Location of direct transitions on the Λ line of the band structure of the noble metals using angle resolved photoelectron spectroscopy (ARUPS)

The triangulation method of angle-resolved photoemission for the absolute localization of direct transitions in k-space has been used on (110) and (111) faces in the ΓKLUX or (1$\text{1}$0) mirror plane in order to determine some points of the electronic bulk band structure of Cu, Ag and Au along the Λ line. It is found that the experimental points for the occupied bands and the unoccupied bands are in good agreement with recent ground state band structure calculations based on the local density functional theory.     

Intrinsic surface state on Be(0 0 0 1)

Using monochromatized synchrotron radiation in the range 24–30 eV, we have recorded angle-resolved photoemission spectra from a clean Be(0 0 0 1) crystal face. A surface state located in a band gap around Γ with an initial state energy of ?2.8 eV in normal emission was found. For k_∥ along the $\text{Γ}$$\text{M}$ line the surface state disperses upwards and passes E_F at about 55% of the distance to the surface Brillouin zone boundary.     

Addendum

Accurate valence band dispersions E$\text{k}$ of LaB₆ have been determined along three main symmetry lines ΓM, ΓX, and XM using one single crystal (001) surface by a simple new photoemission technique of general utility. Using direct interband transitions, E$\text{k}$dispersions are mapped out by suitably scanning polar emission angle and the photon energy. Detailed results agree well with recent Xα-APW energy band calculations.     

Angular resolved photoemission from intrinsic surface states on Al (100)

Using photon energies of 11.7, 16.8 and 21.2 eV, we have recorded angular resolved photoemission spectra from clean Al (100). A dominant, surface sensitive peak is interpreted as emission from a two-dimensional band of surface states. The band mass is $\text{m}{}^1\text{=(1.03±0.10)m}$, and the band minimum, (2.8±0.2) eV below E_F for surface momentum k₆=0, is located within the bulk band gap. The observed existence of the peak for large values of k₆, indicates a transition from a true surface state to a surface resonance.     

Experimental band structure E(kr) of V3Si by angle-resolved photoemission

Band dispersions E($\text{k}$) and critical points of V₃Si have been determined by $\text{k}$-selective angle-resolved photoemission with synchrotron radiation. A V-3d band (Δ_1,2) which is very close to E_F at Γ (Γ₁₂) has been observed which is very flat near Γ along the ΓX direction, in agreement with recent APW calculations. Critical points of valence bands as well as their orbital character and density of states features have been determined.     

Long-wavelength excitations in a Bose gas at zero temperature

The long-wavelength excitations in a simple model of a dilute Bose gas at zero temperature are investigated from a purely microscopic viewpoint. The role of the interaction and the effects of the condensate are emphasized in a dielectric formulation, in which the response functions are expressed in terms of regular functions that do not involve an isolated single-interaction line nor an isolated single-particle line. Local number conservation is incorporated into the formulation by the generalized Ward identities, which are used to express the regular functions involving the density in terms of regular functions involving the longitudinal current. A perturbation expansion is then developed for the regular functions, producing to a given order in the perturbation expansion an elementary excitation spectrum without a gap and simultaneously response functions that obey local number conservation and related sum rules.Explicit results to the first order beyond the Bogoliubov approximation in a simple one-parameter model are obtained for the elementary excitation spectrum ω_k, the dynamic structure function $\text{S}$(k, ω), the associated structure function $\text{S}$_m(k), and the one-particle spectral function $\text{A}$(k, ω), as functions of the wavevector k and frequency ω. These results display the sharing of the gapless spectrum ω_k by the various response functions and are used to confirm that the sum rules of interest are satisfied. It is shown that ω_k and some of the $\text{S}$_m(k) are not analytic functions of k in the long wavelength limit. The dynamic structure function $\text{S}$(k, ω) can be conveniently separated into three parts: a one-phonon term which exhausts the f sum rule, a backflow term, and a background term. The backflow contribution to the static structure function $\text{S}$₀(k) leads to the breakdown of the one-phonon Feynman relation at order k³. Both $\text{S}$(k, ω) and $\text{A}$(k, ω) display broad backgrounds because of two-phonon excitations. Simple arguments are given to indicate that some of the qualitative features found for various physical quantities in the first-order model calculation might also be found in superfluid helium.     

Surface energy bands observed in photoemission from a (1 × 1)-N structure on Cr (100)

The surface structure obtained on Cr (100) by diffusion of nitrogen from the bulk is studied by angle resolved photoemission. It is found that nitrogen is bonded in an ordered (1 × 1) configuration with a crystallographic point group C_4v. The data display a strongly dispersive two dimensional Bloch character for the N2p derived resonances. For these bands the symmetry at the $\text{Γ}$ point and the dispersion along the $\text{Δ}$ and $\text{Σ}$ lines of the surface Brillouin zone are determined. The results indicate a strong interaction of the nitrogen atoms with the substrate and favor the intersticial fourfold hollow position.     

