Electron Gas Model Research Articles

Structures, compressibilities and relative stabilities of the , and phases of Mg2SiO4 deduced from an electron-gas ionic Hamiltonian

The properties of forsterite (α-Mg2SiO4) and its high-pressure polymorphs wadsleyite (β-Mg2SiO4) and ringwoodite (γ-Mg2SiO4) play an important role in the chemical, dynamic and elastic behaviour of the upper 660 km of the Earth's mantle. Mineralogists have tended to rationalize their structures in terms of empirical ionic models, guided by Pauling's rules. Modern electron-gas theory of ionic interactions is accurate enough to encourage a detailed study of the structure and properties of these minerals within an intuitively appealing ionic model that is independent of empirical data. We therefore undertook to obtain the minimum-energy lattice structures, and their corresponding equations of state, of electron-gas models of the Mg2SiO4 polymorphs. We find that the model densities compare very well with actual observations, while compressibilities are somewhat underestimated. Unit cell geometries are also accurately represented, but coordination polyhedra tend to be more distorted than those observed, mainly because of excessive bond-angle variance. We also found that Pauling's rules do not offer a complete accounting for the observed stability of olivine at low pressures. Instead, in the model crystals it is a difference in the magnitude of the Mg–O repulsions that give olivine the energetic advantage. The higher density of ringwoodite, and a rapidly increasing Mg–O repulsion energy in olivine stabilize ringwoodite at high pressure.

Exchange energy in the local Airy gas approximation

The Airy gas model of the edge electron gas is used to construct an exchange-energy functional which is an alternative to those obtained in the local density and generalized gradient approximations. Test calculations for rare gas atoms, molecules, solids and surfaces show that the Airy gas functional performs better than the local density approximation in all cases and better than the generalized gradient approximation for solids and surfaces.

Optical absorption of transition-metal island films: Correlation interaction between conduction electrons of transition metals

Optical plasma-resonance absorption of Pt island films consisting of Pt particles larger than about 25 Å in diameter has been measured in the photon energy range of 0.5–6.5 eV. As in Rh and Pd island films reported previously, the broadening of the optical plasma-resonance absorption reflects a correlation interaction between conduction electrons. Comparison of the broadening for the Pt island films with that for the Rh island films shows that the correlation interaction is strong when the conduction-electron density n is low. In an electron-gas model, the correlation interaction between electrons becomes stronger with lowering electron density, because the magnitude ratio of the Coulomb to kinetic energy increases as the electron density lowers. Thus, the strong correlation-interaction at low n proves that the correlation interaction in transition metals becomes stronger with magnitude ratio. The magnitude ratio in transition metals is pointed out to increase with lowering n and/or with strengthening d character of conduction electrons. Based on the correlation interaction, reflected by the broadening for the Pt, Rh, and Pd island films, and on the strong correlation interaction, found previously for Ir, the order of magnitude ratio is Ir>Pt>Pd>Rh.

The linewidth of surface states of simple metals

The linewidths (inverse lifetimes) Γe-e of Be(0001) and Mg(0001) surface electronic states are calculated as the projection of the imaginary part of the self-energy operator of a quasiparticle onto the state. The screened Coulomb interaction is calculated using a model potential, which takes into account the energy gap in the band structure and a surface state located in this gap. The wave functions and energies of electron states are calculated by a self-consistent film pseudopotential method. It is shown that Γe-e essentially depends on the position of the surface state in the Brillouin zone. The difference between the calculated values of Γe-e and those obtained in a homogeneous electron gas model is shown to be basically due to transitions from surface bands.

Pairing mechanism for electron-doped cuprates in a layered two-dimensional electron gas model

An effective two-dimensional (2D) interaction potential for super-lattice of electron-doped cuprates (Nd 2− x Ce x CuO 4) treated as a layered electron gas is developed which incorporates screening of electrons as carriers by phonons and by plasmons. The layer stacking sequence is modelled with single superconducting CuO 2 layer, which is an isolated free electron layer well, separated by the charge reservoir layers. A model dielectric function in the random phase approximation is set up for two oscillators fulfilling the appropriate sum rules on polarisabilities. Attention is focussed on the description of the inter-layer electron pairing and superconducting transition temperature, T c. Deduced values of the Coulomb repulsive parameter and of the electron–phonon coupling strength from the 2D effective interaction potential indicate that the Nd-doped cuprate superconductor is in the strong coupling regime with effective screening of the electrons. The superconducting transition temperature of Nd 1.85Ce 0.15CuO 4 is estimated as 28 K, which is consistent with the reported data. The implications of the proposed approach and its analysis are discussed.

