Wave-vector Dispersion Research Articles

Wave packet tunneling and imaginary wave vector dispersion

Dispersion associated with the complex band structure of a periodic potential can be used to explain single-electron wave packet tunneling through a finite-sized tunnel barrier. The imaginary k-space dispersion in a tunnel barrier may be viewed as a filter that controls the arrival time, shape, and group velocity of a transmitted wave packet. This k-space filter can be designed to increase or decrease the group velocity of the transmitted pulse and a transmitted peak-pulse probability arrival time can be engineered to occur before or after that of an electron wave packet propagating in the absence of the tunnel barrier.

Influence of CoFeB layer thickness on elastic parameters in CoFeB/MgO heterostructures

The surface acoustic waves, i.e., surface phonons may have huge potential for future spintronic devices, if coupled to other waves (e.g., spin waves) or quasiparticles. In order to understand the coupling of acoustic phonons with the spin degree of freedom, especially in magnetic thin film-based heterostructures, one needs to investigate the properties of phonons in those heterostructures. This also allows us to determine the elastic properties of individual magnetic layers and the effective elastic parameters of the whole stacks. Here, we study frequency versus wavevector dispersion of thermally excited SAWs in CoFeB/MgO heterostructures with varying CoFeB thickness by employing Brillouin light spectroscopy. The experimental results are corroborated by finite element method-based simulations. From the best agreement of simulation results with the experiments, we find out the elastic tensor parameters for CoFeB layer. Additionally, we estimate the effective elastic parameters (elastic tensors, Young’s modulus, Poisson’s ratio) of the whole stacks for varying CoFeB thickness. Interestingly, the simulation results, either considering elastic parameters of individual layers or considering effective elastic parameters of whole stacks, show good agreement with the experimental results. These extracted elastic parameters will be very useful to understand the interaction of phonons with other quasiparticles.

Resolution of zigzag magnetic correlations in Na-deficient NaxIrO3 without long-range ordering

The materials search for Kitaev quantum spin liquids led to the discovery of many honeycomb lattice materials. Much attention has been paid to materials without magnetic order down to the lowest temperatures. The newly synthesized Na-deficient ${\mathrm{Na}}_{x}{\mathrm{IrO}}_{3}$ has been found to bear no sign of long-range magnetic order above 1 K from physical property measurements. In this paper, we report momentum- and energy-resolved excitation spectra in Na-deficient ${\mathrm{Na}}_{x}{\mathrm{IrO}}_{3}$ measured using a resonant inelastic x-ray scattering spectrometer. Orbital excitation spectra show that the octahedral and trigonal crystal field splittings are larger in ${\mathrm{Na}}_{x}{\mathrm{IrO}}_{3}$ than in ${\mathrm{Na}}_{2}{\mathrm{IrO}}_{3}$. On the other hand, the low-energy spectrum at low temperature shows a wave-vector dispersion and a spectral weight distribution that are similar to those of ${\mathrm{Na}}_{2}{\mathrm{IrO}}_{3}$, revealing that the two-dimensional zigzag magnetic correlations in ${\mathrm{Na}}_{x}{\mathrm{IrO}}_{3}$ are similar to those in ${\mathrm{Na}}_{2}{\mathrm{IrO}}_{3}$ in terms of the ordered magnetic moment direction and three dynamically fluctuating zigzag orders. The azimuth angle dependence of the low-energy spectrum corroborates these results. The two-dimensional zigzag magnetic correlations rapidly weaken until 50 K. At high temperatures, the spectral weight distribution of the low-energy excitation resembles that of the pure Kitaev model, indicating that the Kitaev interaction dominates the dynamic magnetic response at high temperature. We suggest that the larger crystal field and distortion and the weakened longer-range Heisenberg exchange interactions due to the Na deficiency in ${\mathrm{Na}}_{x}{\mathrm{IrO}}_{3}$ contribute to bring ${\mathrm{Na}}_{x}{\mathrm{IrO}}_{3}$ away from the zigzag long-range magnetic order phase.

