Abstract:
We present a first principles investigation of the lattice dynamics and electron-phonon coupling of the superconductor MgB_2 and the isostructural AlB_2 within the framework of density functional perturbation theory using a mixed-basis pseudopotential method. Complete phonon dispersion curves and Eliashberg functions \alpha^2F are calculated for both systems. We also report on Raman measurements, which support the theoretical findings. The calculated generalized density-of-states for MgB_2 is in excellent agreement with recent neutron-scattering experiments. The main differences in the calculated phonon spectra and \alpha^2F are related to high frequency in-plane boron vibrations. As compared to AlB_2, they are strongly softened in MgB_2 and exhibit an exceptionally strong coupling to electronic states at the Fermi energy. The total coupling constants are \lambda_{MgB_2}=0.73 and \lambda_{AlB_2}=0.43. Implications for the superconducting transition temperature are briefly discussed.

Abstract:
We present a first principles investigation of the lattice dynamics and electron-phonon coupling of the high-T_c superconductor YBa_2Cu_3O_7 within the framework of density functional perturbation theory using a mixed-basis pseudopotential method. The calculated phonon dispersion curves are in excellent agreement with Raman, infrared and neutron data. Calculation of the Eliashberg function alpha^2F leads to a small electron-phonon coupling lambda=0.27 in disagreement with earlier approximate treatments. Our calculations strongly support the view that conventional electron-phonon coupling is not an important contribution to superconductivity in high-T_c materials.

Abstract:
We have investigated the lattice dynamics of LiBC. Experimental Raman and inelastic neutron scattering results are confronted with density functional calculations. The excellent agreement between experiment and theory indicates that we have attained a high level of understanding for LiBC, which by its structure is closely related to superconducting MgB2 We will show that annealing of the sample is insufficient to cause Li deficiency and thus produce the expected superconductivity.

Abstract:
The phonon density-of-states of transition metal diborides TMB2 with TM = Ti, V, Ta, Nb and Y has been measured using the technique of inelastic neutron scattering. The experimental data are compared with ab initio density functional calculations whereby an excellent agreement is registered. The calculations thus can be used to obtain electron-phonon spectral functions within the isotropic limit. A comparison to similar data for MgB2 and AlB2 which were subject of prior publications as well as parameters important for the superconducting properties are part of the discussion.

Abstract:
Temperature dependent inelastic neutron-scattering measurements of the generalized phonon density-of-states for superconducting MgCNi_3, T_c=8 K, give evidence for a soft-mode behavior of low-frequency Ni phonon modes. Results are compared with ab initio density functional calculations which suggest an incipient lattice instability of the stoichiometric compound with respect to Ni vibrations orthogonal to the Ni-C bond direction.

Abstract:
Interactions with electronic excitations can soften and/or broaden phonons. They are greatly amplified at wavevectors Q+- that connect parallel (nested) sheets of the Fermi surface. In such a case, called a Kohn anomaly, the phonon dispersion sharply dips and its linewidth has a maximum at Q+-. Here we present results of inelastic x-ray scattering measurements that uncovered soft phonons in chromium far from Q+-. They appear in addition to the previously reported soft phonons at Q+-. Calculations in the local density approximation (LDA) show that the new anomalies originate from enhanced electron-phonon coupling. A similar mechanism may explain phonon anomalies away from nesting wavevectors in copper oxide superconductors and other compounds.

Abstract:
Inelastic x-ray scattering and $ab$-$initio$ calculation are applied to investigate the lattice dynamics and electron-phonon coupling of the ternary silicide superconductor CaAlSi ($P/bar{6}m2$). A soft c-axis polarized mode is clearly observed along the $/Gamma$-$A$-$L$ symmetry directions. The soft mode is strongly anharmonically broadened at room temperature, but, at 10 K, its linewidth narrows and becomes in good agreement with calculations of linear electron-phonon coupling. This establishes a coherent description of the detailed phonon properties in this system and links them clearly and consistently with the superconductivity.

Abstract:
The dynamical properties of the high-density Ru(001)-(1$\times$1)-O phase has been investigated by a combined high-resolution electron energy loss spectroscopy and density functional theory study. Due to a strong static outward relaxation of the first Ru layer a soft Rayleigh phonon mode is expected. However, a Rayleigh mode stiffening together with a new high energy in-plane phonon mode above the bulk bands is found which is related to a strong adsorbate-induced intralayer force constant stiffening which counteracts an interlayer softening. This structurally rather simple system with one surface atom per (1$\times$1) unit cell demonstrates the limited applicability of previously adopted models.

Abstract:
We present a detailed study of the lattice dynamics and electron-phonon coupling for a (3,3) carbon nanotube which belongs to the class of small diameter based nanotubes which have recently been claimed to be superconducting. We treat the electronic and phononic degrees of freedom completely by modern ab-initio methods without involving approximations beyond the local density approximation. Using density functional perturbation theory we find a mean-field Peierls transition temperature of approx 40K which is an order of magnitude larger than the calculated superconducting transition temperature. Thus in (3,3) tubes the Peierls transition might compete with superconductivity. The Peierls instability is related to the special 2k_F nesting feature of the Fermi surface. Due to the special topology of the (n,n) tubes also a q=0 coupling between the two bands crossing the Fermi energy at k_F is possible which leads to a phonon softening at the Gamma point.

Abstract:
We have studied the electron-phonon and superconducting properties of the Mg{1-x}AlxB2 and MgB{2(1-y)}C{2y} alloys within the framework of density functional theory using the self-consistent virtual-crystal approximation. For both alloys, the Eliashberg spectral functions and the electron-phonon coupling constants have been calculated in the two-band model for several concentrations up to x(Al)=0.55 and y(C)=0.175. We solved numerically the two-band Eliashberg gap equations without considering interband scattering. Using a single parameter for the Coulomb pseudopotential, which was determined for the undoped compound, we were able to reproduce the experimental doping dependence of Delta_sigma, Delta_pi, and T_c for both alloys on a quantitative level. In particular, the observed differences in the doping range of superconductivity between Al and C doping indicate a pronounced influence of the doping site, which can be explained naturally in the present approach without the need to invoke interband scattering, suggesting that this factor plays only a minor role.