Electronic structure of hydrogen-like impurities in nearly-free-electron metals

Recent developments in our understanding of the electronic structure of hydrogen and its isotopes in simple metals is reviewed. The role of nonlinear electron density distribution in the interpretation of the electronic properties of hydrogen-like impurities is emphasized. Calculated Knight shifts and hyperfine fields at + site and electric field gradients at cubic host nuclear sites due to interstitial + are compared with recent experimental data. The feasibility of using positive muon as a probe of defect structure is discussed. Future experiments and theoretical investigations aimed at a deeper understanding of the electronic properties of + are suggested.Work supported by the National Science Foundation and the U. S. Department of Energy.     

Low-dimensional electronic states at silicon surfaces

Self-assembled atomic chains can be triggered at stepped Si(111) surfaces by adding sub-monolayer amounts of metals, such as gold, silver, platinum, alkali metals, alkaline earths, and rare earths. A common feature of all these structures is the honeycomb chain, a graphitic strip of Si atoms at the step edge that is lattice matched in the direction parallel to the edge but completely mismatched perpendicular to it. This honeycomb chain drives one-dimensional surface reconstructions even on the flat Si(111) surface, breaking its three-fold symmetry. Particularly interesting are metallic chain structures, such as those induced by gold. The Au atoms are locked rigidly to the Si substrate but the electrons near the Fermi level completely decouple from the substrate because they lie in the band gap of silicon. The electronic structure of one-dimensional electrons is predicted to be qualitatively different from that of higher dimensions, since electrons cannot avoid each other when moving along the same line. The single-electron picture has to be abandoned, making way for collective excitations, such as spinons and holons, where the spins and charges of electrons become separated. Although such excitations have yet to be confirmed definitively, the band structure seen in angle-resoled photoemission exhibits a variety of unusual features, such as a fractional electron count and a doublet of nearly half-filled bands. Chains of tunable spins can be created with rare earths. The dimensionality can be controlled by adjusting the step spacing with intra- and inter-chain coupling ratios from 10:1 to >70:1. Thus, metal-induced chain structures on stepped silicon provide a versatile class of low-dimensional materials for approaching the one-dimensional limit and exploring the exotic electronic states predicted for one dimension. PACS 73.20.At; 71.10.Pm; 79.60.Jv; 81.07.Vb; 73.21.Hb     

The Fermi surfaces of the alkali metals

Long before direct experimental studies of the Fermi surfaces of the alkali metals became technically feasible, evidence had accumulated to suggest that their low-lying energy bands are almost free-electron-like. Indeed, the importance of the free-electron model in the development of the theory of metals owes much t o the coincidence that sodium, now known to be the most free-electron-like of all the alkali metals, was the subject of the pioneering cohesive energy calculations of Wigner and Seitz.¹     

Electron states at steps in semiconductor surfaces

Based on the Bethe-Peierls approximation we have developed a method to study surfaces where local deviations from periodicity are present. Since the method leaves out everything but short-range order, the effect of particular local configurations are easily studied. In particular, we apply the method to study the electronic structure of steps in Si surfaces. The results are in fair agreement with photoemission experimental data.     

The calculation of the surface energy of high-index surfaces in metals at zero temperature

We used the molecular dynamics simulation with interatomic potentials of the embedded atom method to calculate the high-index surface energies of the surfaces containing the 〈0 0 1〉 axis or 〈−1 1 0〉 axis in f.c.c. metal Al, Cu and Ni at zero temperature. We generalized an empirical formula based on structural unit model for high-index surfaces and present some new formulas that can be used to estimate the surface energy and structural feature of high-index surfaces very well. The results show that the closest surfaces have the lowest surface energy and the surface energies of the closest (1 1 1) surface and the next closest (1 1 0), (1 0 0) surfaces are the extremum on the curve of surface energy versus orientation angle. We also calculated the b.c.c. metal Fe and obtained a similar result. The difference is that in the b.c.c. metal the surface energies of the closest (1 1 0) surface and the next closest (1 0 0), (1 1 2) surfaces are the extremum on the curve of surface energy versus orientation angle. The results of theoretical simulation and the empirical formula consist well with the experiment data.     

Magnetic field-induced surface electron states in thin films

Analytical expressions are derived for the energy spectrum of magnetic field-induced surface electron states in thin films. The theory is based on investigations of asymptotic solutions of the Weber equation.     