High-frequency conductivity and temperature dependence of electron effective mass in AlGaN/GaN heterostructures

We present calculations of frequency and wavevector dispersion of conductivity of two-dimensional electrons confined in AlGaN/GaN heterostructures at the arbitrary level of the degeneracy and the presence of strongly inelastic scattering mechanism by the optical phonons. We found that the high-frequency conductivity deviates from that of the standard Drude–Lorentz model and changes significantly at elevated temperature. The results were applied for simulation of the spectral characteristics of the grating-based plasmonic structure for wide temperature range. We found that thermal activation of the inelastic scattering leads to significant red-shift of the plasmon resonances. This facilitates refinement of interpretation of experimental results published in series of recent papers. We concluded that for AlGaN/GaN heterostructures, the electron effective mass changes in narrower diapason of 0.22me,…,0.26me, when temperature varies from 77 to 300 K. We suggest that found peculiarities of the high-frequency conductivity and its spatial dispersion are of a general character and can be important for high-frequency and high power devices based on AlGaN/GaN heterostructures.

Omnidirectional nonreciprocal absorber realized by the magneto-optical hypercrystal.

Photonic bandgap design is one of the most basic ways to effectively control the interaction between light and matter. However, the traditional photonic bandgap is always dispersive (blueshift with the increase of the incident angle), which is disadvantageous to the construction of wide-angle optical devices. Hypercrystal, the photonic crystal with layered hyperbolic metamaterials (HMMs), can strongly modify the bandgap properties based on the anomalous wavevector dispersion of the HMM. Here, based on phase variation competition between HMM and isotropic dielectric layers, we propose for the first time to design nonreciprocal and flexible photonic bandgaps in one-dimensional photonic crystals containing magneto-optical HMMs. Especially the zero-shift cavity mode and the blueshift cavity mode are designed for the forward and backward propagations, respectively. Our results show maximum absorption about 0.99 (0.25) in an angle range of 20-75 degrees for the forward (backward) incident light at the wavelength of 367 nm. The nonreciprocal omnidirectional cavity mode not only facilitates the design of perfect unidirectional optical absorbers working in a wide-angle range, but also possesses significant applications for all-angle reflectors and filters.

Domain Textures in the Fractional Quantum Hall Effect.

Impacts of domain textures on low-lying neutral excitations in the bulk of fractional quantum Hall effect (FQHE) systems are probed by resonant inelastic light scattering. We demonstrate that large domains of quantum fluids support long-wavelength neutral collective excitations with well-defined wave vector (momentum) dispersion that could be interpreted by theories for uniform phases. Access to dispersive low-lying neutral collective modes in large domains of FQHE fluids such as long wavelength magnetorotons at filling factor v=1/3 offer significant experimental access to strong electron correlation physics in the FQHE.

A novel graphene based tunable semiconductor metamaterial: A mathematical analysis

Abstract. In this article we have proposed a novel graphene based tunable semiconductor metamaterial which can be effectively tuned in the long wavelength infrared region of the electromagnetic spectrum by only changing the chemical potential of graphene via a gate voltage without needing to vary the doping concentration of semiconductor. The previously reported semiconductor metamaterial constructed from doped InGaAs and intrinsic AlInAs layers shows all angle negative refraction Hoffman et al.. However, it cannot be tuned without changing the doping concentration of semiconductor and changing doping concentration makes the material lossy. Since Graphene possesses tunable surface conductivity which can be tuned effectively by changing the chemical potential of graphene, we have proposed a novel structure where graphene sheet is inserted between the InGaAs and AlInAs layers. Through rigorous mathematical analysis we have shown that by changing only the chemical potential, without needing to modify the structural properties, it is possible to tune the spectral region of permittivity where negative refraction occurs which in turns gives tunability to iso-frequency wave vector dispersion, transmittance, reflectance and absorption coefficient. The proposed method would simplify the tuning process of semiconductor metamaterials. This unique graphene based tunable semiconductor metamaterial would be an attractive feature in the rapid and continuously developing semiconductor industry.

