On the electronic density of states of the transition metals

XIS measurements of the elements Ir, Pt and Au are reported. High precision and reproducibility is obtained by the application of a “π/2-method” which approximates a Bragg angle of 90° at the dispersing crystal. Theoretical densities of states exist for Pt and Au. The agreement with the measured isochromats is good. A rigid-band model for Ir, Pt, and Au is ruled out by the measurements. Rather they suggest (combined with results of photoemission experiments) a narrowing of thed-bands from Ir through Pt to Au. Moreover, thed-band of Ir lies relative to thesp-band at a lower energy than thed-bands of Pt and Au. A fitting parameter concerning the experimental resolution is explained and considered as a possible indication of localization for XIS.     

On thed-electron surface density of states of transition metals

Using the moment method and the continued fraction expansion for the one-particle Green's function we have studied thed-electron surface density of states for a transition metal. Besides the reduction of nearest neighbours for a surface atom compared to a bulk atom we have also taken into account the effect that the atomic environment of a surface atom is quite different from that of a bulk atom. This leads to important modifications in the surface density of states which can effect e.g. magnetic surface properties.Work supported in part by the ESIS program (Universities of Liege and Antwerpen)     

On thed-electron surface density of states of transition metals

It is shown that thed-electron surface density of states of a transition metal is strongly influenced not only by “off-diagonal” surface effects (e.g. reduction of nearest neighbors at the surface) but also by “diagonal” surface effects. Latter result from differences in the effective atomic potential for differentd-orbitals. They lead generally to large resonant contributions to the surface density of states. It is demonstrated that the “diagonal” effects must be included in any realistic calculation of the surface density of states.     

On the electronic specific heat of transition metals

A simple framework to calculate the electronic specific heat enhancement is presented and applied to the case of the electron-electron interaction in transition metals. A substantial contribution has been found in iron and niobium.     

Electronic density of states and crystal structure in IV a transition metals

Bremsstrahlung isochromats of the hcp and bcc phases of Ti, Zr, and Hf are presented. They show directly, that the density of states in the mid-part of the d-band decreases, when the phase transformation hcp → bcc occurs.     

On spectral density of electronic states in disordered systems

In the present paper, the averaged spectral density of electronic states, 〈?(k, E)〉, has been computed for three-dimensional disordered systems with spherical well type atomic potentials. The formula for 〈?(k, E)〉 is derived by using a realistic perturbational approach that takes propagator modification into account, together with a handy approximation due toBallentine. 〈?(k, E)〉 has been computed for various sets of potential strength and concentration, and the dependence of 〈?(k, E)〉 upon these parameters has been discussed. The motivation behind the computations reported here, is to examine the circumstances under which the electron motion in disordered systems is expected to be almost free electronic. Our principal finding is that a simultaneous existence of weak electron-scatterer interaction-potential and high density of scatterers would tend to make the motion of an electron in a disordered system almost like that of a free one.     

On the calculation of electron density of states in disordered metals

It is demonstrated that in a full nonlocal pseudopotential calculation of the density of states, the results from the standard formula, $\text{N(E) = N(E}{}_{\mathrm{<mtext>FE</mtext>}}\text{)k (}\text{?E}{}_{\mathrm{<mtext>k</mtext>}}\text{?k}\text{)}{}^{\mathrm{?1}}$, do not differ significantly from those using the Green-function method and are reliable for simple liquid metals, despite the fact that there is an uncertainty in treating E_k as a dispersion function.     

Site-specific phonon density of states discerned using electronic states

We have performed the measurement of the site-specific phonon densities of states (PDOS) discerned using electronic states. As far as we know, no general method could give the site-specific PDOS, although oscillating properties of the individual atoms in nonequivalent positions are not necessarily equivalent. However, the combination of the energy and time domain measurements of the nuclear resonant scattering of synchrotron radiation allows the identification of site-specific PDOS. We measured the site-specific PDOS of iron atoms in magnetite, which is a mixed valent compound, and the difference between partial phonon densities of the iron sites was clearly observed.     

Electronic surface states in cleaved transition metals

The local densities of states (LDS) on clean low-index surfaces of fcc Ni and bcc Fe are presented. They are calculated within the tight-binding approximation using a moment method and a continued fraction analysis. The d band degeneracy and the charge rearrangement occurring near the surface when cleaving the crystal are fully taken into account by computing exactly a large number of moments (22–26). The surface LDS are found to be strongly dependent on the cleavage plane. Indeed, whereas the LDS on dense planes are rather bulk like, sharp peaks arising from states localized near the surface are obtained near the atomic level of the metal on non-dense planes of cleavage. In addition, the bandwidth is broadened by surface states for Ni. On the contrary, for bcc Fe the surface potential is not strong enough to modify the bandwidth. A comparison is made with spectroscopic observations.The method lends itself to other interesting applications in the surface physics field and, as an example, we present the results of calculations of the spatial distribution of the electronic charge near the surface and its deviation from spherical symmetry. The charge asphericity is slightly increased when going from a bulk to a surface site as the difference between the occupations of two surface orbitals can reach 0.34 ē instead of 0.15 ?c for a bulk site. Diagrams are shown for (100) and (110) cleaved Ni to illustrate the results. The consequences upon preferred adsorption sites according to the electronic affinity and size of the adsorbate are discussed.     