A simple yet comprehensive unified physical model of the 2D electron gas in delta-doped and uniformly doped high electron mobility transistors

This paper presents a new approach to model the 2DEG concentration (n/sub s/) versus gate voltage (V/sub G/) behavior and the equilibrium 2DEG concentration (n/sub s0/) in a HEMT. The approach results in a model which is comprehensive in the following sense. It is valid for both delta-doped and uniformly doped HEMTs. It captures all the three n/sub s/-V/sub G/ nonlinearities (subthreshold, gradual pinchoff, and gradual saturation), and the effects of all the device parameters including temperature, in relation expressing n/sub s/ as an explicit closed-form integrable function of V/sub G/ having continuous first derivatives; thus, the function readily yields a device current-voltage/capacitance-voltage (I-V/C-V) model which can be incorporated in software meant for simulation of circuits, particularly of the analog variety. The simple model is shown to predict the results of complex numerical calculations and experiments. The closed-form n/sub s0/ expression of the model is the first of its kind reported for delta-doped HEMT's, and reveals an interesting feature unexposed by earlier n/sub s0/ models: the reciprocal of n/sub s0/ in both delta-doped and uniformly doped devices decreases linearly with reduction in spacer width, and saturates at low spacer widths in some delta-doped devices. It is shown that the measured n/sub s0/ in delta-doped devices is predicted correctly if the electrons in the V-shaped well are assumed to be trapped at the donor sites rather than to be filling the conduction subbands.

Stochastic electron gas theory of coherence in laser-driven synchrotron radiation

The transition from coherent to incoherent laser-driven synchrotron radiation is studied within the framework of a stochastic electron gas model. The fundamental difference between this approach and a relativistic fluid model resides in the fact that, for any number of incoherently phased point electrons, the 4-current contains Fourier components at arbitrarily short wavelengths, whereas the fluid model introduces an unphysical cutoff scale.

Thermal current generation in semiconductor gaps

The possibilities of converting heat directly into electricity at a current-conducting contact with a discrete temperature drop are investigated. The model of a nondegenerate electron gas is used. It is shown that an energy threshold must be present at the contact in order for an EMF to be generated. It is proposed that a thin layer of a semiconductor be inserted into the gap between the-electrodes in order to decrease the threshold and to obtain a perceptible current at an everage temperature. The EMF, the specific power, and the characteristic (neglecting the phonon and radiative heat conduction) efficiency of such a transducer are calculated, 5 figures, 1 reference.

Universal correlations of one-dimensional interacting electrons in the gas phase

We consider dynamical correlation functions of short range interacting electrons in one dimension at finite temperature. Below a critical value of the chemical potential there is no Fermi surface anymore, and the system can no longer be described as a Luttinger liquid. Its low temperature thermodynamics is that of an ideal gas. We identify the impenetrable electron gas model as a universal model for the gas phase and present exact and explicit expressions for the asymptotics of correlation functions at small temperatures, in the presence of a magnetic field.

Spin and charge dynamics in the Cu-O chains ofYBa2Cu4O8

We report an NQR-NMR study of the chain copper and apex oxygen in the high-temperature superconductor ${\mathrm{YBa}}_{2}{\mathrm{Cu}}_{4}{\mathrm{O}}_{8}$. Above ${T}_{c},$ the temperature dependences of the Cu spin-lattice relaxation rate and the Knight shift are quantitatively described in the framework of the one-dimensional electron gas model, where the anisotropy and the correlation of the chain electron system are taken into account. Electric-field-gradient fluctuations due to charge carriers in the chains contribute partly to the chain Cu relaxation and dominate the apex oxygen relaxation. The different temperature dependences of the magnetic and quadrupolar relaxation rates of the chain Cu seem to confirm the separation of low-energy spin and charge excitations (spin-charge separation), expected in the framework of the one-dimensional electronic gas model. Finally, we present experimental evidence that below ${T}_{c}$ the Cu-O chains become superconducting through the proximity effect.

