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A systematic study of the longitudinal effective mass associated with either shallow impurity states or conduction Landau levels under in-plane magnetic fields is presented for Fibonacci superlattices. We analyze the relation between the mean longitudinal effective masses and the localization length of the corresponding electronic or impurity states. Under appropriate conditions we show that the mean longitudinal effective mass weakly depends on the nature of the electron state and localization length, and is essentially related to the Cantor-like energy spectra or ``band structure.''

Made available in DSpace on 2022-04-29T08:48:53Z (GMT). No. of bitstreams: 0 Previous issue date: 2012-05-07 The localization properties of electromagnetic modes in one-dimensional disordered photonic superlattices are theoretically studied. The multilayered system is considered to be composed of alternating stacks of two different random-thickness slabs, characterized by nondispersive and/or frequency-dependent electric permittivities and magnetic permeabilities. Results for the localization length are evaluated by using an analytical model for weakly disordered systems as well as its general definition through the transmissivity properties of the heterostructure. Good agreement between both results is observed only for small amplitudes of disorder. The critical frequencies at which the localization length diverges are correctly predicted in the whole frequency spectrum by the analytical model and confirmed via the corresponding numerical calculations. The λ2 dependence of the localization length, previously observed in disordered heterostructures made of material of positive refractive indexes, are confirmed in the present work. In addition, new λ4 and λ -4 dependencies of the localization length in positive-negative disordered photonic superlattices are obtained, under certain specific conditions, in the long and short wavelength limits, respectively. The asymptotic behavior of the localization length in these limits is essentially determined by the particular frequency dispersion that characterizes the metamaterial used in the left-handed layers. When the effects of absorption are considered, then a divergence of the localization length is still observed, under some conditions, in the short wavelength limit. © 2012 American Physical Society. Instituto de Física Universidad de Antioquia, AA 1226, Medellín Faculdade de Ciências UNESP-Universidade Estadual Paulista, 17033-360, Bauru-SP Instituto de Física Universidade Federal de Alagoas, Maceió-AL, 57072-970 Instituto de Física Universidade Estadual de Campinas-UNICAMP, Campinas-SP, 13083-859 Faculdade de Ciências UNESP-Universidade Estadual Paulista, 17033-360, Bauru-SP

We have investigated the effects of disorder correlations on light propagation and Anderson localization in one-dimensional dispersive metamaterials. We consider and compare the cases where disorder is uncorrelated to situations where it is totally correlated and anticorrelated. The photonic gaps of the corresponding periodic structure are not completely destroyed by the presence of disorder, which leads to minima in the localization length. In the vicinities of a gap, the behavior of the localization length depends crucially on the physical origin of the gap (Bragg or non-Bragg gaps). Within a Bragg gap, the localization length increases as the degree of disorder increases, an anomalous behavior that only occurs for the uncorrelated and completely correlated cases. In these cases, minima of the localization length at the positions of Bragg gaps are shifted by increasing disorder, which does not occur for the anticorrelated case, where the positions of the minima remain unaltered. Minima in the localization length corresponding to non-Bragg gaps are not shifted by increasing disorder, albeit the widths of these minima are changed. We have found that the asymptotic behavior for the localization length $\ensuremath{\xi}\ensuremath{\propto}{\ensuremath{\lambda}}^{6}$ for disordered metamaterials is not affected by correlations. Finally, we have investigated the role of absorption on the delocalized Brewster modes and argue that it could be mitigated in light of the state-of-the-art of metamaterials research.

Direct and indirect excitons in $\mathrm{Ga}\mathrm{As}\text{\ensuremath{-}}{\mathrm{Ga}}_{1\ensuremath{-}x}{\mathrm{Al}}_{x}\mathrm{As}$ coupled double quantum wells, under growth-direction applied electric and magnetic fields, have been theoretically investigated within a variational procedure in the effective-mass and parabolic-band approximations. The exciton hydrogenic $1s$-like envelope wave function is obtained through a variational procedure and an appropriate expansion in trigonometric functions of the electron and hole wave functions. The applied electric field produces a polarization of the exciton by pushing the electron and hole away from each other, whereas the magnetic field contracts the exciton by pushing the electron and hole closer to each other. Intersubband mixing produced by the Coulomb interaction of electron-hole pairs is taken into account and a detailed analysis of the properties of direct- and indirect-exciton states in $\mathrm{Ga}\mathrm{As}\text{\ensuremath{-}}{\mathrm{Ga}}_{1\ensuremath{-}x}{\mathrm{Al}}_{x}\mathrm{As}$ coupled double quantum wells is presented, with theoretical results in good agreement with available experimental measurements.