Hyperbolic Metamaterials at Microwaves With Stacked Inductive Coiled-Wire Arrays

Metasurfaces made of arrayed wires are inductive only for propagating waves and become capacitive when illuminated by evanescent waves. We show how to extend the inductive behavior of such metasurfaces for the case of illumination by plane waves with large wavenumber, i.e., for evanescent waves. The proposed metasurface exhibits an effective surface inductance that is extended to evanescent waves with large transverse wavenumber using coiled wires. Metasurfaces with inductive response over a wide spatial spectrum can be used for the realization of hyperbolic metamaterials (HMs) at microwave frequencies. Stacking such inductive metasurfaces separated by thin dielectric spacers leads to a negative real part of the in-plane, effective dielectric permittivity, and thus, to hyperbolic wavevector dispersion at microwave frequencies. We establish the requirements for such hyperbolic dispersion condition using arrays of coiled wires, also accounting for losses. We show that the negative in-plane real part of dielectric permittivity stretches up to transverse wavenumbers that are several times larger than the free-space wavenumber, over a broad frequency bandwidth. The theory and important design analytic formulas are presented to demonstrate the inductive behavior, as well as the propagative nature of waves in the proposed HM, in agreement with full-wave simulations.

Experimental demonstration of angle-independent gaps in one-dimensional photonic crystals containing layered hyperbolic metamaterials and dielectrics at visible wavelengths

Photonic gaps are the core of photonic crystals in the manipulation of light. However, in conventional photonic crystals composed of two types of dielectrics, the photonic gaps strongly depend on the angle of incidence, which limits their applications. In this Letter, we present the experimental demonstration of angle-independent gaps in the visible wavelength range in one-dimensional photonic crystals composed of layered hyperbolic metamaterials (HMMs) and dielectrics. HMMs with anomalous wave-vector dispersion can tune the propagating phase of light to an unprecedented extent that usual dielectrics cannot attain. The HMM is mimicked by the layered titanium dioxide and silver with a subwavelength unit cell. Based on the phase-variation compensation effect between the HMM and the dielectric, an angle-independent gap is experimentally realized, which agrees well with the simulated one. This angle-independent gap is very useful in the design of photonic devices such as omnidirectional reflectors with fixed bandwidth or all-angle filters.

Dynamic correlations in the highly dilute 2D electron liquid: Loss function, critical wave vector and analytic plasmon dispersion

Correlations, highly important in low–dimensional systems, are known to decrease the plasmon dispersion of two–dimensional electron liquids. Here we calculate the plasmon properties, applying the ‘Dynamic Many-Body Theory’, accounting for correlated two–particle–two–hole fluctuations. These dynamic correlations are found to significantly lower the plasmon’s energy. For the data obtained numerically, we provide an analytic expression that is valid across a wide range both of densities and of wave vectors. Finally, we demonstrate how this can be invoked in determining the actual electron densities from measurements on an AlGaAs quantum well.

Wave-vector and polarization dependent impedance model for a hexagonal periodic metasurface exemplified through finite-difference time-domain simulations.

An isotropic impedance sheet model is proposed for a loop-type hexagonal periodic metasurface. Both frequency and wave-vector dispersion are considered near the resonance frequency. Therefore both the angle and polarization dependences of the metasurface impedance can be properly and simultaneously described in our model. The constitutive relation of this model is transformed into auxiliary differential equations which are integrated into the finite-difference time-domain algorithm. Finally, a finite large metasurface sample under oblique illumination is used to test the model and the algorithm. Our model and algorithm can significantly increase the accuracy of the homogenization methods for modeling periodic metasurfaces.

Theoretical investigation of polarization control in ultraviolet wavelength region using eigenmode within subwavelength grating

The optical characteristics of a subwavelength grating (SWG) were examined as a means of achieving ultraviolet (UV) polarization control based on the interaction between a light wave and Bloch eigenmode wave in the SWG, which results in a spatial periodic refractive index distribution. The relation of dispersion of the eigenmode wavevector was calculated to reveal the light propagation mechanism in this structure. The expected optical characteristics proved the feasibility of obtaining highly polarized UV light with no significant decrease in light intensity. The effects of the higher-order eigenmode on the SWG optical characteristics were also examined and discussed via the finite-difference time-domain method. This approach provides new insight into the SWG design for UV polarization control using the above interaction.

