Electron Interaction in Solids. Characteristic Energy Loss Spectrum

Characteristic energy loss spectra of copper crystals with surfaces described by LEED

The characteristic energy loss spectra of electrons reflected from freshly evaporated Al and Cu specimens have been measured for various primary electron energies in the range 9-265 ev. Contrary to expectation the ratio of the intensity of the 10 ev surface plasma loss to that of the 15 ev volume loss in Al, for electrons scattered through 90°, is found to decrease with decreasing primary energy in the range from about 240 ev to 80 ev. This appears to be due to the behaviour of the surface loss, which decreases rapidly in intensity with decreasing primary energy. Both the surface and volume plasma losses of Al cease to be excited when the primary energy is less than about 26-29 ev, the surface loss cutting off at a slightly lower primary energy than the volume loss. The modified surface loss of Al resulting from oxidation of the specimen surface is observed at 7.1 ev, and the half-width of the 10 ev surface loss increases from 3.8 ev to 5.3 ev with increasing surface oxidation, indicating that the surface plasma oscillations are damped by the contamination. The energy losses of Cu have been investigated by observing their intensity dependence on (i) the primary electron energy for a fixed scattering angle of 90° and (ii) the electron scattering angle for various fixed primary energies, scattering angles of 90° and 20° being employed. The results indicate that a loss observed at 3.5 ev is possibly due to excitation of surface plasma oscillations.

This paper describes a simple and general method for deriving the inelastic collision term in the electron Boltzmann equation for scattering from a coupled electron-phonon system and applies the method to the case of doped polar semiconductors. In the Born approximation, the inelastic differential scattering rate ${\mathit{W}}^{\mathrm{inel}}$ can be expressed in terms of the nonequilibrium total dynamic dielectric function, which includes both electronic and lattice contributions. Within the random-phase approximation ${\mathit{W}}^{\mathrm{inel}}$ separates into two components: an electron-electron interaction containing the nonequilibrium distribution function for excitations of the electron gas and a Fr\"ohlich interaction including the phonon distribution function and self-energy due to polarization of the electrons. Each of these two interactions is screened by only the electronic part of the total dielectric function, which contains the high-frequency dielectric constant, unlike commonly used expressions that contain the static dielectric constant. The detailed balance between plasmons and electron-hole pairs in steady state is used to eliminate the non- equilibrium plasmon distribution from the Boltzmann equation, resulting in a dynamically screened electron-electron collision term. The phonon self-energy modifies the longitudinal optical-phonon dispersion so that two hybrid normal modes contribute to the electron-phonon collision term.

Reflectance data are presented for Si, Ge, GaP, GaAs, InAs, and InSb in the range of photon energies between 1.5 and 25 eV. The real and imaginary parts of the dielectric constant and the function describing the energy loss of fast electrons traversing the materials are deduced from the Kramers-Kronig relations. The results can be described in terms of interband transitions and plasma oscillations. A theory based on the frequency-dependent dielectric constant in the random phase approximation is presented and used to analyze these data above 12 eV, where the oscillator strengths coupling the valence and conduction bands are practically exhausted. The theory predicts and the experiments confirm essentially free electron-like behavior before the onset of $d$-band excitations and a plasma frequency modified from that of free electrons due to oscillator strength coupling between valence and $d$ bands and $d$-band screening effects. These complications are absent in Si. The energy loss functions obtained from optical and characteristic energy loss experiments are also found to be in good agreement. Arguments for interpreting structure in the reflectance curves above 16 eV in terms of $d$-band excitations are given.

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The work reported here, which deals with the influence of electron-electron interactions on the optical properties of metals, is motivated by existing discrepancies between the observed interband absorption and that calculated within the random-phase approximation (RPA). These interactions are treated systematically using a self-consistent conserving-approximation scheme. Both vertex and quasiparticle renormalization effects transcending the RPA are considered on an equal footing. Repeated first-order scattering of a quasielectron and a quasihole via the dynamically screened Coulomb interaction is the principal process investigated. The contributions are of two kinds: one associated with a statically screened Coulomb interaction and the other with exchange of virtual plasmons. The latter contribution, although larger than the former, is substantially cancelled, to within about 10% in Al, by quasiparticle dressing effects due to virtual plasmons. Those second-order effects in the dynamically screened interactions, whose inclusion guarantees a conserving approximation, are also negligible. Recent experimental data for Al are reviewed and new theoretical calculations within the RPA presented which appreciably reduce the existing discrepancies. These provide support for the present conclusion that electron-electron interactions do not significantly affect the optical absorption. Previous calculations for Na are discussed and the situation there may well be similar.

The boundary value problem for wave propagation on a cylindrical anisotropic rod has been solved for hybrid modes, i.e., those having angular dependence. Solutions for the rod radius, normalized by the free space wavelength, as a function of the phase velocity, are presented for various values of the transverse and longitudinal dielectric constants. When the rod is terminated by conducting end plates, a high <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Q</tex> microwave resonator results. The electric and magnetic energies stored in the rod have been calculated, as has the cavity <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Q</tex> . Experimental resonant frequencies for various modes in an <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">X</tex> -band cavity using a ruby laser rod are compared with theory.

A free-electron gas confined to a thin toroid is studied. Due to the cylindrical symmetry, the longitudinal angular momentum ( L ) is conserved in the electron-electron interactions. The Coulomb matrix elements, which satisfy the conservation of the transverse angular momentum ( J ), are much larger than the others. Therefore, the electronic excitations are well described by L and J . The L - and J -decoupled plasmons are investigated by evaluating the dielectric function within the random-phase approximation (RPA). They, respectively, correspond to the coherent plasma oscillations along the longitudinal and transverse directions. For the ( L , J =0) plasmons, the RPA results are almost the same with those of the Tomonaga model.