Electron spin polarization esp at surfaces of ferromagnetic metals

Fundamental information on surface magnetic order (SMO) of ferromagnetic metals can be obtained from electron-capture, photoemission, fieldemission, spin-dependent tunneling and spin-polarized LEED experiments. The different techniques, new experimental advances and developments are discussed with particular emphasis given to electron-capture spectroscopy. This review will focus on new experimental and theoretical results (long-range and “local” SMO of ferro- and antiferromagnetic metals, surface states, SMO of thin films, new magnetic surface phases, magnetic surface reconstruction, chemisorption) obtained in the years past which have brought outstanding progress towards a deeper comprehension of the physics of ferromagnetism and towards the unravelling of the physical processes inherently involved in the various methods for spin spectroscopy. Recent data on the SMO received from experiments performed at surfaces of single crystals of 3d-TM and 4f-RE metals reveal new scientific insights and perspectives for the theoretical analysis of experimental results within the framework of the currently refined knowledge about ferromagnetism.     

Selfconsistent model calculations of electronic states at narrow-band-metal surfaces

For a nondegenerate narrow energy band spanned by a semiinfinite chain of three-dimensional atoms, the electronic potential and the electron density of states are calculated selfconsistently in the vicinity of the chain end. The electron-electron interaction is treated in the Hartree-Fock approximation, using the Green function method. The results for the potential and the density of states are discussed in terms of the parameters which determine the bulk electronic structure, such as the Fermi energy E_F and the intra- and interatomic Coulomb repulsion k₀ and K₁. Futhermore, the self consistent method is extended to an impurity atom at the chain end. The existence of bonding and antibonding surface states is found to depend on both the bulk and impurity parameters, such as the intraatomic Coulomb repulsion U_α and the nearest neighbour hopping element T.     

Optical properties of dangling-bond states at cleaved silicon surfaces

The spectral dependence of surface photovoltage and surface photoconductance both under continuous illumination as well as LEED I/V spectra were studied with cleaved Si(111)-2 × 1 surfaces at 130 K. Between 0.23 and 0.5 eV a doubly peaked absorption band was found with opposite sign compared to the SPV and SPC signals at higher photon energies. This band is due to electronic transitions from occupied to empty dangling-bond states located at the raised and the lowered rows of atoms in the 2 × 1 reconstruction, respectively. This absorption shows a pronounced dependence on the polarization of the incident light which correlates with the spatial symmetry of the dangling-bond states. Anneals at up to 500 K remove the low-energy absorption peak and equalize the 2 × 1 reconstruction: The homogeneous Si(111)-2 × 1 structure exhibits a buckling of 0.3 Å and a dangling-bond absorption with a threshold at 0.42 eV and a maximum at 0.47 eV. An anneal at 750 K, forming the 7 × 7 structure, destroys the peak of opposite sign in SPV and SPC and only leaves a broad tail with a threshold of 0.32 eV.     

Magnetic states at the oxygen surfaces of ZnO and Co-doped ZnO

First principles calculations of the O surfaces of Co-ZnO show that substitutional Co ions develop large magnetic moments which long-range order depends on their mutual distance. The local spin polarization induced at the O atoms is 3 times larger at the surface than in the bulk, and the surface stability is considerably reinforced by Co. Moreover, a robust ferromagnetic state is predicted at the O (0001) surface even in the absence of magnetic atoms, correlated with the number of p holes in the valence band of the oxide, and with a highly anisotropic distribution of the magnetic charge even in the absence of spin-orbit coupling.     

Many-body effects in the binding energies of image states at surfaces

A study of the influence of many-body effects on binding energies and effective masses of image potential induced surface states is presented. The binding energies calculated using experimentally measured ε(ω) response functions show a dependence on the electron density different from that obtained using a plasmon model, and are in agreement with recent experimental data of diesen et al. [Phys. Rev. B33 (1986) 5241]. The effects of plasmon dispersion and single particle excitations on binding energies are evaluated with a simple model, and it is shown that they result in a strong cancellation in the range of r_s values where most experimental data have been obtained (r_s ≈ 3), if realistic values of the surface plasmon dispersion relation are used. Corrections to the effective masses due to many-body effects are shown to be of the order of 1%.     