The variational procedure, in the effective-mass and parabolic-band approximations, is used in order to investigate the effects of crossed electric and magnetic fields on the exciton states in $\mathrm{Ga}\mathrm{As}∕{\mathrm{Ga}}_{1\ensuremath{-}x}{\mathrm{Al}}_{x}\mathrm{As}$ coupled double quantum wells. Calculations are performed for double quantum wells under applied magnetic fields parallel to the layers and electric fields in the growth direction. The exciton envelope wave function is obtained through a variational procedure using a hydrogenic $1s$-like wave function and an expansion in a complete set of trigonometric functions for the electron and hole wave functions. We take into account intersubband mixing brought about by the Coulomb interaction of electron-hole pairs in double quantum wells and present a detailed analysis of the properties of direct and indirect exciton states in these systems. The present study clearly reveals anticrossing effects on the dispersion with applied voltage (or growth-direction electric field) of the photoluminescence peaks associated with direct and indirect excitons. Calculated results are found in good agreement with available experimental measurements on the photoluminescence peak position associated with direct and indirect excitons in $\mathrm{Ga}\mathrm{As}\text{\ensuremath{-}}{\mathrm{Ga}}_{1\ensuremath{-}x}{\mathrm{Al}}_{x}\mathrm{As}$ double quantum wells under growth-direction applied electric fields or under applied in-plane magnetic fields.

The variational procedure in the effective-mass and parabolic-band approximations is used in order to investigate the effects of crossed electric and in-plane magnetic fields on the electronic and exciton properties in semiconductor heterostructures. Calculations are performed for bulk GaAs and $\mathrm{Ga}\mathrm{As}∕{\mathrm{Ga}}_{1\ensuremath{-}x}{\mathrm{Al}}_{x}\mathrm{As}$ quantum wells, for applied magnetic fields parallel to the layers and electric fields in the growth direction, and it is shown that the combined effects on the heterostructure properties of the applied crossed electric and magnetic fields and the direct coupling between the center-of-mass and internal exciton motions may be dealt with via a simple parameter representing the spatial distance between the centers of the electron and hole magnetic parabolas. Exciton properties are analyzed by using a simple hydrogenlike envelope excitonic wave function and present theoretical results are found in fair agreement with available experimental measurements on the diamagnetic shift of the photoluminescence peak position of $\mathrm{Ga}\mathrm{As}∕{\mathrm{Ga}}_{1\ensuremath{-}x}{\mathrm{Al}}_{x}\mathrm{As}$ quantum wells under in-plane magnetic fields.

A theoretical study, within the effective-mass approximation, of the effects of applied magnetic fields on excitons trapped in quantum dots/interface defects is presented. Actual traps are formed by fluctuations either incomposition or structure size in narrow GaAs/Ga 1 - x Al x As quantum wells. Exciton trapping is taken into account through a model quantum dot formed by monolayer fluctuations in the z direction, and lateral confinement, via a parabolic potential, in the exciton-in plane coordinate. Magnetic fields are applied in the growth direction of the semiconductor heterostructure, and the various magnetoexciton states are obtained in the effective-mass approximation by an expansion of the exciton-envelope wave functions in terms of products of hole and electron quantum-well states with appropriate Gaussian functions for the various excitonic states. Theoretical results are found in overall agreement with available experimental measurements.

The energy spectra of shallow donors and acceptors in GaAs-${\mathrm{Ga}}_{1\mathrm{\ensuremath{-}}\mathrm{x}}$${\mathrm{Al}}_{\mathrm{x}}$As quantum-well structures have been calculated. The binding energies of the impurities were obtained within a variational calculation in the effective-mass approximation. Calculations were performed for simple neutral and double singly ionized impurities as functions of the position of the impurity in a GaAs quantum well of infinite depth and for various slab thicknesses. The effect of the spatially dependent screening is modeled with a dielectric response of the form ${\ensuremath{\epsilon}}^{\mathrm{\ensuremath{-}}1}$(r)=${\ensuremath{\epsilon}}_{0}^{\mathrm{\ensuremath{-}}1}$+(1-${\ensuremath{\epsilon}}_{0}$ $^{\mathrm{\ensuremath{-}}1}$)${e}^{\mathrm{\ensuremath{-}}r/a}$, with a screening parameter a\ensuremath{\approxeq}1.1 a.u. characteristic of bulk GaAs. Results are compared with Bastard's theory, which is based on a constant-${\ensuremath{\epsilon}}_{0}$ screening, and it is found that spatially dependent screening effects are small for donors down to very thin slab thicknesses, but can be quite important for all acceptors in GaAs quantum wells over a large range of slab thicknesses. Calculated results with improved statistics are in quantitative agreement with experimental data on neutral donors and acceptors.

