We show that the resonant Raman cross section for the scattering of light from two-dimensional electrons in GaAs quantum wells in the fractional quantum Hall regime, to a good approximation, has a piece proportional to the projected structure factor and another piece coming from hole shakeup proportional to a specific higher-order structure factor. Exact numerical results for up to ten particles at all momentum transfers are presented and discussed.

A strong-coupling theory of the polaron is developed to study the electron-phonon interaction in quantum-well structures consisting of strong polar crystals. By introducing a two-parameter trial wave function to take care of the strong anisotropy, the Landau-Pekar theory is extended to investigate polaronic effects in a quantum well. It is shown that the theory yields correct results in both the two-dimensional and three-dimensional limits. The ground-state properties of quasi-two-dimensional polarons are calculated as functions of the well width for two choices of the coupling constant α.

We have calculated the persistent current and the conductance of a normal metal loop connected to two electron reservoirs in the presence of magnetic flux. The geometry considered here facilitates simultaneous measurement of the persistent current and the conductance. We show that, in general, the magnitude of the persistent current in a loop depends on the direction of the direct current flow from one reservoir to another, a feature that can be experimentally verified.

The effective action of nonrelativistic fermions in 2+1 dimensions is analyzed at finite temperature and chemical potential in the presence of a uniform magnetic field perpendicular to the plane. The method used is a generalization of the derivative expansion technique. The induced Chern-Simons term is computed and shown to exhibit Hall quantization. Effects of dissipation due to collisions are also analyzed.

The self-consistent theory of Anderson localization derived by Vollhardt and Wölfle has been extended to treat the influence of small electric and magnetic fields. Numerical results are obtained for the negative magnetoresistance even for higher scattering strengths (${\mathit{k}}_{\mathit{F}}$λ≳1) which cannot be treated by the weak-localization theory. We compare with experimental data and theoretical results derived from a microscopic approach. A dc electric field gives rise to a delocalization edge which agrees for one-dimensional systems with the exact value and which depends exponentially on ${\mathit{k}}_{\mathit{F}}$λ for two-dimensional disordered electron systems. Remnants of the two-dimensional delocalization edge should only be observed experimentally in low-mobility heterostructures (${\mathit{k}}_{\mathit{F}}$λ∼1) at the lowest temperatures.

A macroscopic continuum model coupling the mechanical vibrational amplitude and electrostatic potential is applied to obtain the optical vibrational modes in quantum-dot structures. A unified method of solution (valid for any type of nanostructure) that reduces the four coupled second-order differential equations to Helmholtz’s and Laplace’s equations is described. Analytical solutions for the vibrational amplitude and the Fröhlich-type electron-phonon interaction are given for quantum dots with spherical geometry. The existence of surface modes and their relation to the matching boundary conditions are studied. A qualitative discussion of the ir and Raman activity of the calculated modes is given together with a comparison with the few existing experimental data.

We investigate the static nonlinear screening of a single point charge (Coulombic impurity) by a two-dimensional electron gas (2DEG) in a strong perpendicular magnetic field at low temperature. The electron-electron interactions are treated in the Hartree-Fock approximation (HFA). The results are compared to earlier results for Hartree interacting electrons showing quite different screening properties due to the enhancement of the spin splitting of the Landau levels within the HFA. The possibility of different occupation of the spin levels of the impurity and the surrounding 2DEG is discussed in light of experiments.

We study variable-range hopping in the quantum Hall effect regime in the presence of a metallic gate parallel to the plane of a two-dimensional electron gas. Screening of the Coulomb interaction by the gate causes the partial ‘‘filling’’ of the Coulomb gap in the density of localized states. At low enough temperatures this leads to a substantial enhancement and a different temperature behavior of the hopping conductivity. As a result, the diagonal conductivity peaks become much wider. The power-law dependence of the width of the peaks on the temperature changes: the corresponding exponent turns out to be twice as small as that for gateless structures. The width dependences on the current in the non-Ohmic regime and on the frequency for the absorption of the electromagnetic waves experience a similar modification. The experimental observation of the crossovers predicted may demonstrate the important role of the Coulomb interaction in the integer quantum Hall regime.

