High-frequency susceptibility of a superlattice with 2D inhomogeneities

We investigate the high-frequency susceptibility (Green function) of an initially sinusoidal 1D superlattice with 2D phase inhomogeneities that model the deformations of the interfaces between the superlattice layers. For waves propagating along the superlattice axis (the geometry of a photon or magnon crystal), we have found a peculiar behavior of the imaginary part of the Green function that consists in a significant difference between the peaks corresponding to the edges of the band gap in the wave spectrum. The peak corresponding to the lower-frequency band edge remains essentially unchanged as the root-mean-square fluctuation of the 2D inhomogeneities γ₂ increases, while the peak corresponding to the higher-frequency band edge broaden and decreases sharply in height until its complete disappearance with increasing γ₂. This behavior of the peaks corresponds to a band gap closure mechanism that differs from the traditional one characteristic of 1D and 3D inhomogeneities. These effects can be explained by a peculiarity of the energy conservation laws for the incident and scattered waves for 2D inhomogeneities in a 1D superlattice.     

Spectral properties of waves in superlattices with 2D and 3D inhomogeneities

We investigate the dynamic susceptibility and one-dimensional density of states in an initially sinusoidal superlattice containing simultaneously 2D phase inhomogeneities simulating correlated rough-nesses of superlattice interfaces and 3D amplitude inhomogeneities of the superlattice layer materials. The analytic expression for the averaged Green’s function of the sinusoidal superlattice with two phase inhomogeneities is derived in the Bourret approximation. It is shown that the effect of increasing asymmetry in the peak heights of dynamic susceptibility at the Brillouin zone boundary of the superlattice, which was discovered earlier [15] upon an increase in root-mean-square (rms) fluctuations, also takes place upon an increase in the correlation wavenumber of inhomogeneities. However, the peaks in this case also become closer, and the width and depth of the gap in the density of states decrease thereby. It is shown that the enhancement of rms fluctuations of 3D amplitude inhomogeneities in a superlattice containing 2D phase inhomogeneities suppresses the effect of dynamic susceptibility asymmetry and leads to a slight broadening of the gap in the density of states and a decrease in its depth. Targeted experiments aimed at detecting the effects studied here would facilitate the development of radio-spectroscopic and optical methods for identifying the presence of inhomogeneities of various dimensions in multilayer magnetic and optical structures.     

Effects of cross correlations between 1D and 3D inhomogeneities on the high-frequency susceptibility of superlattices

Cross correlations between components of a mixture of one-dimensional (1D) and three-dimensional (3D) inhomogeneities are described by introducing a distribution function taking into account correlations between absolute values of two random variables in the absence of correlations between the variables themselves. This distribution function is used for derivation and analysis of the superlattice correlation function containing a mixture of cross-correlated 1D and 3D inhomogeneities. The effect of such inhomogeneities on the high-frequency susceptibility at the edge of the first Brillouin zone of the superlattice is investigated. It is shown that positive cross correlations partly suppress the effect of a mixture of 1D and 3D inhomogeneities on the wave spectrum: the gap at the boundary of the Brillouin zone increases, and wave damping decreases as compared to the effect produced by a mixture of 1D and 3D inhomogeneities in the absence of cross correlations. Negative cross correlations lead to the opposite effect: the gap decreases and wave damping increases. Cross correlations also lead to the emergence of new resonance effects: a narrow dip or a narrow peak at the center of the band gap (depending on the sign of the correlation factor).     

Spin-wave susceptibility of partially randomized ferromagnetic superlattices

This paper is a theoretical investigation of the effect of inhomogeneities in the period of a ferromagnetic superlattice on the high-frequency superlattice susceptibility. The calculations are done for a model in which the uniaxial magnetic anisotropy is taken as the physical parameter that characterizes both the ideal superlattice and a partially randomized superlattice. It is found that as the inhomogeneities become more intense, the two resonance peaks corresponding to the splitting of the spectrum at the edge of the Brillouin zone of the superlattice broaden, move closer to each other, and finally merge into one. The height of this peak increases and the peak width decreases as the intensity of the inhomogeneities increases further. The effect of inhomogeneities on the susceptibility differs dramatically in the two limits of short-and long-wave inhomogeneities: in the latter case (in contrast to the former) the dependence of the separation of the susceptibility peaks on the intensity and correlation properties of the inhomogeneities is nonmonotonic. The possibility of observing these effects in spin-wave resonance experiments involving multilayer magnetic films is also discussed. Zh. éksp. Teor. Fiz. 116, 1335–1345 (October 1999)     

