Surface free energies of solid metals: Estimation from liquid surface tension measurements

An equation is derived on semi-theoretical grounds which expresses the solid-vapour surface free energy as a function of the liquid surface tension and the solid-liquid interfacial free energy. A means of calculating reliable values for the solid-liquid energy is presented, which then allows an accurate estimate of solid surface energy at the melting temperature, T_m, to be made for the large number of elements for which dependable liquid surface tension data exist. A method of estimating surface entropy is presented, and has been used to calculate the energies typical of “average”, high-index surfaces at temperatures ranging from 0 K to T_m. It is felt that this paper describes the most accurate method presently available for the calculation of the surface energy of solids in the absence of direct experimental measurement.     

Electronic Structure of FeSe Monolayer Superconductors: Shallow Bands and Correlations

Electronic spectra of typical single FeSe layer superconductor—FeSe monolayer film on SrTiO₃ substrate (FeSe/STO) obtained from ARPES data reveal several puzzles: what is the origin of shallow and the so called “replica” bands near the M-point and why the hole-like Fermi surfaces near the Γ-point are absent. Our extensive LDA+DMFT calculations show that correlation effects on Fe-3d states can almost quantitatively reproduce rather complicated band structure, which is observed in ARPES, in close vicinity of the Fermi level for FeSe/STO. Rather unusual shallow electron-like bands around the M-point in the Brillouin zone are well reproduced. Detailed analysis of the theoretical and experimental quasiparticle bands with respect to their origin and orbital composition is performed. It is shown that for FeSe/STO system the LDA calculated Fe-3d _xy band, renormalized by electronic correlations within DMFT gives the quasiparticle band almost exactly in the energy region of the experimentally observed “replica” quasiparticle band at the Mpoint. However, correlation effects alone are apparently insufficient to eliminate the hole-like Fermi surfaces around the Γ-point, which are not observed in most ARPES experiments. The Fermi surfaces remain here even if Coulomb and/or Hund interaction strengths are increased while overall agreement with ARPES worsens. Increase of number of electrons also does not lead to vanishing of this Fermi surface and makes agreement of LDA+DMFT results with ARPES data much worse. We also present some simple estimates of “forward scattering” electron-optical phonon interaction at FeSe/STO interface, showing that it is apparently irrelevant for the formation of “replica” band in this system and significant increase of superconducting T _c .     

États de surface du sodium dans l'approximation des électrons quasi-libres

Electron states located near a (110) surface of a Na crystal are investigated by the method of matching the crystal wave function to the outside solution at the surface. The lower energetic states are in the fundamental state. An “anormal” optical band situated about 1.8 eV is discussed when the imaginary part of the dielectric function ?₂ has been determinated considering transitions with the k-vector component parallel to the surface.     

Scanning tunneling microscopy of the nonequilibrium interaction of impurity states at semiconductor surfaces

Interaction of two localized impurity states of Si atoms at a GaAs surface was studied by scanning tunneling microscopy and spectroscopy. The effects of a twofold “switching” on and off of the states of each of the interacting atoms, the tunneling-interaction-induced mutual level pulling of these states, and the level stabilization near E _F were observed. These effects are explained in terms of the extended Anderson model.     

Defects at surfaces and interfaces — A scattering theoretical approach

A theory for isolated defects at surfaces and interfaces of semiinfinite solids is presented and applied to vacancies at or near surfaces. Vacancy-induced changes in the surface electronic structure of a simple cubic s-band model are discussed in detail and are found to converge very slowly to corresponding bulk vacancy results when the defect is moved into the solid. Results for Ga and As vacancies at GaAs surfaces are discussed in connection with recent experimental data.     

Surface photovoltage spectroscopy and surface piezoelectric effect in GaAs

“Real” (111) surfaces of n-type GaAs were investigated employing surface photovoltage spectroscopy and the surface piezoelectric effect. Surface states at the energy position E_c ? E_t ? 0.72 eV were found on both the Ga and the As surfaces. Both types of surfaces exhibited a barrier of about 0.55 V. No variations in the surface barrier or the energy position of the surface states were observed in various ambients at atmospheric pressure (dry air, wet air, ammonia and ozone). However, the capture cross-section of the surface states for electrons, as determined from the surface piezoelectric effect transients (of the order of 10^?13 cm²), was found to be sensitive to the ambient. It decreased in wet air and increased in ozone. This effect was more pronounced on the As than on the Ga surfaces. Additional surface states were found to be present in the energy region of 0.9 to 1.0 eV, below the bottom of the conduction band. However, their exact energy positions could not be determined due to interference caused by the carrier trapping of the surface states at E_c ? E_t ? 0.72 eV.     