Spatially dispersive dynamical response of hot carriers in doped graphene

We study theoretically wave-vector and frequency dispersion of the complex dynamic conductivity tensor (DCT), σlm(k,ω), of doped monolayer graphene under a strong dc electric field. For a general analysis, we consider the weak ac field of arbitrary configuration given by two independent vectors, the ac field polarization and the wave vector k. The high-field transport and linear response to the ac field are described on the base of the Boltzmann kinetic equation. We show that the real part of DCT, calculated in the collisionless regime, is not zero due to dissipation of the ac wave, whose energy is absorbed by the resonant Dirac quasiparticles effectively interacting with the wave. The role of the kinematic resonance at ω=vF|k| (vF is the Fermi velocity) is studied in detail taking into account deviation from the linear energy spectrum and screening by the charge carriers. The isopower-density curves and distributions of angle between the ac current density and field vectors are presented as a map which provides clear graphic representation of the DCT anisotropy. Also, the map shows certain ac field configurations corresponding to a negative power density, thereby it indicates regions of terahertz frequency for possible electrical (drift) instability in the graphene system.

Hot-electron noise properties of graphene-like systems

We study the hot-electron noise properties of two-dimensional materials with a graphene-like energy dispersion under a strong applied electric field which drives the system far from equilibrium. Calculations are based on a Boltzmann--Green-function method within a two-relaxation-time approximation that allows for both inelastic scattering coming from electron-phonon scattering and elastic scattering coming from electron-impurity scattering. The steady-state distribution function is used to calculate the average current and the low-frequency spectral density for current fluctuations (noise) in the nonequilibrium steady-state. We find that as the electric field strength increases, the noise decreases from its equilibrium thermal noise value. This is in contrast with semiconductors with a quadratic energy--wave-vector dispersion where the noise increases in a constant-relaxation-time model with the square of the electric field due to the Joule heating of the electron gas by the electric field. We have also studied these properties for an electronic dispersion with a gap introduced into the Dirac spectrum. The inclusion of the gap in the electronic dispersion causes an initial increase in the noise as a function of external electric field due to the heating of the electron gas for large gap values. At high electric fields, the noise decreases with increasing electric field as in the case of gapless dispersion at higher fields.

Graphene–dielectric composite metamaterials: evolution from elliptic to hyperbolic wavevector dispersion and the transverse epsilon-near-zero condition

We investigated a multilayer graphene-dielectric composite material, comprising graphene sheets separated by subwavelength-thick dielectric spacer, and found it to exhibit hyperbolic isofrequency wavevector dispersion at far- and mid-infrared frequencies allowing propagation of waves that would be otherwise evanescent in a dielectric. Electrostatic biasing was considered for tunable and controllable transition from hyperbolic to elliptic dispersion. We explored the validity and limitation of the effective medium approximation (EMA) for modeling wave propagation and cutoff of the propagating spatial spectrum due to the Brillouin zone edge. We found that EMA is capable of predicting the transition of the isofrequency dispersion diagram under certain conditions. The graphene-based composite material allows propagation of backward waves under the hyperbolic dispersion regime and of forward waves under the elliptic regime. Transition from hyperbolic to elliptic dispersion regimes is governed by the transverse epsilon-near-zero (TENZ) condition, which implies a flatter and wider propagating spectrum with higher attenuation, when compared to the hyperbolic regime. We also investigate the tunable transparency of the multilayer at that condition in contrast to other materials exhibiting ENZ phenomena.

Determining the Thickness of Pb Film Similar to Bulk with Energy Dispersion Derived from Quantum Well States

It is known that the energy spacing between adjacent empty quantum well (QW) states in Pb islands on Cu(111) would reveal the shrinking characteristic originating from the effect of the image potential. Using the phase accumulation model, including a phase factor contributed from the image potential, the shrinking energy spacing can be quantitatively explained with the assumption of the parabolic energy versus wave vector (E–k) dispersion. However, an experimental dispersion acquired from analyzing the energies of the QW state reveals a linear E–k relationship corresponding to the Pb bulk band structure, implying the assumed parabolic dispersion is not appropriate. By combining the linear dispersion with the image potential effect in the calculation, it is found that the calculated values of energy spacing of island thickness below eight atomic layers are not in agreement with the experimental measurements. This implies that the electronic structure of Pb islands would be similar to that of the bulk when their thicknesses reach eight-atomic layers.