States on the current algebra

We introduce the field algebra Σ$\text{D}$(M;ⁿ?ⁿ$\text{g}$) associated with the current algebra $\text{D}$_r(M;$\text{g}$) for the Lie algebra $\text{g}$ over physical space M. The Heisenberg magnet model is generalized to this continuum. It is shown that the Hamiltonian can be given meaning as implementing a derivation of the field algebra in certain representations.We introduce new representations of the current algebra. For example, if G = SU(2), a representation in L²(R³)?³ is [σ(?)F]^j = ε^jkl?_kψ_l for (?_k) = ? in $\text{D}$_r(M;$\text{g}$)(ψ_l = F. This has cyclic subrepresentations with prime parts.     

Coherent and incoherent laser spectroscopy of spatial and temporal fluctuations

Information on spatial and temporal fluctuations of the transition frequency is theoretically shown to be obtained from transient four-wave mixing (FWM) at $\text{k}\text{=2}\text{k}{}_1\text{?}\text{k}{}_2$ or $\text{2}\text{k}{}_2\text{?}\text{k}{}_1$ under coherent excitation by two laser pulses with wave vectors k₁ and k₂. The same information is available from the FWM by two CW incoherent laser beams k₁ and k₂ split off from a single source as a function of the relative delay time. In these cases, we can select a specified diagram for the FWM which depends on double sites. This makes it possible to observe the spatial fluctuations in addition to the temporal ones.     

Theory of electron states at random alloy surfaces - surface states on Cu-Ni (111)

We present first principles calculations (based on the KKRCPA) of the angle-resolved photocurrent emitted from the (111) surfaces of single crystals of $\text{Cu}$-Ni random alloys, and compare the results with new experimental data. Surface states close to the Fermi level are observed, even for concentrated alloys, and their behaviour as a function of composition and $\text{k}$_∥ is correlated with features in the bulk spectral density. Calculations for alloys with a non-uniform concentration profile at the surface (surface segregation) are described, and the effect on the surface states is discussed.     

Optical transitions on GaAs [110] surface

Modulation techniques have been employed in optical reflection measurements on GaAs [110] cleaved surface. Spectral bands at 2.62 and 2.83 eV observed for the light polarization $\text{E6[}\text{1}\text{10]}$ have been assigned to the surface state transitions. The E₁ and E₁ + Δ₁ bulk transitions were found to be sensitive to the surface conditions.     

Pionic and radiative decay widths of charmed hadrons in a badly broken SU(4) symmetry

The width of ψ(4.414) is surprisingly small for a c$\text{c}$ state far above the charm threshold, Γ_exp ≈ 33 MeV. This fact can be qualitatively understood if one makes the conservative assignment 4 ³S₁. The nodes of the wave function reflect as zero's of the decay amplitude in the momentum of the decay products, and are responsible for the suppression of the couplings to the ground state charmed mesons, Γ(ψ(4.414)→D$\text{D}$+ D$\text{D}$¹ + $\text{D}$D¹ + D¹$\text{D}$¹ + F$\text{F}$ + F$\text{F}$¹ + $\text{F}$F¹ + F¹$\text{F}$¹) ≈ 15 MeV. All the modes are suppressed by factors of the order of 10³ with respect to the k³ spin counting prediction. The dominant modes are predicted to be D¹$\text{D}$¹, F$\text{F}$¹ + $\text{F}$F¹ and D$\text{D}$. Moreover, we show that the contributions from P-wave charmed mesons are reasonably expected to be suppressed either by phase space or by the nodes if their masses lie within certain range. We emphasize however that the smallness of the photon coupling remains to be understood.     

Modelling of kink nucleation and propagation along steps of finite length

A discrete model for kink nucleation and propagation along steps of finite length is developed. The step velocities were calculated as a function of the step length, the first order rate constants, k_s and k_K, for kink nucleation and propagation respectively, and a kink interaction parameter. The two limiting kinetic regimes of short and long steps as well as the intermediate transitional regime were considered. For very short steps, S² ? $\text{k}{}_{\mathrm{<mtext>K</mtext>}}\text{k}{}_{\mathrm{<mtext>s</mtext>}}$, the velocity varied directly with the number of sites S. Steps which met the criterion S² ? $\text{k}{}_{\mathrm{<mtext>K</mtext>}}\text{k}{}_{\mathrm{<mtext>s</mtext>}}$, were shown to have velocities on the order (2k_Kk_s)^{$\text{1}\text{2}$}, independent of step length. Step velocities were constant over large ranges of the kink interaction parameter. The steps were shown to be “sharp” for zero or attractive kink interaction, but with sufficiently large kink repulsion very diffuse steps could be formed. The density of kinks and numbers of kinks nucleated along an atom row were also calculated.     

