Study of the initial stage of yttrium oxidation using characteristic electron-energy-loss spectroscopy

The characteristic electron-energy-loss (EEL) spectra of the pure surface of metallic yttrium and of this surface in the initial stages of oxidation are recorded. The energy of the primary electron beam E _p is 200–1000 eV. The spectra exhibit high-and low-frequency peaks. During oxidation, the positions of the basic peaks in the EEL spectra are significantly shifted. The peaks corresponding to the bulk energy loss shift toward higher energies upon oxidation. The peak corresponding to the low-frequency surface oscillations also shifts, but toward lower energies, and its intensity monotonically decreases with increasing oxygen dose. The differences between the spectra recorded at different E _p are explained as resulting from an increase in the electron escape depth with E _p .     

Soliton dynamics in a spin nematic

One-dimensional localized waves, which can be considered as soliton elementary excitations, exist in a magnet with a unit spin and comparable bilinear and biquadratic spin-spin interactions, with which the state of spin nematic is realized. These excitations are characterized by a certain momentum P and a certain energy E. The structure of these solitons has been found, and the E = E(P) dependence, which plays the role of the dispersion law of these soliton elementary excitations, has been constructed. The energy of a soliton with a certain momentum is shown to be lower than that of the quasiparticles of a linear theory. At small momenta, these E = E(P) dependences of the soliton and quasiparticles coincide asymptotically. The dependence of the soliton energy on the soliton momentum is a periodic function with a period P ₀ = π?/a, whose value does not depend on exchange integrals and depends only on a single crystal parameter, namely, the interatomic distance a. These soliton excitations have common features with the so-called Lieb states, which are well known in many condensed matter models.     

Effect of the hexagonal warping on the dynamical conductivity of surface states in a topological insulator

We report on the effect of hexagonal warping on the dynamical conductivity of the surface states of a topological insulator in the presence of nonmagnetic impurities. It is found that the photon energy dependent conductivities are determined by a polarization-function-liked term,  Π₂ (q,ω), which contains a velocity term corresponding to the difference of group velocities between the two states due to an electron-impurity scattering. This is different from the conductivity of 2-dimentional electron systems where the conductivity depends on the inverse imaginary part of the dielectric function Im [1/κ(q,ω)]. We present both the real part and imaginary part of the polarization function with different warping strength. It is found that the warping strength can both enhance single particle excitations (SPEs) and suppress the screening effect of electrons. As a result the inverse scattering time is enhanced by up to about two orders of magnitudes. The real part of the longitudinal conductivity of the intra-band process is analog to the case with a conductivity of σ ~ μδ(ω). The broadening of the spectrum in the low energy is not only determined by chemical potential, but also dependent on the warping strength. At higher frequency, the real part of conductivity shows a jump at the threshold photon energy of μ, where the inter-band contribution takes over.     

Optical effects caused by coincidence between the energies of the plasma oscillations and the band-to-band transition in bismuth crystals doped with an acceptor impurity

The energy of plasma oscillations of free charge carriers in bismuth crystals ?ω_p can be qual to the band gap at the L point of the Brillouin zone E _gL as a result of doping with an acceptor impurity. Variation in the edge shape and splitting of the minimum in the plasma reflection are observed in experimental studies of reflection under normal incidence of radiation on the crystal. An analysis of the totality of available experimental data shows that the above special features are caused by interaction of elementary excitations (such as the plasma oscillations) with band-to-band transitions. It became possible for the first time to ascertain the composition of the bismuth crystals for which the condition ?ω_p=E _gL is satisfied and observe the variation in the characteristics of the plasma oscillations of free charge carriers, which occurs as a result of electron-plasmon interaction.     

Dynamical screening of AMM and QED effects for large-<Emphasis Type="Italic">Z</Emphasis> hydrogen-like atoms

The effective interaction ΔU_AMM of the anomalous magnetic moment (AMM) of an electron with the Coulomb field of an extended nucleus is analyzed. As soon as the q² dependence of the electron formfactor F₂(q²)is taken into account from the beginning, the AMM is found to be dynamically screened at small distances of r ? 1/m. The ΔU_AMM effects on the low-lying electronic levels of a superheavy extended nucleus with Zα > 1are analyzed using the nonperturbative approach. The growth rate of the ΔU_AMM contribution with increasing Z is shown to be essentially nonmonotonic. At the same time, the energy shifts of electronic levels in the vicinity of the threshold of the lower continuum monotonically decrease in the region Z ?Z_cr,1s. The latter result is generalized to the whole self-energy contribution to energy shifts of electronic levels, thus also referring to the possible behavior of QED radiative effects with virtual-photon exchange, considered beyond the framework of the perturbative expansion in Zα.     