The electronic structure of the interstitial hydrogen atom in alkaline-earth fluorides has been studied using the self-consistent-field multiple-scattering ${X}_{\ensuremath{\alpha}}$ method. In the calculations we have used a cluster constituted by the hydrogen atom and its first anion and cation neighbors. The contact parameters with the proton and the fluorine nuclei have been evaluated. The agreement obtained with the experimental results is in general good and indicates that this method is also appropriate to study defects in ionic crystals.

The self-consistent-field multiple-scattering method in the $X\ensuremath{\alpha}$ approximation is used to calculate the electronic structure and the optical transition energies of the $U$ center in Ca${\mathrm{F}}_{2}$, Sr${\mathrm{F}}_{2}$, and Ba${\mathrm{F}}_{2}$.

The binding energies of D/sup -/ states in P- and As-doped silicon crystals are calculated as functions of uniaxial compressive stress along the (100) direction within a variational scheme in the effective-mass approximation and with a Chandrasekhar-type variational function. A model Hamiltonian which takes into account valley-orbit corrections, electron-electron interaction, and stress effects is proposed. Our calculation shows that as the stress is applied, the outer electron orbital is driven readily into the two stress-deepened valleys, which leads to a strong decrease in the D/sup -/ binding energy. With further increase in stress, the inner electron orbital changes gradually from a function almost evenly distributed among the six conduction valleys into one in which the two stress-deepened valleys are dominant, and the D/sup -/ binding energy increases. Our results agree qualitatively with previous theoretical calculations and are in good agreement with far-infrared photoconductivity measurements in Si:P.

A two-band model, which previously was used successfully to evaluate the optical absorption in A1, is applied to derive the $\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}}$- and $\ensuremath{\omega}$-dependent dielectric function ${\ensuremath{\epsilon}}_{M}(\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}},\ensuremath{\omega})$ for $\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}}$ parallel to the [100] direction with use of degenerate perturbation theory. Within the nearly-free-electron approximation, it is shown that a pair of (200) Bragg planes gives rise to another pole in the energy-loss function $\mathrm{Im}[\frac{\ensuremath{-}1}{\ensuremath{\epsilon}}]$ and hence to a collective mode. Both the dispersion of the mode throughout the first Brillouin zone and the strength of the mode are evaluated and are found to agree very well with electron-energy-loss spectroscopy data. A detailed discussion of the nature of this mode is given. The mode is of the same origin as the so-called zone-boundary collective state (ZBCS) first proposed by Foo and Hopfield in Na. Comparison is made with a numerical calculation of ${\ensuremath{\epsilon}}_{M}(\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}},\ensuremath{\omega})$ by Singhal for some discrete $\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}}$ values. The general importance of the ZBCS for the understanding of the energy-loss spectrum and for more complicated systems is pointed out.

Anisotropic structures in the inelastic-scattering cross section of x rays from single-crystal Li and of fast electrons from single-crystal Na and Al are found to arise from zone-boundary collective states (ZBCS) that, in contrast to the classical plasmon, depend strongly on the symmetry and on the strength of the crystal potential. We show that within the random-phase approximation (RPA), a nearly-free-electron-like two-band model is able to describe these states existing for q along various high-symmetry directions of the crystal. In Li in particular, a 〈200〉 ZBCS appears as a continuation of the plasmon beyond the cutoff wave vector ${q}_{c}$. For many years structures in this (q,\ensuremath{\omega}) regime have been associated with correlation effects beyond the RPA. Furthermore, due to the high sensitivity on the crystal potential, measured ZBCS's yield valuable information on the band structure, which are currently intensively studied by angularly resolved photoemission.