Quantum well and quantum wire states at metal surfaces

Novel effects in magnetic multilayer structures, such as oscillatory magnetic coupling and "giant" magnetoresistance, have created new materials that allow for an order of magnitude higher sensitivity in the detection of magnetically-recorded data. Determination of their electronic and magnetic structures with angle-resolved photoemission and inverse photoemission reveals quantized states in the noble metal spacer layers which are connected with oscillatory magnetic coupling and have implications on magnetoresistance. These states can be understood by a simple interferometer model, including the spin-dependent interface reflectivity that polarizes them and transmits the magnetic coupling through the noble metal spacer.Current efforts are discussed, which aim towards fabricating quantum wires and lateral superlattices on metals by decorating steps at vicinal surfaces. STM work on the growth mode of such structures is presented, which uses spectroscopic contrast to distinguish different metals. Specific electronic states at decorated step edges are found with inverse photoemission.     

Dissociative chemisorption and localized oxidation states at titanium surfaces

Dissociative chemisorption of carbon monoxide and nitric oxide is shown to result in the formation of discrete localised oxidation states of titanium; Ti²⁺ with CO and Ti²⁺ and Ti³⁺ with NO. The results are compared with dioxygen (Ti²⁺, Ti³⁺ and Ti⁴⁺). A correlation is shown to exist between the extent of dissociative chemisorption i.e. overlayer growth and the emergence in a step-wise manner of Ti²⁺, Ti³⁺ and Ti⁴⁺. Attention is drawn to the significance of the Madelung energy in determining the oxidation states generated within the overlayer by this molecule-specific process.     

The law of corresponding states for metals

Using the similarity of the effective potentials seen by ions in metals a reduced phonon equation of state is derived. It is shown that the melting point T_m(0) and the atomic volume Ω₀ at T = 0 K and at p = 0 are suitable macroscopic parameters for scaling ? and σ characterizing the interatomic potentials of metals having similar structures. The temperature and pressure dependence of thermodynamical quantities reduced with the above parameters are discussed and the results are compared with the experiment. It is shown that the pressure dependence of the reduced thermodynamic quantities can be described by the pressure dependence of the scaling parameters T_m(p) and Ω₀(p).The general form of the reduced equation of state (containing the electronic contributions as well) obtained gives that the reduced pressure is a universal function of the following reduced variables: the volume, temperature, de Broglie wavelength, Gibbs free energy of electrons $\text{3}\text{5}\text{zE}{}_{\mathrm{fo}}\text{?}$ (E_fo is the Fermi energy at T = 0 K) and depe of the valence z as well. It is shown that $\text{E}{}_{\mathrm{fo}}\text{?}$ is a function of $\text{Ω}{}_{\mathrm{o}}{}^{\mathrm{<mtext>?1</mtext><mtext>2</mtext>}}$ and $\text{(}\text{E}{}_{\mathrm{fo}}\text{/?}\text{)Ω}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ is approximately constant within the same sub-group of the periodic table.     

Decay of electronic excitations in bulk metals and at surfaces

We present a brief survey of the contemporary state of theoretical study of quasiparticles (excited electrons and holes) dynamics in bulk metals and at metal surfaces. Quasiparticle decay mechanisms are discussed in terms of electron-electron (e-e) and electron-phonon (e-ph) interactions. The e-ph decay channel is shown to be important for all materials considered. It is especially important for systems with the thickness of one monolayer. In the e-e decay channel the quasiparticle decay can be realized via one-electron transfer processes, via creation of electron-hole pairs, and via plasmon excitation. In ferromagnetic systems the electron (hole) decay via the Stoner pair excitation or/and magnon excitation is made possible.     

Vacancies at the surfaces of F.C.C. metals

The vacancy formation energy is calculated using the inserted atom method for faces with high and low indices and in the near-surface atomic layers of aluminum, nickel, copper, palladium, silver, platinum, and gold. The transition of the calculated quantities to the bulk quantities is traced for successive insertion of a defect deeper into the near-surface layer of the material. The relaxation contribution to the energetics is revealed for each type of surface. A correlation is seen between the energies of formation at surfaces with high and low indices. V. D. Kuznetsov Siberian Physicotechnical Institute at Tomsk State University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 3, pp. 62–73, March, 1997.