Pseudojellium, ideal metals, and stabilized jellium

Two new electron gas models, introduced in the early 1990s, describe the energetics of metals better than the conventional electron gas, jellium. The first, the ``ideal metal,'' was derived by starting with jellium at a specified density and requiring that no forces act on the positive background when the system is cleaved. The second, ``stabilized jellium,'' was derived by starting with the pseudopotential model of metals, requiring that this model yield equilibrium at the specified average electron density and then averaging the potential seen by the electrons to obtain an equivalent electron gas. Even though these derivations are conceptually quite different, their results, the ideal metal and stabilized jellium models, are very nearly identical. We explain their great similarity by deriving both the ideal metal and stabilized jellium in a unified way from pseudojellium---a stabilized electron gas model derived in the middle 1980s that includes the average electron-ion interaction, while maintaining the uniform ground state and computational simplicity of jellium. This derivation explains the near identity of the ideal metal and stabilized jellium and allows us to understand the small differences between them.

Local phonon–plasmon modes in layered conductors

The dispersion equations for bulk and local phonon–plasmon (PP) waves in layered conductors and superlattices are obtained in the frame of a model which neglects electron hopping between layers but assumes an arbitrary charge–charge response function within the layers. The local modes propagate in the defect layer which differs from the rest of the layers by density and mass of charge carriers. The response function is found in the model of a two-dimensional electron gas interacting with acoustic lattice vibrations in the long wavelength approximation. It is shown that in this model two bulk PP waves propagates within the narrow low-frequency and broad high-frequency bands and three local modes exist beyond these bands. Depending on the sign and magnitude of the defect layer parameter Δ : (which is a relative variation of the ratio: density to mass of charge carriers) two acoustic and one optic local PP modes exist in the system.

CORRELATIONS WEAK AND STRONG: DIVERS GUISES OF THE TWO-DIMENSIONAL ELECTRON GAS

The three-dimensional electron-gas model has been a major focus for many-body theory applied to the electronic properties of metals and semiconductors. Because the model neglects band effects, whereas electronic systems are generally more strongly correlated in narrow band systems, it is most widely used to describe the qualitative physics of weakly correlated metals with unambiguous Fermi liquid properties. The model is more interesting in two space dimensions because it provides a quantitative description of electrons in quantum wells and because these can form strongly correlated many-particle states. We illustrate the range of possible many-particle behaviors by discussing the way correlations are manifested in 2D tunneling spectroscopy experiments.

ANALYSIS ON ENERGY ABSORPTION EDGE AND ELECTRON POPULATIONS OF Al

A theoretical explanation for L core-shell absorption edge of electron energy loss spectrum of Al, an analysis of the electronic populations and a comparison between different partial cross sections are given. The edge was first normalized to the same atomic ionization cross section (per atom per electronvolt). The contributions for the cross section come from three respects:the first one is the electronic transitions from the core-shell to valence-shell calculated by extended Hückel band model, the second one is the final ionization state obtained by electron gas model, the third comes from the elastic backscatting of outgoing waves by the atoms that neighbor the excited atom. The agreement between the calculation result and the experimental result is good.

A comparative study of equations of state for MgO

The pressure–volume–temperature relationship, isothermal bulk modulus K T and pressure derivative of K T have been evaluated for MgO in the temperature range 300–2000 K and down to a compression of V/ V 0=0.60 using six different phenomenological forms for the isothermal equation of state (EOS). The results are discussed and compared with the values for MgO obtained by Isaak et al. using the potential induced breathing electron gas model based on the first principles approach. It is found that phenomenological isothermal equations are applicable even at a high temperature if the input parameters ( K 0 and K 0′) corresponding to that temperature are used. The results obtained from the Vinet EOS and the Shanker EOS are very similar and also close to the ab initio values determined by Isaak et al.