Multidimensional elastic waves excited by oscillating domain walls

Magnetoelastic excitations with a fine structure in the 50kHz range have been observed in the study of the domain wall resonance (DWR) in magnetic garnet thin films. DWR excites standing transverse elastic waves which have a resonance frequency given by $\text{f=}\text{nv}\text{2d}$, where f is the frequency, n is an integer, v=3.5×10⁵ cm/sec is the transversal velocity of the elastic wave, and d=0.05 cm is thickness of the film/substrate system. A fine structure associated with each of these modes has been identified as due to two dimensional bulk elastic waves by using a set of parallel microstrip lines. The dispersion relation of these elastic waves is ω²=v²(k²₁+k²₂), where ω is the radial frequency, k₁ and k₂ are the wave vectors in the orientation perpendicular and parallel to the sample surface respectively. In the case of k₁?k₂, $\text{f=}\text{f}{}_0\text{+v}{}^2\text{k}{}^2{}_2\text{f}{}_0$, where f₀ is the resonance when k₂=0. The experimental results are in excellent agreement with this model. A linear dispersion, observed when using a shorted slot-line structure, is understood as the excitation of three dimensional modes due to the complex structure of the slot-line and the sample geometry.     

Angular momentum decomposition of k = 0 Bloch functions in group IV and zincblende crystals

The angular momentum contents of $\text{k}\text{= 0}$ Bloch functions for a number of group IV and zincblende crystals are examined using a pseudopotential approach. The large amplitudes for d and f character functions found even for valence electron wave functions are related to the overlap of p and s symmetry states on different atoms. In zincblende crystals the strength of the d and f components increases around cations and decreases around anions for the valence bands. The f-like component is appreciable for the Γ₁ conduction band particularly around a cation.     

Atom-surface scattering with velocity-selected H and D atomic beams from LiF and NaF (001)

Hydrogen and deuterium atoms with an energy between 20 and 140 meV have been scattered from LiF and NaF (001) cleavage planes in UHV. The atomic beam was nearly monoenergetic by use of a slotted disk type velocity selector with a velocity resolution of $\text{Δv}\text{v}\text{=12\%}$ (FWHM). The scattering showed diffraction with a pronounced specular beam. The energies of several bound surface states have been determined by analysis of selective adsorption minima. These energies together with relative intensities of diffracted beams and specular intensity versus incident energy measurements may be represented by an interaction potential of Morse-type with additional terms which are periodic parallel to the surface. The parameters of the Morse-potential have been found to be: depth D=17.8 meV and reciprocal range $\text{κ=1.04}\text{A}\text{?}{}^{\mathrm{?1}}$ for H₁/LiF (001) and D = 17.9 meV, k = 1.15 Å^?1 for H₁/NaF (001); the additional periodic terms have relative strength β₁₀=0.04 and $\text{β}{}_{11}\text{≈}\text{β}{}_{10}\text{2}$ in the case of H ₁/LiF, but β₁₁≈β₁₀=0.03 in the case of H₁/NaF. From the observed influence of surface temperature on the position of selective adsorption minima the coefficient of thermal expansion of the topmost surface layer turns out to be approximately twice the bulk value.     

Neutron diffraction studies of the magnetic ordering in the rare earth compounds TbNi2Si2, HoCo2Si2 and TbCo2Si2

Neutron diffraction studies and magnetic measurements on the compounds TbNi₂Si₂ (1), HoCo₂Si₂ (2) and TbCo₂Si₂ (3) revealed a collinear antiferromagnetic order below T_N = 10 ± 1 K (1), T_N = 13 ± 1 K (2) and T_N = 30 ± 2 K (3) with the rare earths moments oriented along the c-axis [m₀ = 8.8 ± 0.2 μ_B (1), m₀ = 8.1 ± 0.2 μ_B (2), m₀ = 8.8 ± 0.2 μ_B (3)] and the corresponding wavevector are $\text{k}\text{= [}\text{1}\text{2}\text{1}\text{2}\text{0] (1)}\text{and}\text{k}\text{= [ 0 0 1] (2) (3)}$. The magnetic structure of the compounds HoCo₂Si₂ and TbCo₂Si₂ consists of ferromagnetic layers perpendicular to the c-axis coupled antiferromagnetically (+?+?) while for TbNi₂Si₂ the ordering within (0 0 1) plane is antiferromagnetic and the planes (0 0 1) are indeed decoupled.     

Eigenfunction expansions of operators admitting separation of an infinite number of variables

Let A_k be a self-adjoint operator in a Hilbert space H_k (k = 1, 2, …) and let $\text{L}$ be an operator of the form $\text{L}\text{= A}{}_{\mathrm{r}}\text{? 1 ? 1 ? … + 1 ? A}{}_2\text{? 1 ? 1 ? … + …}$ acting in the infinite tensor product $\text{?}\text{k=1}\text{∞}\text{H}{}_{\mathrm{k}}$. We construct the spectral theory of these operators. In particular, the expansion is generalized eigenvectors of this operator is constructed using the eigenvectors of the operators A_k.