Effect of the correlation properties of one-and three-dimensional inhomogeneities on the high-frequency magnetic susceptibility of sinusoidal superlattices

The effect of one-(1D) and three-dimensional (3D) inhomogeneities on the high-frequency magnetic susceptibility at the boundary of the first Brillouin zone of a ferromagnetic superlattice is studied. The study is performed with an earlier developed method of random spatial modulation (RSM) of the superlattice period. In this method, structural inhomogeneities are described in terms of the random-phase model, in which the phase depends on three coordinates in the general case. The frequency spacing Δν_m between two peaks in the imaginary part of the averaged Green’s function, which characterizes the gap width in the frequency spectrum at the boundary of the Brillouin zone, is calculated as a function of both the root-mean-square fluctuations γ_i and the correlation wavenumbers η_i of phase inhomogeneities (i = 1 and 3 for 1D and 3D inhomogeneities, respectively). The function Δν_m(γ₁, η₁) for 1D inhomogeneities is shown to be symmetric with respect to interchanging the variables γ ₁ ² and η₁, whereas the function Δν_m(γ₃, η₃) for 3D inhomogeneities is strongly asymmetric with respect to interchanging γ ₂ ³ and η₃. This effect is associated with the difference in form between the correlation functions of 1D and 3D inhomogeneities and can be used to determine the dimensionality of inhomogeneities from the results of spectral studies of such superlattices.     

Bulk plasma waves in a randomly inhomogeneous conductor

The modification of the spectrum and damping of bulk plasma waves due to three-dimensional random inhomogeneities of the density of a degenerate electron gas in a conductor have been investigated using the averaged Green??s function method. The dependences of the frequency and damping of the averaged plasma waves, as well as the position ?? _m and width ???? of the peak of the imaginary part of the Fourier trans-form of the averaged Green??s function, on the wave vector k have been determined in the self-consistent approximation, which makes it possible to take into account multiple scattering of plasma waves by inhomogeneities. It has been found that, in the long-wavelength region of the spectrum, the decrease revealed in the frequency of the plasma waves is caused by the inhomogeneities, which agrees qualitatively with the behavior of the position of the peak ?? _m . In the range of large values of the correlation length of inhomogeneities and small values of k, the damping of the plasma waves tends to zero, whereas the width of the peak ???? remains finite, which is due to the nonuniform broadening. A comparison with the data of numerical calculations has been performed.     

Band structure of a two-dimensional resonant photonic crystal

The band structure of two-dimensional resonant photonic crystals of two types has been calculated using the expansion of eigenfunctions in plane waves. Crystals of one type consist of infinite dielectric cylinders forming a square lattice filled with a resonant gas, and crystals of the other type consist of infinite cylindrical holes filled with a resonant gas and forming a square lattice in a dielectric matrix. It has been shown that, in both cases, the dispersion of a resonant gas in combination with the dispersion of a two-dimensional structure with a photonic band gap leads to the appearance of an additional narrow transmission band near the edge of the band gap or an additional band gap in the continuous spectrum of the photonic crystal. The calculations performed have demonstrated that new dispersion properties substantially depend on the density of the resonant gas, the position of the resonant frequency with respect to the edge of the band gap, and the direction of propagation of electromagnetic waves.     

Electromagnetic waves in a randomly inhomogeneous Josephson junction

Spectrum modification and damping of Josephson plasma waves induced by random inhomogeneities of the critical current through the superconductor contact and the averaged Green function of such excitations are analyzed. In the self-consistent approximation that makes it possible to take into account multiple wave scattering on the inhomogeneities, the frequency and damping of averaged waves, as well as position ν _m and peak width Δν of the Fourier transform imaginary part of the averaged Green function, are determined as functions of wavevector k. The evolution of such functions with the variation of the correlation radius and the relative r.m.s. fluctuations of inhomogeneities is studied. The inhomogeneity-induced wave frequency decrease observed in the long wavelength spectral region qualitatively agrees with the ν _m behavior. It is established that in the case of “long-range” inhomogeneities, the linear dependence of damping on k changes to the inversely proportional one, and damping tends to zero as k → 0, while Δν at small k attains its maximal values due to nonuniform broadening. In the presence of “short-range” inhomogeneities, the wave damping and Δν are found to be similar functions of k. The results are compared to the numerical calculation data.     