We consider electrons tunneling through a double-barrier resonant-tunneling structure (DBRTS) and interacting with a defect which has internal degrees of freedom. Usually such a defect has two (or more) metastable configurations and can switch between them due to its interaction with a thermal bath. Interaction between the tunneling electron and the dynamic defect creates a noisy environment surrounding the DBRTS, and leads to fluctuations in time of the resonant level. Such fluctuations result in inelastic tunneling and low-frequency noise. This paper is focused on the problem of inelastic resonant tunneling. We have calculated the average transparency for various relations between the switching rate of the dynamic defect, the escape rate of the electron from the resonant level in the well, the coupling strength between the electron and the dynamic defect, and the temperature. The results derived here are entirely different from those found in phonon-assisted resonant tunneling, because phonons obey the Bose statistics but a two-level fluctuator behaves as an effective spin.

We consider an ideal mesoscopic cylinder in which a steady azimuthal current is generated. We show that the closed interacting-electron system in the presence of the current is described by a density matrix which is that of an equilibrium system without current but with a constrained Hamiltonian.

We have developed a nonperturbative method to compute the dynamics of electrons in quantum wells driven by oscillating electric fields. Floquet theory enables us to compute, in the local-density approximation, solutions of the Schrödinger equation for zero temperature which are self-consistent and for which the density is periodic in time. The method is demonstrated by computing harmonic generation from a tilted square well, which agrees with perturbation theory, and second-harmonic emission from an ${\mathrm{Al}}_{0.3}$${\mathrm{Ga}}_{0.7}$As heterojunction, which agrees with recent experiments of Bewley et al.

An optimized self-consistent method for determination of the quantal electron density is presented. It is applied, in the zero-temperature case, to devices with either partial or full donor ionization. A Thomas-Fermi approximation for the T=0 limit is developed and shown to be appropriate for systematic studies of the two-dimensional electron density, ${\mathrm{\sigma }}_{\mathrm{-}}$. A suitable linear approximation is found that provides simple and accurate analytic expressions for ${\mathrm{\sigma }}_{\mathrm{-}}$ in terms of the physical parameters of the device.

We have studied systematically the normal-incidence-radiation absorption for the intersubband transition in the quantum well of n-type indirect-gap semiconductors. By a special choice of the coordinate system related to the sample growth direction, we have proposed a simple method to calculate the elements of the inverse effective-mass tensor. Using the concept of the invariance of the ellipsoidal constant-energy surface under coordinate transformations, the general expression for the absorption coefficient of the intersubband transition has been derived as a function of the sample growth direction. We have also investigated the maximal value of the normal-incidence radiation absorption, the optimal growth direction for quantum-well detectors, and the comparison between normal- and parallel-incidence-radiation absorptions. These are of great utility for designing and optimizing the quantum-well infrared detector for normally incident radiations.

We consider variations of the low temperature chemical potential and magnetization of laterally confined two-dimensional interacting electrons in a strong magnetic field. Cases of axially symmetrical (a quantum dot) and strongly elongated (a quantum wire) spatial distributions of electron density are studied. We commonly refer to both types of systems as ‘‘islands.’’ The calculations are performed in the mean-field approximation. In this approximation the system consists of alternating regions of compressible and incompressible liquids. We are focusing on islands with typical widths b, which are much larger than the Bohr radius in a semiconductor ${\mathit{a}}_{\mathit{B}}$, and argue that the density profile is formed mainly by electrostatic forces, has a domelike shape, and changes only slightly in the whole range of magnetic fields. We calculated numerically the chemical potential and the magnetization as functions of the magnetic field and found them to be in sharp contrast to the conventional result for noninteracting electrons. We suggest a simple analytic theory adequately explaining these functional dependences. The results are compared with the experimental data.

Ag L-edge x-ray-absorption near-edge-structure spectra have been obtained for a series of Au-Ag alloys: ${\mathrm{Au}}_{0.75}$${\mathrm{Ag}}_{0.25}$, ${\mathrm{Au}}_{0.67}$${\mathrm{Ag}}_{0.33}$, ${\mathrm{Au}}_{0.5}$${\mathrm{Ag}}_{0.5}$, and ${\mathrm{Au}}_{0.25}$${\mathrm{Ag}}_{0.75}$. The results show a significant decrease in the Ag ${\mathit{L}}_{2,3}$-edge white-line area relative to pure Ag upon dilution of Ag in Au, indicating an increase in d charge at the Ag site. The value of the transition matrix element ${\mathit{R}}_{\mathit{d}}^{2\mathit{P}}$=1.2(1)×${10}^{\mathrm{-}10}$ cm for Ag has been derived based on the experimental results. A semiquantitative analysis of the results shows that the number of unoccupied d states (4d hole counts) at the Ag site in the alloys decreases by as much as 0.130 in ${\mathrm{Au}}_{0.75}$${\mathrm{Ag}}_{0.25}$. The relevance of this finding to Friedel charge screening and Au-Ag d-d interaction is discussed.