GOR'KOV'S EXPANSION AND THE dHvA EFFECT IN THE VORTEX STATE

The validity of Gor'kov's expansion in the small superconducting order parameter near the upper critical field H c2 of type II superconductors at low temperatures is examined in the light of the accumulated experimental data of the dHvA effect in the vortex state. Using a 2D electron gas model, it is shown that a small amount of thermal smearing is sufficient to ensure the validity of the expansion within a significantly broad field range below H c2 . The lowest order (i.e. quadratic) term in this expansion is insensitive to the inhomogeneity of the pair potential in the vortex state and tends to cancel the zeroth order (i.e. normal electrons) term. Higher order terms are found, in the asymptotic limit, E F/ℏω c ≫1 , to be much smaller than the corresponding terms in the random vortex lattice model, thus reflecting weak `scattering' of quasi-particles by the vortex lattice. This picture seems to account qualitatively for a common feature observed in almost all experiments so far, namely the crossover of the Dingle plot from a relatively large slope just below H c2 to a smaller slope at lower fields.

Dynamic screening of fast ions moving in solids

The electron charge polarization induced by a fast ion moving on a solid medium is considered in a linear response model. An inhomogeneous electron gas model is introduced to describe the contribution to this dynamic screening by the bound target electrons. The action of the bound electrons is to increase the effective number of electrons of the uniform electron gas that reproduces features of the induced potential. We find that the value of the induced potential at the ion position is equivalent to that produced by a jellium of a given density, smaller than that required for the jellium to reproduce the value of the induced electric field at the ion. For the case of fast bare charges we find the precise value of jellium densities required to describe the experimental values of the stopping power in several solid targets. For the case of hydrogenic Kr projectiles in a Cu target, the mixing of its n53 states by the induced potential is just that required to explain recent measurements of radiative decay. @S0163-1829~98!05212-6#

Al L core edge fine structure in Al, AlN and α-Al 2 O 3 : A comparison of microelectron energy loss spectra with theory

The Al L near-edge fine structures of aluminum and its compounds with nitrogen and oxygen are studied using electron energy loss microspectroscopy in a transmission electron microscope. These edges are normalized to the same scattering cross section per Al atom per electronvolt. The cross section is calculated by using the Born approximation. The contributions to the cross section are from the valence shell crystal states obtained by using the extended Huckel band calculation and the ionization states obtained by using the electron gas model. The chemical effects in the ionization region are taken into account by including the contributions from the elastic backscattering of outgoing plane waves by the atoms that neighbor the excited atoms. The results by theoretical calculation agree semiquantitatively with experimental results.

Negative Poisson's ratios as a common feature of cubic metals

Poisson's ratio is, for specified directions, the ratio of a lateral contraction to the longitudinal extension during the stretching of a material. Although a negative Poisson's ratio (that is, a lateral extension in response to stretching) is not forbidden by thermodynamics, this property is generally believed to be rare in crystalline solids1. In contrast to this belief, 69% of the cubic elemental metals have a negative Poisson's ratio when stretched along the [110] direction. For these metals, we find that correlations exist between the work function and the extremal values of Poisson's ratio for this stretch direction, which we explain using a simple electron-gas model. Moreover, these negative Poisson's ratios permit the existence, in the orthogonal lateral direction, of positive Poisson's ratios up to the stability limit of 2 for cubic crystals. Such metals having negative Poisson's ratios may find application as electrodes that amplify the response of piezoelectric sensors.

Nonlinear corrections to the image potential of charged particles moving parallel to a metal surface

A nonlinear quantum hydrodynamical model of simple metal surfaces is developed for predicting nonlinear corrections to the image potential acting on a highly charged ion moving near a planar surface. The classical image potential acting between a classical point charge, Z 1 e, and a metal surface may be derived, within a linear hydrodynamical model, as the virtual excitation of a surface plasmon due to the interaction with the external charge. On the other hand, a nonlinear quantum hydrodynamical model of the homogeneous electron gas has been recently developed to study second order corrections to the wake potential of fast charged particles passing through matter, and this model is now extended to study the bounded electron gas.