First-principles studies of the electronic structure and optical properties of AgBO<Subscript>3</Subscript> (B=Nb,Ta) in the paraelectric phase

The electronic energy-band structure, density of states (DOS), and optical properties of AgBO₃ in the paraelectric cubic phase have been studied by using density functional theory within the local density approximation for exchange-correlation for the first time. The band structure shows a band gap of 1.533 eV (AgNbO₃)and 1.537 eV (AgTaO₃)at (M-⌈)point in the Brillouin zone. The optical spectra of AgBO₃ in the photon energy range up to 30 eV are investigated under the scissor approximation. The real and imaginary parts of the dielectric function and — thus the optical constants such as reflectivity, absorption coefficient, electron energy-loss function, refractive index, and extinction coefficient — are calculated. We have also made some comparisons with related experimental and theoretical data that is available.      

Spatial–frequency selection of magnetostatic waves in a two-dimensional magnonic crystal lattice

Features of the propagation of magnetostatic waves in a tangentially magnetized magnonic crystal structure based on iron–yttrium garnet with a two-dimensional array of grooves on the surface are studied. Numerical simulation is performed by the finite element method and the dispersion characteristics and the spatial distribution of fields of eigenmodes of surface magnetostatic waves propagating in this structure are calculated. The characteristics of waves in the magnonic crystal structure are experimentally studied by means of Brillouin scattering. It is shown that the formation of waveguide channels is possible when the frequency of the input signal is close to the frequency of the band gap of the structure.     

应变超晶格(ZnS)1/(ZnSe)1的光学性质

用linear mufin tin orbital能带方法，计算Si衬底上（ZnS）_n/（ZnSe）_n（001）超晶格的能带结构，计算中采用外加调整势进行带隙修正．在得到较准确的能带结构和波函数的基础上，计算该超晶格系统的光学介电函数虚部ε₂（ω）．结果表明，该超晶格系统的光学性质结合了ZnS和ZnSe体材料光学性质的特点，在相当宽的能量范围内有较好的光谱响应．并且该超晶格系统是直接带隙材料，在光电器件应用中有很大潜力． 关键词：     

Simultaneous occurrence of structure-directed and particle-resonance-induced phononic gaps in colloidal films

We report on the observation of two hypersonic phononic gaps of different nature in three-dimensional colloidal films of nanospheres using Brillouin light scattering. One is a Bragg gap occurring at the edge of the first Brillouin zone along a high-symmetry crystal direction. The other is a hybridization gap in crystalline and amorphous films, originating from the interaction of the band of quadrupole particle eigenmodes with the acoustic effective-medium band, and its frequency position compares well with the computed lowest eigenfrequency. Structural disorder eliminates the Bragg gap, while the hybridization gap is robust.     

Waves in a superlattice with anisotropic inhomogeneities

Dependences of the dispersion laws and damping of waves in an initially sinusoidal superlattice on inhomogeneities with anisotropic correlation properties are studied for the first time. The period of the superlattice is modulated by the random function described by the anisotropic correlation function K_?(r) that has different correlation radii, k _∥ ^?1 and k _⊥ ^?1 , along the axis of the superlattice z and in the plane xy, respectively. The anisotropy of the correlation is characterized by the parameter λ=1?k_⊥/k_∥ that can change from λ=0 to λ=1 when the correlation wave number k⊥ changes from k_⊥=k_∥ (isotropic 3D inhomogeneities) to k_⊥=0 (1D inhomogeneities). The correlation function of the superlattice K(r) is developed. Its decreasing part goes to the asymptote L that divides the correlation volume into two parts, characterized by finite and infinite correlation radii. The dependences of the width of the gap in the spectrum at the boundary of the Brillouin zone δν and the damping of waves ξ on the value of λ are studied. It is shown that decreasing L leads to the decrease of δν, and increase of ξ, with the increase of λ.     

Dynamical conductivity of type-I semiconductor superlattices

We calculated longitudinal and transverse macroscopic as well as microscopic dynamical conductivity for a modulation-doped type-I superlattice. Our computed long wavelength macroscopic conductivity significantly differs from Drude conductivity in the low-frequency regime (microwave and infrared radiations). Macroscopic conductivity shows oscillatory behaviour along the direction of growth of the superlattice. Propagation of transverse electromagnetic waves in a superlattice has been studied for all possible values of frequency and wavevector. It is found that microscopic transverse conductivity exhibits poles along both real and imaginary axes of frequency. Depending on the values of wavevector components, along and perpendicular to the direction of the superlattice, both poles can lie on real or imaginary axes of frequency. We also find that there can be more than one penetration depth for a superlattice and one of them decreases with frequency for frequencies below the microwave regime.     