Nonlinear interference in a mean-field quantum model

Using similar nonlinear stationary mean-field models for both a 2D axisymmetricalBose-Einstein Condensate and an electron pair in a parabolic trap, we propose to describethe original many-particle ground state as a one-particle mixed state (in contrast to apure state), i.e. as a statistical ensemble of several one-particle quantum states. Thesequantum states are the eigenfunctions of the corresponding stationary nonlinearSchrödinger equation (hence called “nonlinear eigenstates”). Due to their nonlinearity,they are not orthogonal. Therefore, taking the simple example of a two-level system, weshow that each of these two nonlinear eigenstates |i? and|j? occurs with a probability (or statistical weight) that isdefined by their non-orthogonality ?i|j? 0. We givethe corresponding density matrix. We search for physical grounds in the interpretation ofour two main results, namely, a quantum-classical nonlinear transition and theinterference between two “nonlinear eigenstates”.     

Can the Bogoliubov–de Gennes equation be interpreted as a ‘one-particle’ wave equation?

The solutions of the Bogoliubov–de Gennes (BdG) equation are usually interpreted as the excitations from the superconducting ground state. This viewpoint is not easily applied to a strongly coupled heterojunction since the ground state changes across the interface and it is not clear how the ground state should be connected across the heterointerface. In this paper, we present a different viewpoint that does not suffer from this conceptual drawback. We show that the BdG equation can be viewed as a ‘one-particle’ wave equation whose eigenstates (including the negative energy states) can be filled up systematically to describe the superconducting state, in much the same way that we fill the eigenstates of the Schrödinger equation to describe normal conductors. The only difference is that we need to start from a special vacuum | V〉, consisting of a full band of down-spin electrons, instead of the usual vacuum devoid of all particles. Any quantity of interest, A (such as the charge density or the current density), can be interpreted as the sum of a ‘vacuum contribution’A_{V AC}due to the vacuum | V〉 and a one-particle contribution A_BdGdue to the filled eigenstates of the BdG equation. This picture is easily applied even to strongly coupled heterojunctions since the vacuum | V〉 is the same on both sides of a heterointerface. As such, we believe it puts the scattering theory of transport for superconductors on a firmer conceptual basis.     

Itinerant electron surface magnetism

Although many experiments have been applied to study the surface magnetism, only a few give a direct and unambiguous answer to a so simple question as “what is the value of the surface magnetic moment”. Some examples of all these experiments are reviewed to show the main differences between two- and three-dimensional magnetism. Then we show that the magnetic moment can be enhanced near the surface in itinerant electron magnetism. This may be the case of He₃ atoms in confined geometries, or of transition metal surfaces or more generally when the local surface density of states at the Fermi level is much larger than the bulk one.     

X-ray and UV photoelectron-spectroscopic studies of pyridine adsorbed on evaporated nickel and palladium in the temperature range 140–385 k

The states of pyridine adsorbed on evaporated nickel and palladium films have been investigated as a function of temperature in the range 140–385 K by means of X-ray and UV photoelectron spectroscopy. At ～ 140 K, pyridine “N-bonded” on the metal surfaces gives C 1s and N 1s peaks whose binding energies are very close to those for condensed pyridine and “N-bonded” pyridine on pre-oxidized nickel. The high-lying valence orbitals, 2b₁ (π) and 1a₂ (π) + 7a₁ (n), of pyridine show shifts similar to those for the “N-bonded” molecule on pre-oxidized nickel. At ～ 290 K, “π-bonded” pyridine shows large shifts in the C 1s and N 1s peaks and in the high-lying valence orbitals, as observed for “π-bonded” benzene on nickel. The assignments of the adsorbed states are supported by work-function change data. A large proportion of pyridine converts from the “N-bonded” to the “π-bonded” form between 220 and 290 K. Formation of “α-pyridyl” is suggested at ～ 375 K on nickel.     