Resonant Inelastic Light Scattering Investigation of Low-Lying Gapped Excitations in the Quantum Fluid atν=5/2

The low-lying neutral excitation spectrum of the incompressible quantum Hall fluid at ν=5/2 is investigated by inelastic light scattering. Gapped modes are observable only in a very narrow filling factor range centered at 5/2 at energies that overlap estimates from transport activation gaps. The modes are interpreted as critical points in the wave-vector dispersion of excitations that preserve spin orientation. For very small changes |δν|≲0.01 the gapped modes disappear and a continuum of low-lying excitations takes over indicating the transition from an incompressible fluid at 5/2 to a compressible state. Observations of spin wave modes indicate spin polarization of the 5/2 and 2+1/3 quantum Hall fluids.

Hyperbolic metamaterial as super absorber for scattered fields generated at its surface

We show that hyperbolic metamaterials (HMs) that exhibit hyperbolic wave-vector dispersion diagrams possess two important features related to super absorption: The total power scattered by a nanosphere is (i) greatly enhanced when placed at the HM surface, compared to other material surfaces, and (ii) almost totally directed into the HM. We show that these two features are peculiar of HM interfaces, and we support them using a spectral theory study of transverse-electric and magnetic waves scattered by a subwavelength nanosphere. We analyze the nanosphere's scattered power absorbed by various substrate configurations. We also consider various nanosphere materials.

Circuit analysis in metal-optics

We provide electrical circuit descriptions for bulk plasmons, single surface plasmons, and parallel-plate plasmons. Simple circuits can reproduce the exactly known frequency versus wave-vector dispersion relations for all these cases, with reasonable accuracy. The circuit paradigm directly provides a characteristic wave-impedance, Zo, that is rarely discussed in the context of plasmonics. The case of a single-surface-plasmon is particularly interesting since it can be modeled as a transmission line, even though there is no return current conductor. The capacitance/unit length and the Faraday inductance/unit length, of a flat metal surface, are C′=2ɛokW, and L′=μo/2kW, respectively (where k is the wave-vector, and W is the width of the flat metal surface). We believe that many other metal-optic geometries can be described within the circuit paradigm, with the prerequisite that the distributed capacitance and inductance must be calculated for each particular geometry.

Core hole and surface excitation correction parameter for XPS peak intensities

In XPS analysis, surface excitations and excitations originating from the static core hole created during the photoexcitation process are usually neglected. However, both effects significantly reduce the measured peak intensity. In this paper we have calculated these effects. Instead of considering the two effects separately, we introduce a new parameter, namely the Correction Parameter for XPS (or CP XPS ) defined as the change in probability for emission of a photoelectron caused by the presence of the surface and the core hole in comparison with the situation where the core hole is neglected and the electron travels the same distance in an infinite medium. The CP XPS calculations are performed within the dielectric response theory by means of the QUEELS-XPS software determining the energy-differential inelastic electron scattering cross-sections for X-ray photoelectron spectroscopy (XPS) including surface and core hole effects. This study has been carried out for electron energies between 300 eV and 3400 eV, for angles to the surface normal between 0° and 60° and for various materials, especially metals, semiconductors and oxides. For geometries and energies normally used in XPS, i.e. for emission angle ≤ 60° and photoelectron energy ≤ 1500 eV, we find that CP XPS values are significantly larger for oxides, (0.55 ≲ CP XPS ≲ 0.75) than for metals and semiconductors (0.45 ≲ CP XPS ≲ 0. 6). We show that this behavior is due to the difference in the wave vector dispersion of the energy loss function. This dispersion has been determined from analysis of REELS and is found to be free electron like ( α ≅ 1) for metals but is substantially smaller ( α ≈ 0.02–0.05) for materials with a wide band gap. As a result, the group velocity of the valence electrons is very small for oxides with a large band gap. This leads to a reduction in the screening of the core-hole potential before the photoelectron has left the region of interaction and thereby to an increase in the intrinsic excitations caused by the core hole.