Effects of the mixture of one-and three-dimensional inhomogeneities on the wave spectrum of superlattices

Dependences of the dispersion laws and damping of waves in an initially sinusoidal superlattice on the dimensionality of inhomogeneities modulating the period of the superlattice are studied. The cases of one-and three-dimensional modulations, as well as modulation by a mixture of inhomogeneities of both of these dimensionalities, are considered. The correlation function of the superlattice K(r) has the form of a product of the same periodic function and a decreasing function that is significantly different for these different cases. The decreasing part of the correlation function for the mixture of inhomogeneities of different dimensionalities has the form of a product of the decreasing parts of the correlation functions of the components of the mixture. This leads to the nonadditivity of the contributions of the components of different dimensionalities to the resulting modification of the parameters of the wave spectrum that are due to the inhomogeneities (the damping of waves for the mixture of these components is smaller than the sum of the dampings of the components, the maximum gap in the spectrum corresponds to the simultaneous presence of both components of the mixture, not only of the three-dimensional inhomogeneities).     

The electronic structure of InAs/GaSb(001) superlattices-two dimensional effects

Detailed calculations of the two dimensional effects in the electronic structure of InAs/GaSb(001)superlattices are presented for the first time. Comparison of the calculated thickness dependence of the superlattice band gap with optical absorption measurements shows that, at the Γ-point, the conduction band edge of InAs lies about 60 meV below the valence band edge of GaSb. Eigenfunctions of the highest light and heavy hole bands, and the lowest two conduction bands exhibit spatially confined nature in the GaSb and InAs regions respectively, thus establishing the two-dimensional nature of these bands. The calculated conduction band effective mass in the plane of the superlattice near the Γ-point is found to be enhanced by a factor of 2.5 over the bulk InAs value and compares very well with the appropriate mass extracted from recent magnetoresistance measurements.     

Waves in a superlattice with arbitrary interlayer boundary thickness

The transmittance D(ω), reflectance R(ω), and dispersion ω(k) are investigated for waves of various nature propagating through a one-dimensional superlattice (multilayer structure) with arbitrary thickness of the interlayer boundary. The dependences of the band gap widths δω_m and their positions in the wave spectrum of the superlattice on the interlayer boundary thickness d and the band number m are calculated. Calculations are performed in terms of the modified coupled-mode theory (MCMT) using the frequency dependence of R(ω), as well as in the framework of perturbation theory using the function ω (k), which made it possible to estimate the accuracy of the MCMT method; the MCMT method is found to have a high accuracy in calculating the band gap widths and a much lower accuracy in determining the gap positions. It is shown that the m dependence of δω _m for electromagnetic (or elastic) waves is different from that for spin waves. Furthermore, the widths of the band gaps with m=1 and 2 are practically independent of d, whereas the widths of all gaps for m>2 depend strongly on d. Experimental measurements of these dependences allow one to determine the superlattice interface thicknesses by using spectral methods.     

First-principles investigation of electronic and optical properties in wurtzite Zn<Subscript>1-x</Subscript>Mg<Subscript>x</Subscript>O

A first-principles study has been performed to evaluate the electronic and optical properties of wurtzite Zn_1-xMg_xO. Substitutional doping is considered with Mg concentrations of x = 0, 0.0625, 0.125, 0.1875 and 0.25, respectively. Mg incorporation can induce band gap widening due to the decrease of Zn 4s states. The imaginary part of the dielectric function shows that the optical transition from band edge emission decreases slightly with increasing Mg contents. The optical band gap also increases from 3.2 to 3.7 eV with increasing Mg contents from 0.0625 to 0.25. The calculated results suggest that relatively high Mg concentration is necessary for effective band gap engineering of wurtzite Zn_1-xMg_xO.     

Switchable nonlinear two-dimensional ferroelectric photonic crystal

A two-dimensional photonic crystal with a system of electrodes providing interaction of the incident and transmitted light waves has been developed on the basis of an epitaxial ferroelectric BaSrTiO₃ film. Investigation of the spectral characteristics has revealed the presence of a photonic band gap near 1.5 eV. A possibility of spatial frequency reconstruction of the second-harmonic wave generated by the photonic crystal is shown. The switching efficiency is as high as 6000%.