The characteristic electron energy loss spectra of the elements of the first group of transition metals, Ti to Cu, have been obtained using the reflection technique. In the spectrum of each metal one loss peak is identified as a plasma loss, and another, except in Ti and V, as a lowered plasma loss. Two other series of loss values are associated with ionization of the M1 and M2,3 shells, whilst a peak observed with most metals at about 5 ev loss could be ascribed to ionization of the M4,5 shell. Other losses have been interpreted as due to interband transitions, or as combinations or multiples of other loss values. The plasma loss values were found to agree with the theoretical values of hwp, assuming all 3d and 4s electrons to be `free', for the first elements of the series and then to fall below the predicted values.

The characteristic electron energy loss spectra of Na, K, Ca and Ba have been obtained using the reflection technique and primary electron energies of 800 and 1500 ev. All of the energy losses observed in these metals can be explained as arising from three types of loss mechanism, namely the excitation of plasma-type oscillations, electronic transitions involving excited states and ionization. Plasma excitation energies of 5.87 and 3.87 ev were observed in Na and K respectively, though the first plasma loss peak in the spectra of these metals was displaced from its expected position. The loss peaks in K, Ca and Ba which are considered to be associated with excited states have been related to a previously unexplained series of peaks in Ti, V and Cr, and a peak in Zr. The specific form of the excited state involved cannot be determined from this data alone, but evidence is presented which suggests that an intense broad peak of this nature will occur in the spectra of all the elements which immediately precede or are at the beginning of each of the series of transition metals in the periodic table of elements.

A review is presented of the longitudinal and transverse dielectric properties of KDP-type crystals. An extended pseudo-spin model of Blinc-de Gennes tunneling model is studied. The model is solved within the molecular field approximation and the four-cluster expansion. A detailed quantitative comparison is presented between the theoretical predictions and the experimental data for KH2PO4, KD2PO4 and varioius antiferroelectric ADP-type crystals. For KD2PO4, very good quantitative fit is obtained to the measured temperature dependence of the spontaneous polarization Pc , and the longitudinal and transverse dielectric constants ϵ c and e a for both the paraelectric and the ferroelectric regime with a single set of parameters e0 ≃ 92K, e1,=907K, γ = 37K and γ = 0 K. For KH2PO4, quantitative agreement is obtained with the data for ϵc and e a in the paraelectric regime with a single set of parameters e0 = 92 K, e1, = 900 K, γ = 53 K and Γ = 300 K. The antiferroelectric version of the extended pseudo-s...

A closed form for the dielectric function of a charged Bose gas is found in the random-phase approximation. This dielectric constant is used to explore the quasiparticle energy spectrum (i.e., the allowed modes of oscillation of the gas), the damping of these quasiparticles, and the long-ranged form of the electrostatic potential around a test charge in the gas. We do this around the three temperature regions of interest; namely, $T=0$, $T=\ensuremath{\infty}$, and $T={T}_{c}$, where ${T}_{c}$ is the transition temperature of the gas.

Biologically functional liquid–liquid phase separation of intrinsically disordered proteins (IDPs) is driven by interactions encoded by their amino acid sequences. Little is currently known about the molecular recognition mechanisms for distributing different IDP sequences into various cellular membraneless compartments. Pertinent physics was addressed recently by applying random-phase-approximation (RPA) polymer theory to electrostatics, which is a major energetic component governing IDP phase properties. RPA accounts for charge patterns and thus has advantages over Flory–Huggins (FH) and Overbeek–Voorn mean-field theories. To make progress toward deciphering the phase behaviors of multiple IDP sequences, the RPA formulation for one IDP species plus solvent is hereby extended to treat polyampholyte solutions containing two IDP species plus solvent. The new formulation generally allows for binary coexistence of two phases, each containing a different set of volume fractions for the two different IDP sequences. The asymmetry between the two predicted coexisting phases with regard to their ratios for the two sequences increases with increasing mismatch between their charge patterns. This finding points to a multivalent, stochastic, ‘fuzzy’ mode of molecular recognition that helps populate various IDP sequences differentially into separate phase compartments. An intuitive illustration of this trend is provided by FH models, whereby a hypothetical case of ternary coexistence is also explored. Augmentations of the present RPA theory with a relative permittivity that depends on IDP volume fraction lead to higher propensities to phase separate, in line with the case with one IDP species we studied previously. Notably, the cooperative, phase-separation-enhancing effects predicted by the prescriptions for we deem physically plausible are much more prominent than that entailed by common effective medium approximations based on Maxwell Garnett and Bruggeman mixing formulas. Ramifications of our findings on further theoretical development for IDP phase separation are discussed.

The spectrum of a photoexcited electron pair carries detailed information on the electron-electron interaction in metals. This is deduced from the results of a theoretical model presented here for the treatment of the double-photoelectron emission from surfaces. Main features in the two-particle spectra are assigned to (a) the exchange-correlation interaction, (b) the electronic band structure, (c) the photoelectron diffraction, and (d) the specific experimental setup. Comparison with experiments is made and common features and differences to the atomic case are pointed out.

We demonstrate that the plasmon frequency and Drude weight of the electron liquid in a doped graphene sheet are strongly renormalized by electron-electron interactions even in the long-wavelength limit. This effect is not captured by the Random Phase Approximation (RPA), commonly used to describe electron fluids and is due to coupling between the center of mass motion and the pseudospin degree of freedom of the graphene's massless Dirac fermions. Making use of diagrammatic perturbation theory to first order in the electron-electron interaction, we show that this coupling enhances both the plasmon frequency and the Drude weight relative to the RPA value. We also show that interactions are responsible for a significant enhancement of the optical conductivity at frequencies just above the absorption threshold. Our predictions can be checked by far-infrared spectroscopy or inelastic light scattering.