Interpretation of the electronic spectra of phthalocyanines with transition metals from quantum-chemical calculations by the density functional method

Using the time-dependent formalism of the density functional theory (time-dependent density functional theory (TDDFT)), the energies and intensities of the electronic transitions of some metal phthalocyanines of transition metals and of their anionic forms with different electron localization are studied quantum chemically. It is shown that, in all the cases studied, calculations using the B3LYP functional with even a comparatively narrow basis set (6–31G) are quite consistent with the previous calculations of the same objects by the ZINDO/S-CI semiempirical method taking into account double excitations. For a number of particular examples, it is shown that a lack of consideration of doubly excited configurations in the calculation of excited states by the TDDFT method can be compensated by the contribution from single excitations, which proves to be more significant due to the presence of the correlation component of the exchange-correlation functional.     

On singularities of electronic state density in liquid metals and disordered metallic alloys

We have performed a qualitative consideration of the problem of structurally dependent singularities of the density of electronic states,N(E), in disordered metallic systems: liquids, glasses and alloys. The appearance of Kohn anomalies atq ₀2K _F (q ₀ being the maximum position of the structure factorS(q);K _F , the Fermi momentum) in thermodynamic properties of liquid and amorphous metals is analyzed. It has been shown that the appearance of these contributions is due to the presence of a diffuse (inelastic) part ofS(q) and that they are no analogs of the Van Hove singularities (VHS) in crystals. The corollary of the hypothesis about the quasicrystalline structure of liquids, i.e. the appearance of blurred VHS's inN(E), is treated. A strict solution of the problem of the Gaussian static disorder effect on the VHS in crystalline alloys is presented. A new energy scale in the relaxation time and, consequently, in kinetic coefficients has been revealed.     

Dependence of Tc on electronic density of states

From the Eliashberg gap equations generalized to include approximately an energy dependence in the electron density of states N(ε) we compute the functional derivative of the critical temperature T_c with N(ε). It is found to be a rapidly decreasing function of the increasing energy away from the Fermi energy. In an appropriate limit, a comparison with the predictions of the McMillan equation shows that it is inadequate in a study of δT_c/δN(ε).     

Spin-polarized electronic density of states in amorphous iron

The spin-polarized electronicd-band density of states in amorphous iron are reported using recursion method. The magnetic moment of amorphous iron is found to be almost as high as BCC iron. This lends support to the view expressed by Kemény et al. that the extrapolation of experimental results obtained on samples containing less than 2% impurities to deduce the magnetic moment of pure amorphous iron may not be justified.     

The density of unoccupied electronic states in copper

The density of unoccupied electronic states in Cu has been measured employing soft X-ray appearance-potential spectroscopy (SXAPS). The L_III le     

On the electronic structure of liquid metals

We consider the electronic structure of liquid metals as a problem of multiple scattering. The total scattering operator is developed in terms of the reaction operators of a single scattering event, having a ‘standing wave’ boundary condition. This method has several advantages with respect to the approach where the total scattering operator is developed in terms of the scattering operators of a single scattering. Since the reaction operators are hermitian, the occurring perturbation expansions have a real perturbation parameter, which is more easily handled. Furthermore, if in the expansion of the total scattering operator, only terms up to the second order are maintained, this approximate expression satisfies already the ‘optical theorem’, just as the exact total scattering operator. Finally, spurious damping terms are eliminated at the outset. For very dense systems we obtain practically non-attenuated waves and this can be understood as if the damping due to a single scattering event is compensated by the reaction of the surrounding scatterers.     

Pseudogap in the electronic density of states of superconducting glasses

Two loop order results for the electronic density of states (DOS) of both Ising- and XY-type superconducting glass phases are presented. Maximal depression of the DOS by critical fluctuation corrections to its finite mean field value is found to occur at the Fermi energyE _F . The theory is renormalizable and exponentiation of the loop expansion yields (E _F)=0 for the DOS in two dimensions and for arbitrarily small disorder. It is also concluded that the DOS assumes nonzero values, when either |E–E _F|, or magnetic field H, or temperature T become nonzero. A pseudogap (atT=0,H=0) or a smeared gap (forH0 orT0) is thus obtained with a DOS-minimum at the Fermi level. A rough estimate of the effective width is given. In three dimensions, the DOS atE _F vanishes like (n _c ^I –n)^1/2 for the Ising-type glass and like (n _c ^XY –n)¹ for the XY-type glass as the impurity concentrationn exceeds characteristic values. At second loop order, the calculation contains a nontrivial indication of a lower critical dimension two.     

Zero bias anomaly in the density of states of low-dimensional metals

We consider the effect of Coulomb interactions on the average density of states (DOS) of disordered low-dimensional metals for temperatures T and frequencies ω smaller than the inverse elastic life-time 1/τ. Using the fact that long-range Coulomb interactions in two dimensions (2d) generate ln²-singularities in the DOS ν(ω) but only ln-singularities in the conductivity σ(ω), we can re-sum the most singular contributions to the average DOS via a simple gauge-transformation. If σ(ω) > 0, then a metallic Coulomb gapν(ω) ∝ |ω|/e ⁴ appears in the DOS at T = 0 for frequencies below a certain crossover frequency Ω ₂ which depends on the value of the DC conductivity σ(0). Here, - e is the charge of the electron. Naively adopting the same procedure to calculate the DOS in quasi 1d metals, we find ν(ω) ∝ (|ω|/Ω ₁)^1/2exp(- Ω ₁/|ω|) at T = 0, where Ω ₁ is some interaction-dependent frequency scale. However, we argue that in quasi 1d the above gauge-transformation method is on less firm grounds than in 2d. We also discuss the behavior of the DOS at finite temperatures and give numerical results for the expected tunneling conductance that can be compared with experiments. Received 28 August 2001 / Received in final form 28 January 2002 Published online 9 July 2002