Dynamical exchange corrections to the dielectric function in a two-dimensional electron gas

The effect of dynamical exchange interactions on the dielectric function of a two-dimensional electron gas is studied using a variational approach. Exchange effects are introduced via the local-field correction. The variationally obtained local-field factor is compared to the earlier perturbative result to first order in the electron-electron interaction.     

Dynamical exchange corrections to the dielectric function in a two-dimensional electron gas

The effect of dynamical exchange interactions on the dielectric function of a two-dimensional electron gas is studied using a variational approach. Exchange effects are introduced via the local-field correction. The variationally obtained local-field factor is compared to the earlier perturbative result to first order in the electron-electron interaction.     

Dynamical exchange effects in the dielectric function of the two-dimensional electron gas

Dynamical exchange interactions can be introduced in the dielectric function via a dynamic local field factor. We study the effects of this inclusion on both the static and the frequency dependent dielectric function of a two-dimensional electron gas, using the dynamic local field factor that we derived recently via the dynamical exchange decoupling method. The results are compared with the dielectric function in the Random Phase Approximation and with different dynamic and static approximations of the local field factor.Received: 7 May 2003, Published online: 22 September 2003PACS: 71.45.Gm Exchange, correlation, dielectric and magnetic response functions, plasmons - 77.22.Ch Permittivity (dielectric function) - 77.55.+f Dielectric thin filmsJ.T. Devreese: , jtd@uia.ua.ac.be     

Application of a dielectric function to the exchange energy and specific heat of a two-dimensional electron gas

A new theory based on a dielectric function and its sum rule is presented for the exchange energy and specific heat of a two-dimensional electron gas. The results are exact towards absolute zero.     

Wigner function of a two-dimensional electron gas in a magnetic field

The Wigner function of a two-dimensional electron gas in an arbitrary magnetic field perpendicular to the plane in which the electrons are confined is constructed rigorously. The function is useful in taking various statistical averages and illuminates the roles played by the hyperbolic functions of the field which appear in the expressions of the susceptibility and other physical quantities.     

Realization of a spin-polarized two-dimensional electron gas via image-potential-induced surface states

Electrons in image-potential-induced surface states form a two-dimensional electron gas in front of the surfaces. In the case of ferromagnets, their binding energies as well as lifetimes depend on the orientation of their spin magnetic moment with respect to the magnetization direction. Various experiments with inverse photoemission and two-photon photoemission to detect the spin dependence of image states are reviewed. A new and successful approach to achieve and detect a spin-polarized two-dimensional electron gas is presented, namely polarization-dependent and spin-resolved two-photon photoemission. Additional time resolution opens the way to study spin-dependent electron dynamics.     

Longitudinal dielectric behavior of a harmonically bound two-dimensional electron gas in a uniform magnetic field

We have employed random-phase approximation to determine the inverse dielectric function for a harmonically confined two-dimensional electron gas in a magnetic field. We examine the plasmon dispersion relation and show the results for the variation of plasmon frequency with the magnetic field strength and confinement energy.     

Second-order theory of the dielectric response function of the electron gas

Using the Green function formalism an expression for the dielectric response function (or density-density function) is derived which is of second order with respect to the Coulomb interaction and applies for arbitrary wave vector and frequency. The employed procedure is somehow lengthy but quite clear from the mathematical point of view. Decoupling methods for Green functions are not used. The theory contains the well-known expressions of the HFA, RPA and the first-order local field theory. In addition to this all four-particle processes (two electrons and two holes) are taken into account and represented in a closed formula, which is the four-particle analog to the Lindhard function. As a first application the plasmon damping is investigated.     

The microwave Hall effect of a two-dimensional electron gas

The integer Quantum Hall effect has been recently observed in the Hall conductivity _xy at microwave frequencies. Here we present a calculation of the wave propagation in the crossed waveguide system used in the experiments. The field pattern is more complicated than in the case of a pure plane wave. The essential result, however, remains unchanged: The field strength in the second (crossed) waveguide is proportional to _xy of the two-dimensional electron gas. Dedicated to Professor Karlheinz Seeger on the occasion of his 60th birthday     

Effect of dielectric coating on the electron work function and the surface stress of a metal

The electron work function, contact potential difference, and surface stress of the elastically deformed faces of the metal covered by a dielectric are calculated by using the Kohn–Sham method and stabilized jellium model. Our calculations demonstrate the opposite deformation dependencies of the work function and contact potential difference. Dielectric coating leads to a negative change in the work function and a positive change in the contact potential difference. It is shown that the measurements of the contact potential difference of a deformed face by the Kelvin method give only the change in the value of the one-electron effective potential in the plane of a virtual image behind the surface, rather than the value of the electron work function. The obtained values of the electron work function and surface stress for Al, Au, Cu, and Zn are in agreement with the results of experiments for polycrystals.     

Magnetic susceptibility of a one-dimensional Fermi system and dielectric function of a two-dimensional Coulomb gas

A relation between the magnetic susceptibility(k, ) of an interacting 1-D Fermi system and the dielectric function(q) of a 2-D Coulomb gas is established. By applying a cluster-expansion technique and by using known results for the pair-correlation function of the Coulomb gas we obtain a number of expressions for(q) which apply in different regions of theq-plane and in different temperature intervals. These results supplement the existing picture of the transition from non-metallic to metallic behaviour occurring in the 2-D Coulomb gas as the temperature increases. The relation between(q) and(k, ) is then used to derive explicit expressions for(k, ) from these results for(q). The change in the dielectric response of the 2-D Coulomb gas is reflected by a change in the magnetic response of the 1-D Fermi system: as a function of the spin non-flip coupling constant the susceptibility of the Fermi system changes from normal paramagnetic behaviour to non-magnetic behaviour characteristic of a bound singlet-spin ground state, as decreases. Our result for the gap in the spin excitation spectrum of the Fermi system is in agreement with the results of other authors.On sabbatical leave from Institut für Theoretische Physik, TU Hannover, GermanyWork at U.C.S.B. supported in part by the National Science Foundation     

Width of the quasiparticle spectral function in a two-dimensional electron gas with spin-orbit interaction

The results of an investigation of the width of the electron and hole spectral functions in an isotropic electron gas with the Rashba spin-orbit interaction as a function of the wave vector within the G ⁰ W ⁰ approximation are reported. This kind of electron gas is used to simulate two-dimensional systems formed by electrons in In _x Ga_{1 − x} As layers of various heterostructures and by surface electron states on Au(111). It is demonstrated how the width of the spectral function changes as a result of the spin-orbit interaction and how it depends on the branch index of the energy spectrum split by this interaction.     

Spatial correlations of a two-dimensional electron gas

The pair distribution function of a two-dimensional degenerate electron gas is evaluated in the chain diagram approximation and its asymptotic behavior is investigated. It shows characteristic oscillations at large distances. A sum rule of the eigenvalues of the free particle propagator is obtained. It can be used for the evaluation of the exchange energy and other purposes.This work was supported by the National Science Foundation.     

The surface energy of an electron gas in model crystals

The surface energy of an electron gas in a crystal is considered. The results obtained for a quadratic spectrum are generalized to an arbitrary energy spectrum in certain crystal models. The surface energy of an electron gas with a quadratic spectrum is found for a sample with a rough boundary when the height of irregularities is small compared with the electron wavelength.