Geometry of two dimensional tori in phase space: Projections,sections and the Wigner function

The invariant manifolds (or “classical eigenstates”) in the phase space of bound integrable dynamical systems are known to be tori. Sections and projections of general, and special, two dimensional tori in four dimensional phase space are considered. Particular attention is paid to the families of projections accessed by linear canonical transformation since these can (in a certain sense) be considered to be different views of the same torus. The Wigner phase space representation of the corresponding semiclassical quantum eigenstate for a torus of any dimensionality is examined following the analysis of M. V. Berry (Phil. Trans. Roy. Soc.287 (1977), 237) for one dimensional tori. In this, the value of the semiclassical Wigner function at any phase space point depends on the behaviour of the chords of the torus centred on that point. It is found that for a two dimensional torus the number of such chords is always even. The three dimensional surfaces across which the number of chords changes constitute a (double) fold catastrophe on which the function oscillates with large amplitude. On the torus manifold itself this “Wigner caustic” generally exhibits a hyperbolic umbilic singularity (possibly interspersed with elliptic regions). At special lines and points on the torus, however, higher catastrophes up to E₈ are generic.     

Study of Ag/Si(111) submonolayer interface: I. Electronic structure by angle-resolved UPS

Angle-resolved ultraviolet photoelectron spectra have been measured for well defined Ag/Si(111) submonolayer interfaces of (1) $\text{Si(111)(}\text{3}\text{×}\text{3}\text{)R30°-Ag}$, (2) “Si(111)(6 × 1)-Ag”, and (3) Ag/Si(111) as deposited at room temperature. Non-dispersive and very narrow (FWHM ～ 0.4–0.5 eV) Ag 4d derived peaks are found at 5.6 and 6.5 eV below the Fermi level for surface (1) and at 5.3 and 6.0 eV for surface (2). Dispersions of sp “binding” states in the energy range between E_F and Ag 4d states have been precisely determined for surface (1). Electronic structures similar to those of the Ag(111) surface, including the surface state near E_F, have been observed for surface (3).     

Surface studies by modulation spectroscopy

Surface barrier and electronic surface states are important parameters for characterizing semiconductor surfaces. Qualitative information on the surface electric field can be deduced from electroreflectance studies. Energetic positions of surface states have been determined by spectroscopic methods using effect modulation techniques. Besides the field effects of surface conductivity and absorption, which are limited to low densities of surface states, new information on surface states was gained by investigating the spectral dependence of surface photoconductivity. Also surface phonons were detected in “spectral oscillations” of photoconductivity. The measurement of surface photovoltage at photon energies where the bulk is transparent promises a new tool for surface state research in the future. To demonstrate these modulation techniques examples are given for Ge, Si, ZnO, and CdS surfaces.     

Effective surface potential method for calculating surface states

A novel formalism (the effective surface potential method) is developed for calculating surface states. Like the Green function method of Kalkstein and Soven and the transfer matrix method of Falicov and Yndurain, the technique is exact for simple tight binding Hamiltonians. As well as offering an alternative viewpoint, the present method provides a simple analytic expression describing the surface states. At each point k_s in the surface Brillouin zone the semi-infinite solid is viewed as an effective linear chain where each element of the chain is a planar layer. The solution to the linear chain problem can be expressed in terms of an effective potential h(k_s,E) at each energy E. A number of examples are presented in detail; “sp^d” Hamiltonians for a linear chain (d = 1), the honeycomb lattice (d = 2), the 111 surface of silicon (d = 3), and a dissected Bethe lattice. Various exact results are given, e.g. the extremities of surface state bands and the surface density of states of p-like (delta function) bands. The results of Kalkstein and Soven for the 100 surface of a simple cubic solid with a perturbation on the surface layer are rederived.     

Theoretical study of the chemisorption of H2 on boron cluster surfaces

“Ab initio” RHF calculations are used to investigate the chemisorption of a H₂ molecule on boron cluster surfaces. Potential energy surfaces and electron charge difference density plots are given. The results obtained indicate that the H₂ molecule in certain cases is dissociated on the surface, and that the hydrogen atoms are individually bound to different boron atoms. It is also found that the chemisorbed hydrogen atoms can move almost freely in certain directions parallel to the boron surface.     