A nonmetal-to-metal transition in Mg monolayers on Mo(112) has been indicated by photoemission and resonant photoemission. The dramatic changes of the density of states, the dispersion of bands near ${\mathit{E}}_{\mathit{F}}$, and screening are observed across the nonmetal-to-metal transition. The changes of the resonance photon energy and the intensity of Mg 2p→εd excitation, with different coverages, indicate that there exists a correlation between the electronic structure (particularly final-state screening effects) and the overlayer structure. The commensurate-to-incommensurate transition beyond 0.5 monolayer of coverage corresponds to the overlayer nonmetal-to-metal transition, which is due to the hybridization of Mg s and p bands and represents a transition from a localized (bondlike) to a delocalized (bandlike) phase for divalent atoms.

A theory of resonance ionization (RI) of metastable ${\mathrm{He}}^{\mathrm{*}}$ atoms in interaction with a clean and NO-covered Pd(111) surface is presented which is based on stationary scattering theory. The exact electron scattering states and the RI-inducing potential as well as the adsorption behavior of ${\mathrm{He}}^{\mathrm{*}}$ and NO on Pd(111) are obtained within the same self-consistent quantum-mechanical mean-field approach. The rate of ${\mathrm{He}}^{\mathrm{*}}$ 2s resonance ionization is nearly a factor 35 larger on the NO-covered Pd(111) surface compared to clean Pd(111) at the same perpendicular distance with respect to the first layer of Pd atoms. This is in contrast to earlier expectations that molecular species (NO, CO) adsorbed on transition-metal surfaces should play a shielding role with respect to the RI of metastable ${\mathrm{He}}^{\mathrm{*}}$ atoms. The enhanced rate of RI on NO/Pd(111) is due to the strong direct (electrostatic and quantum-mechanical) and indirect interactions (through the metal surface, including the interactions with the image potential) in the adsorption layer. The broadening of the diffuse unoccupied NO states through coupling to unoccupied metal band states leads to quasidegeneracy with the ${\mathrm{He}}^{\mathrm{*}}$ 2s state, which provides the necessary condition for a resonance process.

We present a medium-energy ion-scattering investigation of Pb surfaces with orientations in the [11¯0] zone vicinal to Pb (111), at high temperature. Both surfaces inclined towards the (110) orientation and surfaces inclined towards the (001) orientation exhibit surface-melting-induced faceting. Faceting occurs not only close to the bulk melting point, but over a range of temperatures extending at least from 589.6 K up to the bulk melting point (600.7 K). Just below the melting point, the dry facet orientation for vicinal surfaces inclined towards (110) is 3.1°±0.6°, the dry facet orientation towards the (001) surface is 7.3°±0.8°, and for both directions the melted facet orientation is approximately 14.5° with respect to the (111) plane. Between 593.8 and 600.7 K, the observed dry facet orientations vary less than 3°. A model calculation in terms of interfacial free energies is used to describe the facet orientations and their temperature dependence. We relate our results to recent equilibrium shape observations of Pb crystallites.

Core-ionization potentials (CIP’s) are computed for Be(0001). Three core features are observed in corresponding photoelectron spectra, with CIP’s shifted relative to the bulk core level by -0.825, -0.570, and -0.265 eV. The computed CIP shifts for the outer and subsurface layers, -0.60 and -0.29 eV, respectively, agree with the latter two of these. It is surmised that the -0.825-eV shift is associated with a surface defect. The negative signs of the Be(0001) surface core-level shifts do not fit into the thermochemical picture widely used to explain CIP shifts. The reason is that a core-ionized Be atom is too small to bond effectively to the remainder of the unrelaxed Be lattice.

Brillouin light-scattering experiments have been performed on tungsten-carbide containing amorphous-hydrogenated-carbon (WC–a-C:H) films which were prepared on (111) silicon wafers by a reactive rf sputtering process. From the measured velocity of the Rayleigh surface modes the shear modulus G is calculated as a function of the tungsten-carbide volume fraction, reflecting a phase transition of the films from an a-C:H-dominated to a crystalline β-WC-dominated WC–a-C:H mixture. The elastic constants determined agree well with results obtained from depth-sensing indentation measurements. Theoretical calculation of the elastic constant of the composite was also performed as a function of WC volume fraction. The results show a small deviation from the experimental data in the range of low WC fraction, which is probably caused by the phase change of the a-C:H matrix. The relatively large discrepancy of the theoretical calculation in the high-WC-fraction region may be a result of the invalidity of the theory.