Feedback effects and the self-consistent Thouless criterion of the attractive Hubbard model

We propose a fully microscopic theory of the anomalous normal state of the attractive Hubbard model in the low-density limit that accounts for propagator renormalization. Our analytical conclusions, which focus on the thermodynamic instabilities contained in the self-consistent equations associated with our formulation, have been verified by our comprehensive numerical study of the same equations. The resulting theory is found to contain no transitions at non-zero temperatures for all finite lattices, and we have confirmed, using our numerical studies, that this behaviour persists in the thermodynamic limit for low-dimensional systems.Comment: 6 pages, 2 eps format figure

The Isotope Effect in d-Wave Superconductors

Based on recently proposed anti-ferromagnetic spin fluctuation exchange models for $d_{x^2-y^2}$-superconductors, we show that coupling to harmonic phonons {\it{cannot}} account for the observed isotope effect in the cuprate high-$T_c$ materials, whereas coupling to strongly anharmonic multiple-well lattice tunneling modes {\it{can}}. Our results thus point towards a strongly enhanced {\it{effective}} electron-phonon coupling and a possible break-down of Migdal-Eliashberg theory in the cuprates.Comment: 12 pages + 2 figures, Postscript files, all uuencoded Phys. Rev. Lett. (1995, to be published

Effect of an Electron-phonon Interaction on the One-electron Spectral Weight of a d-wave Superconductor

We analyze the effects of an electron-phonon interaction on the one-electron spectral weight A(k,omega) of a d_{x^2-y^2} superconductor. We study the case of an Einstein phonon mode with various momentum-dependent electron-phonon couplings and compare the structure produced in A(k,omega) with that obtained from coupling to the magnetic pi-resonant mode. We find that if the strength of the interactions are adjusted to give the same renormalization at the nodal point, the differences in A(k,omega) are generally small but possibly observable near k=(pi,0).Comment: 10 pages, 14 figures (color versions of Figs. 2,4,10,11,12 available upon request

Magnetic state of Yb in Kondo-lattice YbNi₂B₂C

We report neutron scattering experiments performed to investigate the dynamic magnetic properties of the Kondo-lattice compound YbNi2B2C. The spectrum of magnetic excitations is found to be broad, extending up to at least 150 meV, and contains inelastic peaks centred near 18 meV and 43 meV. At low energies we observe quasielastic scattering with a width Gamma = 2.1 meV. The results suggest a Yb3+ ground state with predominantly localized 4f electrons subject to (i) a crystalline electric field (CEF) potential, and (ii) a Kondo interaction, which at low temperatures is about an order of magnitude smaller than the CEF interaction. From an analysis of the dynamic magnetic response we conclude that the crystalline electric field acting on the Yb ions has a similar anisotropy to that in other RNi2B2C compounds, but is uniformly enhanced by almost a factor of 2. The static and dynamic magnetic properties of YbNi2B2C are found to be reconciled quite well by means of an approximation scheme to the Anderson impurity model, and this procedure also indicates that the effective Kondo interaction varies with temperature due to the crystal field splitting. We discuss the nature of the correlated-electron ground state of YbNi2B2C based on these and other experimental results, and suggest that this compound might be close to a quantum critical point on the non-magnetic side.Comment: Revised version to be published in Phys Rev