Magnetic states of the surface and bulk of ferrites near a phase transition at the Curie temperature

Investigations of the magnetic state of a surface layer ~200 nm thick and of the bulk in macroscopic ferrite crystals of the type Ba-M (BaFe₁₂O₁₉) are performed in the phase transition region around the Curie temperature (T _c). The method of simultaneous gamma, x-ray, and electron Mössbauer spectroscopy, which made it possible to compare directly the phase states of the surface and bulk of the sample, is used for the measurements. It is observed experimentally that in BaFe₁₂O₁₉ the transition of a surface layer ~200 nm thick to the paramagnetic state occurs at temperatures below T _c. It is established that the transition temperature T _c(L) of a thin layer localized at depth L from the surface of the crystal increases with distance from the surface and reaches the value T _c at the lower boundary of the “critical” surface layer. Therefore, near T _c a nonuniform state in which the crystal is magnetically ordered in the bulk but disordered at the surface is observed. A phase diagram of the states of the surface and of the bulk of macroscopic magnets near the Curie (or Néel) point is proposed on the basis of all the experimental results obtained in the present work as well as previously published results.     

Collective states in highly symmetric atomic configurations and single-photon traps

We study correlated states in circular and linear-chain configurations of identical two-level atoms containing the energy of a single quasi-resonant photon in the form of a collective excitation, where the collective behavior is mediated by exchange of transverse photons between the atoms. For a circular atomic configuration containing N atoms, the collective energy eigenstates can be determined by group-theoretical means making use of the fact that the configuration possesses a cyclic symmetry group Z _N . For these circular configurations, the carrier spaces of the various irreducible representations of the symmetry group are at most two-dimensional, so that the effective Hamiltonian on the radiationless subspace of the system can be diagonalized analytically. As a consequence, the radiationless energy eigenstates carry a Z _N quantum number p = 0, 1, …, N, which is analogous to the angular momentum quantum number l = 0, 1, … carried by particles propagating in a central potential, such as a hydrogen-like system. Just as the hydrogen s states are the only electronic wave functions that can occupy the central region of the Coulomb potential, the quasi-particle corresponding to a collective excitation of the circular atomic sample can occupy the central atom only for vanishing Z _N quantum number p. When a central atom is present, the p = 0 state splits into two, showing level crossing at certain radii; in the regions between these radii, damped oscillations between two “ extreme” p = 0 states occur, where the excitation occupies either the outer atoms or the central atom only. For large numbers of atoms in a maximally subradiant state, a critical interatomic distance of λ/2 emerges both in the linear-chain and in the circular configuration of atoms. The spontaneous decay rate of the linear configuration exhibits a jumplike “critical” behavior for next-neighbor distances close to a half-wavelength. Furthermore, both the linear-chain and the circular configurations exhibit exponential photon trapping once the next-neighbor distance becomes less than a half-wavelength, with the suppression of spontaneous decay being particularly pronounced in the circular system. In this way, circular configurations containing sufficiently many atoms may be natural candidates for single-photon traps.     

The adsorption of oxygen and carbon monoxide on cleaved polar and nonpolar ZnO surfaces studied by electron energy loss spectroscopy

Electron energy loss spectroscopy (ELS) with primary energies e₀ ? 80 eV has been performed on ultrahigh vacuum (UHV) cleaved nonpolar (11?00) and polar zinc (0001) and oxygen (0001?) surfaces of ZnO to study the adsorption of oxygen and carbon monoxide. Except for CO on the nonpolar surface where no spectral changes in ELS are observed a surface transition near 11.5 eV is strongly affected at 300 K on all surfaces by CO and O₂. At 300 K clear evidence for new adsorbate characteristic transitions is found for oxygen adsorbed on the Zn polar surface near 7 and 11 eV. At 100 K on all three surfaces both CO and O₂ adsorb in thick layers and produce loss spectra very similar to the gas phase, thus indicating a physisorbed state.     

On quantum solitons and their classical relatives: Bethe Ansatz states in soliton sectors of the sine-Gordon system

Previously we have found that the semiclassical sine-Gordon/Thirring spectrum can be received in the absence of quantum solitons via the spin $\text{1}\text{2}$ approximation of the quantized sine-Gordon system on a lattice. Later on, we have recovered the Hilbert space of quantum soliton states for the sine-Gordon system. In the present paper we present a derivation of the Bethe Ansatz eigenstates for the generalized ice model in this soliton Hilbert space. We demonstrate that via “Wick rotation” of a fundamental parameter of the ice model one arrives at the Bethe Ansatz eigenstates of the quantum sine-Gordon system. The latter is a “local transition matrix” ancestor of the conventional sine-Gordon /Thirring model, as derived by Faddeev et al. within the quantum inverse-scattering method. Our result is essentially based on the N < ∞, Δ = 1, m ? 1 regime. Consequently, the spectrum received, though resembling the semiclassical one, does not coincide with it at all.