Photoelectron Energy Loss in Al(002) Revisited: Retrieval of the Single Plasmon Loss Energy Distribution by a Fourier Transform Method

A Fourier transform (FT) algorithm is proposed to retrieve the energy loss function (ELF) of solid surfaces from experimental X-ray photoelectron spectra. The intensity measured over a broad energy range towards lower kinetic energies results from convolution of four spectral distributions: photoemission line shape, multiple plasmon loss probability, X-ray source line structure and Gaussian broadening of the photoelectron analyzer. The FT of the measured XPS spectrum, including the zero-loss peak and all inelastic scattering mechanisms, being a mathematical function of the respective FT of X-ray source, photoemission line shape, multiple plasmon loss function, and Gaussian broadening of the photoelectron analyzer, the proposed algorithm gives straightforward access to the bulk ELF and effective dielectric function of the solid, assuming identical ELF for intrinsic and extrinsic plasmon excitations. This method is applied to aluminum single crystal Al(002) where the photoemission line shape has been computed accurately beyond the Doniach–Sunjic approximation using the Mahan–Wertheim–Citrin approach which takes into account the density of states near the Fermi level; the only adjustable parameters are the singularity index and the broadening energy Г (inverse hole lifetime). After correction for surface plasmon excitations, the q-averaged bulk loss function, <Im[??1 / ε(E, q)]> _q , of Al(002) differs from the optical value Im[??1 / ε(E, q?=?0)] and is well described by the Lindhard–Mermin dispersion relation. A quality criterion of the inversion algorithm is given by the capability of observing weak interband transitions close to the zero-loss peak, namely at 0.65 and 1.65 eV in ε(E, q) as found in optical spectra and ab initio calculations of aluminum.     

Bond-breaking excitations with diverging coupling matrix of response density functional theory from highest-level functionals

Bond-breaking excitations ω _α are the problematic case of adiabatic time-dependent density functional theory (TDDFT). The calculated ω _α erroneously vanishes with the bond elongation, since the Hartree-exchange-correlation kernel and the corresponding response coupling matrix K of standard approximations lack the characteristic divergence in the dissociation limit. In this paper an approximation for K is proposed constructed from the highest-level functionals, in which both occupied and virtual Kohn-Sham orbitals participate with the weights w _p . The latter provide the correct divergence of K in the limit of dissociating two-electron bond. The present K brings a decisive contribution to the energy of the ¹Σ _u ⁺ in the prototype H₂ molecule calculated for various H-H separations. At shorter separations it improves ω _α compared to the zero-order TDDFT estimate, while at the largest separation it reproduces near-saturation of the reference excitation energy.     

Proximity effect of a superconductor on an antiferromagnetic metal

There should be two contributions to the pair breaking energy in an antiferromagnetic metal. The first, already discussed byde Gennes andSarma, is due to disorder on the magnetic sites. The second is a temperature dependent contribution from electron magnon scattering. This term is calculated for the temperature rangeT _N(J/μ)²?T?T _N and found to be of orderT ²/T _N. (T _N = Néel temperature,μ = Fermi energy,J = exchange coupling between conduction electrons and magnetic ions.)     

Plasmons in double quantum wells in a parallel magnetic field

Collective intraband charge-density excitations in the quasi-two-dimensional electron system of double GaAs/AlGaAs quantum wells in an external parallel magnetic field B_∥ are studied by inelastic light scattering. It has been found that the energy of the excitations under study (acoustic and optical plasmons) exhibits anisotropy depending on the mutual orientation of B_∥ and the excitation quasi-momentum k. It is shown theoretically that, in a strong parallel magnetic field, the effects associated with the finite width of the quantum wells dominate over the effects associated with interlayer tunneling and determine the anisotropy of plasmons. The experimental data are compared with a theoretical calculation.     

Investigation of zero-frequency solutions to the pion dispersion equation

The instability of nuclear matter is considered for the case where it is generated by the vanishing of the frequencies of collective excitations belonging to specific types (specifically, excitations that have the pion quantum numbers J ^π = 0^?). The behavior of zero-frequency solutions to the pion dispersion equation is analyzed versus the strength G′ of spin—isospin particle—hole interaction. It is shown that there exists a strength value G′_tr (|G′_tr| ? 1) such that, for G′ < G′_tr, zero-frequency solutions are excitations of the ω _P type, while, for G′ ≥ G′_tr, such solutions are excitations of the ω _c type. Excitations of the ω _P type for G′ < ?1 describe the instability of nuclear matter against small density fluctuations (Pomeranchuk’s instability), while excitations of the ω _c type are responsible for the instability associated with pion condensation at G′ ≈ 2. For stable nuclear matter, the solutions ω _P(κ) and ω _c (κ) lie on unphysical sheets of the complex plane of frequency.     

