waves supported by the film. Analysis of the perturbation solution reveals that the background scattering exhibits minima and maxima as functions of the thickness. By studying the behavior of the scattering as a function of the absorption index of the film, it is shown that the amplitudes of the peaks are low when k ~ 10(-2) and high when k ~ 10(-4).     

Low-frequency scattering from perfectly conducting spheroidal bodies in a conductive medium with magnetic dipole excitation

Inductive electromagnetic means that are currently employed in the exploration of the Earth’s subsurface and embedded voluminous bodies often call for an intensive use, primary at the modeling stage and later on at the inversion stage, of analytically demanding tools of field calculation. Under the aim of modeling implementation, this contribution is concerned with some interesting aspects of the low-frequency interaction of arbitrarily orientated (i.e. three-dimensional) time-harmonic magnetic dipoles, with 3-D perfectly conducting spheroidal bodies embedded in an otherwise homogeneous conductive medium. For many practical applications involving buried obstacles such as Earth’s subsurface electromagnetic probing at low-frequency or any other physical cases (e.g. geoelectromagnetics), non-axisymmetric spheroidal geometry approximates sufficiently such kind of metallic shapes. On the other hand, our analytical approach deals with prolate spheroids, since the corresponding results for the oblate spheroidal geometry can be readily obtained through a simple transformation. The particular physical model concerns a solid impenetrable (metallic) body under a magnetic dipole excitation, where the scattering boundary value problem is attacked via rigorous low-frequency expansions for the incident, scattered and total electric and magnetic fields in terms of positive integral powers of (ik), that is (ik)ⁿ for n ? 0, where k stands for the complex wavenumber of the exterior medium. The purpose of the modeling is to contribute to a simple yet versatile tool to infer information on an unknown body from measurements of the three-component electric and magnetic fields nearby. Our goal is to obtain the most important terms of the low-frequency expansions of the electromagnetic fields, that is the static (for n = 0) and the dynamic (n = 1, 2, 3) terms. In particular, for n = 1 there are no incident fields and thus no scattered ones, while for n = 0 the Rayleigh electromagnetic expression is easily obtained in terms of infinite series. Emphasis is given on the calculation of the next two non-trivial terms (at n = 2 and at n = 3) of the aforementioned fields. Consequently, those are found in closed form from exact solutions of coupled (at n = 2, to the one at n = 0) or uncoupled (at n = 3) Laplace equations and they are given in compact fashion, as infinite series expansions for n = 2 or finite forms for n = 3. Nevertheless, the difficulty of the Poisson’s equation that has to be solved for n = 2 is presented, whereas our analytical approach demands the use of the well-known cut-off method in order to obtain an analytical closed solution. Finally, this research adds useful reference results to the already ample library of scattering by simple shapes using analytical methods.     

Multiple Scattering of Thermal Waves from a Subsurface Cylindrical Inclusion in Semi-infinite Functionally Graded Materials Using Non-Fourier Model

In this study, a theoretical method is applied to investigate the multiple scattering of thermal waves and temperature field resulting from a subsurface cylindrical inclusion in a semi-infinite functionally graded material (FGM). The adiabatic boundary condition at the semi-infinite surface is considered. The thermal waves are excited at the surface of semi-infinite functionally graded materials by modulated optical beams. The model includes the multiple scattering effects of the cylindrical thermal wave generated by the line heat source. According to the wave equation of heat conduction, a general solution of scattered thermal waves is presented. Numerical calculations illustrate the effect of subsurface inclusion on the temperature and phase change at the sample surface under different physical and geometrical parameters. It is found that the temperature above the conducting cylindrical inclusion decreases because of the existence of the inclusion. The effect of the inclusion on the temperature and phase change at the surface is also related to the non-homogeneous parameter of FGMs, the wave frequency of thermal waves, and the distance between the inclusion and the semi-infinite surface. Finally, the effect of the relaxation time of buried inclusion on the temperature and phase change at the surface is examined.     

Decoherence in grazing scattering of fast H and He atoms from a LiF(001) surface

The influence of decoherence on the diffraction during grazing scattering of fast hydrogen and helium atoms from a LiF(001) single crystal surface with projectile energies of some keV, is investigated by two-dimensional angular distributions for scattered projectiles in coincidence with their energy loss and emitted electrons from the target surface. For keV hydrogen atoms, we identify the excitations of electrons and excitons of the target surface as the dominant mechanisms for decoherence, whereas for keV helium atoms these contributions are negligibly small. The suppression of electronic excitations owing to the band gap of insulators plays an essential role for preserving quantum coherence and thus for the application of fast atom diffraction as a surface analytical tool.     

Mathematical modeling of electromagnetic separation of inclusions from magnesium melt in a rectangular channel

A mathematical model was developed to study the effect of electromagnetic forces on non-metallic inclusions removal from magnesium melts passing through a channel. The electromagnetic force exerted on the inclusion induced by a DC current field was calculated. In order to compute the velocity field within the channel, the Navier-Stokes equations were solved numerically. The trajectories of the inclusions were calculated using the equations of motion for inclusions. Parametric studies were carried out to evaluate the effect of various parameters on the inclusions removal efficiency.     

A new features on S-waves propagation in a nonhomogeneous anisotropic incompressible medium under influence of gravity field and initial stress with and without electromagnetic field and rotation

The present article is concerned with the investigation of the propagation of shear waves in a nonhomogeneous anisotropic incompressible medium under the effect of the electromagnetic field, gravity field, rotation, and initial stress taking into account a comparison between presence and absence of magnetic field, initial stress, and rotation. Analytical analysis reveals that the velocity of propagation of the shear waves depends upon the direction of propagation, the anisotropy, magnetic field, rotation, gravity field, nonhomogeneity of the medium, and the initial stress. The frequency equation that determines the velocity of the shear waves has been obtained. Some special cases are also deduced from the present investigation. In fact, these equations are an agreement with the corresponding classical results when the medium is isotropic. Numerical results have been given and illustrated graphically in each case considered. The results indicate that the effects of gravity field, initial stress, magnetic field, electric field, anisotropy, and rotation are very pronounced. Also, the absence of initial stress, magnetic field, and rotation tends to increasing of the S-waves velocity compared with presence of them.