Plasmon Branches Research Articles

Exchange effects in the plasmon dispersion of one-dimensional systems

The dynamic exchange decoupling method for including exchange in the dielectric function of the homogeneous electron gas has been extended to one-dimensional systems, in both the free-electron and the tight-binding limit. In the free-electron model, the slope of the plasmon branch is almost unaffected by exchange effects. In the tight-binding model, the exchange interaction appreciably lowers this slope, except if the band is almost filled.

Dispersion of surface plasmons in inhomogeneous media. II.

In a revision of an earlier calculation of surface-plasmon dispersion for an interface between a homogeneous medium and an inhomogeneous one with exponentially varying dielectric function $\ensuremath{\epsilon}$, Guidotti and Rice claim to have proven the existence of a second plasmon branch. Their new dispersion relation is incorrect, however. A second plasmon branch should exist for an inhomogeneity that involves a discontinuity, but need not exist for the continuous $\ensuremath{\epsilon}$ assumed by them.

Exchange effects in the plasmon dispersion of one-dimensional systems

The influence of the exchange interaction on the plasmon dispersion in one-dimensional model systems has been studied by applying the dynamical exchange decoupling method. In a tight-binding model, the exchange effects result in a decrease of the slope of the plasmon branch for nearly half filled bands, and can even yield a negative dispersion.

Plasmons in a quasi-one-dimensional metal in the random-phase and screened-Hartree-Fock approximations

We consider plasmons in a lattice with chain structure. The electrons are treated in a one-band tight-binding model. From the corresponding longitudinal dielectric matrix ${\ensuremath{\epsilon}}_{G{G}^{\ensuremath{'}}}(q\ensuremath{\omega})$ the plasmon dispersion is determined in the random-phase approximation and in the screened-Hartree-Fock approximation. In comparing these results we find a remarkable decrease of the short-wavelength part of the plasmon dispersion relative to the long-wavelength limit, caused by the exchange corrections. The inclusion of overlap matrix elements is important for bands which are not half-filled. Furthermore, this inclusion of overlap is a necessary but not sufficient precondition for the existence of a second acoustical plasmon branch in our model.

Fluorescence lifetime of a molecule near a diffuse surface: Coupling to surface polaritons

For surfaces in which the electron density does not drop abruptly from its bulk value to zero, the spectrum of surface polaritons includes, besides the usual plasmon branch, additional branches, referred to as higher multipoles. The complete spectrum of polaritons is given for a simple two-step model of a surface. The coupling of these modes to an excited fluorescent molecule located near the surface is discussed. The change in the width of the molecular transition, due to decay via the surface polariton channels, should reflect the structure in the density of surface polariton states.

The influence of local‐field corrections on the collective behaviour of the homogeneous electron gas

AbstractThe dynamic structure factor of the electron gas is studied using different static local‐field corrections, and a comparison is made with the Hartree approximation. The plasmon dispersion relation is rather insensitive to the approximations used. However, the relative contributions of the plasmon branch and the pair creation region change substantially from one approximation to the other. This point is investigated by a Kramers‐Kronig analysis of the different approximations.

Theory of a condensed charged-bose, charged-fermi gas

Field-theoretic methods are used to derive the low-temperature properties of a dense, neutral gas of condensed charged (+Ze) bosons (mass M) and degenerate charged (− e) fermions (mass m). The density-density correlation function exhibits two collective modes for m ⪡ M: a plasmon branch and a phonon branch with speed c = V F( Zm 3M ) 1 2 . Boson single-particle excitations are gapless and coincide with the phonon mode at low k. Inclusion of the two interacting dynamical components leads to small shifts in the boson and fermion ground-state energy and boson depletion relative to the values obtained for models with rigid, inert, neutralizing backgrounds.

Surface plasmons in liquid mercury: Propagation in a nonuniform transition layer

We have examined the propagation of nonradiative surface plasmons in the presence of an inhomogeneous transition zone in the surface region of a conductor. The model we treat in the present paper is the Epstein stratified conductivity profile that has been proposed by Bloch and Rice for liquid mercury. Assuming that photon-plasmon coupling occurs through frustrated total reflection, we evaluate the optical response of mercury to surface-plasmon excitation and find it to be sensitive to the existence of such a zone. Measurements of the dispersion relation should, therefore, provide valuable information regarding the range and degree of such electronic inhomogeneity; preliminary measurements are in good agreement with the theory (Sec. VI). In addition to inhomogeneity in the conductivity of nearly-free electrons in the liquid metal, we have also investigated the effect of the localized resonances near the surface, and we speculate under what conditions the surface-plasmon dispersion relation may exhibit "anomalous dispersion" due to plasmon-localized-state interaction. Finally, the existence of an upper plasmon branch induced by the inhomogeneity is treated. In general, the results of the present investigation suggest that optical surface-plasmon spectroscopy should be a useful technique for the study of nonuniform conducting surfaces.

Electrodynamics of a layered electron gas. II. Periodic array

A hydrodynamic model is used to study the electrodynamics of a layered electron gas arranged in a periodic array and neutralized by a rigid inert positive background. The plasma oscillations differ qualitatively from those in a bulk three-dimension medium; the corresponding dielectric function and dynamic conductivity are evaluated. Static screening of a point charge displays considerable anisotropy. A generalized model with a compressible background yields a spectrum containing an acoustic branch in addition to the optical (plasmon) branch.

Collective excitations of the polaron-gas

The dispersion of the collective excitations of a polaron-gas is calculated. It is found that the interaction between the L.O. phonons and the plasmons induces a relatively strong wave vector dependence in the ω +, ω - modes. This dispersion is primarily a consequence of the interaction of the L.O. phonons with the resonant plasmon branch in the pair excitation spectrum.

Plasmons propagating in periodic lattices and their dispersion

Starting from the equation of motion for the electron density in terms of the momentum flux density, a non-local r space theory is developed for describing the propagation of plasmons in a periodic lattice. The theory is valid for long wavelengths, and is shown to yield correct results for the dispersion relation w(k) for a uniform electron gas in the high density limit, to order k 2 , k being the wavenumber. By using a local density approximation, corrected by higher order terms involving gradients of the density, the non-local equation for the density change can be expressed explicitly in terms of the periodic lattice density. The way in which the dispersion relation w(k) can be obtained around k = 0 in the various plasmon branches is discussed, a method paralleling the Wigner-Seitz theory in electronic energy band structure being proposed. Numerical calculations are planned within such a spherical cell model. The connexion with Bloch’s hydrodynamic model of collective oscillations is finally discussed.

Plasmon Excitation Spectra for an Electron Gas with an Energy Gap

The plasmon excitation spectrum of an electron gas in a real crystal is analyzed in the random-phase approximation without exchange for the weak-binding case. The features of this spectrum are studied as a function of energy gap and electron density. Several plasmon branches, which do not always go down to $q=0$, appear with increasing energy gap and with the filling of the valence band. The contribution of normal and umklapp processes to the behavior of the real part of the dielectric constant is analyzed and correlated with a phenomenological model.