Electron–phonon heat exchange in quasi-two-dimensional nanolayers

We study the heat power P transferred between electrons and phonons in thin metallic films deposited on free-standing dielectric membranes. The temperature range is typically below 1 K, such that the wavelengths of the excited phonon modes in the system is large enough so that the picture of a quasi-two-dimensional phonon gas is applicable. Moreover, due to the quantization of the components of the electron wavevectors perpendicular to the metal film’s surface, the electrons spectrum forms also quasi two-dimensional sub-bands, as in a quantum well (QW). We describe in detail the contribution to the electron–phonon energy exchange of different electron scattering channels, as well as of different types of phonon modes. We find that heat flux oscillates strongly with thickness of the film d while having a much smoother variation with temperature (T _e for the electrons temperature and T _ph for the phonons temperature), so that one obtains a ridge-like landscape in the two coordinates, (d, T _e ) or (d, T _ph ), with crests and valleys aligned roughly parallel to the temperature axis. For the valley regions we find P ∝ T _e ^3.5 – T _ph ^3.5 . From valley to crest, P increases by more than one order of magnitude and on the crests P cannot be represented by a simple power law. The strong dependence of P on d is indicative of the formation of the QW state and can be useful in controlling the heat transfer between electrons and crystal lattice in nano-electronic devices. Nevertheless, due to the small value of the Fermi wavelength in metals, the surface imperfections of the metallic films can reduce the magnitude of the oscillations of P vs. d, so this effect might be easier to observe experimentally in doped semiconductors.     

“Negative” gap in the spectrum of localized states of (In<Subscript>2</Subscript>O<Subscript>3</Subscript>)<Subscript>0.9</Subscript>(SrO)<Subscript>0.1</Subscript>

The reflection R(?ω), transmission t(?ω), absorption α(?ω), and refraction n(?ω) spectra of polycrystalline In₂O₃–SrO samples with low optical transparency, which contain In₂O₃ and In₂SrO₄ crystallites with In₄SrO_{6 + δ} interlayers, are examined. In the region of small ?ω values, the reflection coefficient decreases as the resistance of samples saturated with oxygen increases. Spectral dependences n(?ω) and α(?ω) are calculated using the classical electrodynamics relations. The results are compared to the data based on the t(?ω) spectra. The calculated absorption spectra are interpreted within the model with an overlap of tails of the density of states in the valence band and in the conduction band. A “negative” gap E _gn in the density of states with a width from–0.12 to–0.47 eV is formed in highly disordered samples in this model. It is demonstrated that the high density of defects and the band of deep acceptor states of strontium in the major matrix In₂O₃ phase are crucial to tailing of the absorption edge and its shift toward lower energies. The direct gap E _gd = 1.3 eV corresponding to the In₂SrO₄ phase is determined. The energy band diagram and the contribution of tunneling, which reduces the threshold energy for interband optical transitions, are discussed.     

Europium luminescence in fluorite upon high-energy excitation

The reflection and luminescence excitation spectra of CaF₂ crystals containing europium ions in divalent (Eu²⁺) and trivalent (Eu³⁺) states were measured in the range from 4 to 16 eV. It was established that, in CaF₂ : Eu³⁺ crystals, luminescence of Eu³⁺ ions (the f-f transitions) is effectively excited both in the charge-transfer band (at ～8 eV) and in the region of the 4f–5d transitions (at ～10 eV) but is virtually not excited in the fundamental region of the crystal (at an energy higher than 10.5 eV). Luminescence of Eu²⁺ ions (the 427-nm band) in CaF₂ : Eu³⁺ is effectively excited in the fundamental region of the crystal; i.e., luminescence of divalent europium ions occurs through the trapping mechanism. Emission of Eu²⁺ ions in CaF₂ : Eu²⁺ crystals is characterized by the excitation band at an energy of 5.6 eV (the 4f → 5d,t _2g transitions), as well as by the exciton and interband luminescence excitations. The results obtained and data available in the literature are used to construct the energy level diagram with the basic electron transitions in the CaF₂ : Eu crystals.     

Method for determining the electron and positron work function from a metal containing vacancies

A method is proposed that combines self-consistent solutions for a monovacancy in metal without regard to the outer surface and the solution in the stable jelly model for metal with homogeneous volume and flat surface, but a lowered vacancy density due to the presence of a superlattice of vacancy voids with relative concentration c _v . When using c _v as a small parameter, all energy characteristics are expanded in a functional series. Zero expansion terms relate to defect-free metal, and linear in c _v corrections are expressed in terms of its characteristics. Exact formulas allowing the consideration of the effect of vacancies on the electron and positron work function are derived. Characteristics are calculated at various temperatures for Al and Na by the Kohn–Sham method. The method application to spherical clusters is briefly discussed.     

An approximate analysis of the diffraction losses in corner reflectors

The fundamental mechanism of energy loss from a Gaussian beam scattered by the edge of a corner reflector is considered. An independent calculation is performed to estimate the relative losses for different polarizations with allowance for the Goos-Hanchen shift effect. For the angle of incidence α = π/4, the relative energy losses by waves polarized along the reflector’s edge and normally to this direction are estimated at (W _dif/W _inc)_E ? 7.03(λ₀/a) and (W _dif/W _inc)_H ? 3.82(λ₀/a), respectively, where λ₀ is the wavelength in free space and a is the effective radius of the beam.     

Excitonic representation: Collective excitation spectra in the quantized Hall regime and spin biexciton

The excitonic representation method for describing collective excitations in the quantized Hall regime makes it possible to simplify analysis of the spectra and to obtain new results in the strong magnetic field limit, when E _C ??ω_c (ω_c is the cyclotron frequency and E_C is the characteristic Coulomb energy). For an integer odd filling factor ν greater than unity (i.e., for ν = 3, 5, 7,...), the spectra of one-cyclotron magneto-plasma excitations are calculated. For unit filling factor, the existence of a spin biexciton (bound state of two spin waves) corresponding to excitation with a spin change (δ_S = δ_Sz = ?2) is proved. The exact equation determining the ground state of the biexciton is derived in the thermodynamic limit N_Φ → ∞ (_N? is the system degeneracy). The exchange energy of this state is lower than for a single spin wave (with δ_S = δ_Sz = ?1) for the same value of the 2D wavevector q. In the limit q → ∞ corresponding to the decay of a biexciton into a pair of quasiparticles one of which is a trion with a spin of ?3/2, the energy is found to be lower than the energy (e²/εl _B )√π/2 required for exciting an electron-hole pair in the strictly 2D case (l_B is the magnetic length and ε is the dielectric constant), although this energy is higher than another “classical” result (e²/εl _B )√π/2, corresponding to the excitation of a skyrmion-antiskyrmion pair (|δS|=|δS _z |?1). The solution of the exact equation gives the trion binding energy and the activation gap for quasiparticles whose excitation corresponds to a change in the total spin by δS = δ S_z =?3. The energy of a spin biexciton is calculated for values of the wavevector such that ql _B ?1.     

Der Einfluß von Plasmawellen auf das Reflexionsvermögen von Metallen (I)

The wellknown derivation ofFresnel's formula for the reflection coefficient of a metal surface in the case of an oblique incident wave polarized parallel to the plane of incidence includes a mistake concerning the boundary conditions and neglecting the possibility of optical excitation of plasma waves. The right formula for this case is derived in the following paper byForstmann. The discussion of an approximate formula obtained by a simplified method leads in the case of vanishing reflectivity forΩ>Ω _p to a real Brewster-angleα _B . ForΩ<Ω _p there exists another solution with a complex Brewster-angle, representing a surface wave in form of a Zenneck-wave. For large wave numbers and for light velocity ? electron velocity the dispersion formula for these surface waves is nearly identical with that obtained byRitchie andWagner, while for small wave numbers there is a great difference between these two formulas. In the middle region the frequenceΩ is nearlyΩ _p /√2.     

On the Theory of Plasmon Dispersion in Electron-Doped Cuprates

An explicit expression for the dynamic charge susceptibility for electron-doped cuprates has been derived. This expression accurately reproduces the wave vector dependence of the plasmon frequency observed in inelastic X-ray scattering experiments for Nd_{2 – x}Ce_xCuO₄. The imaginary part of the charge susceptibility along the triangular path in the Brillouin zone is plotted. It is demonstrated that the spectral weight of the plasmon mode near q = 0 is negligibly low. The calculated frequencies of the plasmon mode for all wave vectors in the Brillouin zone turn out to lie outside the range of damping related to electron?hole excitations. A formula for the charge susceptibility is derived within the t?t′?t″?J model supplemented by the Coulomb interaction operator and three-site terms. The derivation is performed by the Green’s function technique employing the formalism of composite Hubbard operators and the Mori projection method, which have proved themselves in the analysis of collective spin excitations. The used Fourier transform of the Coulomb interaction corresponds to the monolayer model with a spatially periodic structure, which is embedded in a three-dimensional crystal lattice.