Fermi-liquid based theory for the in-plane magnetic anisotropy in untwinned high-Tc_c superconductors

Using a generalized RPA-type theory we calculate the in-plane anisotropy of the magnetic excitations in hole-doped high-$T_c$ superconductors. Extending our earlier Fermi-liquid based studies on the resonance peak by inclusion of orthorhombicity we still find two-dimensional spin excitations, however, being strongly anisotropic. This reflects the underlying anisotropy of the hopping matrix elements and of the resultant superconducting gap function. We compare our calculations with new experimental data on {\it fully untwinned} ${YBa}_2{Cu}_3{O}_{6.85}$ and find good agreement. Our results are in contrast to earlier interpretations on the in-plane anisotropy in terms of stripes (H. Mook {\it et al.}, Nature {\bf 404}, 729 (2000)), but reveal a conventional solution to this important problem.Comment: 5 pages, 6 figure

Theory for ultrafast nonequilibrium dynamics in d-wave superconductors

We use density-matrix theory to calculate the ultrafast dynamics of unconventional superconductors from a microscopic viewpoint. We calculate the time evolution of the optical conductivity as well as pump-probe spectra for a d-wave order parameter. Three regimes can be distinguished in the spectra. The Drude response at low photon energies is the only one of those which has been measured experimentally so far. At higher energies, we predict two more regimes: the pair-breaking peak, which is reduced as Cooper-pairs are broken up by the exciting pulse; and a suppression above the pair-breaking peak due to nonequilibrium quasiparticles. Furthermore, we consider the influence of the electron-phonon coupling, and derive rate equations which have been widely used so far.Comment: 4 pages, 4 figure

Electronic Raman response in anisotropic metals

Using a generalized response theory we derive the electronic Raman response function for metals with anisotropic relaxation rates. The calculations account for the long--range Coulomb interaction and treat the collision operator within a charge conserving relaxation time approximation. We extend earlier treatments to finite wavenumbers ($|{\bf q}|\ll k_{\rm F}$) and incorporate inelastic electron--electron scattering besides elastic impurity scattering. Moreover we generalize the Lindhard density response function to the Raman case. Numerical results for the quasiparticle scattering rate and the Raman response function for cuprate superconductors are presented.Comment: 5 pages, 4figures. accepted in PRB (Brief Report), in pres

Unconventional superconductivity and magnetism in Sr2_2RuO4_4 and related materials

We review the normal and superconducting state properties of the unconventional triplet superconductor Sr$_2$RuO$_4$ with an emphasis on the analysis of the magnetic susceptibility and the role played by strong electronic correlations. In particular, we show that the magnetic activity arises from the itinerant electrons in the Ru $d$-orbitals and a strong magnetic anisotropy occurs ($\chi^{+-} < \chi^{zz}$) due to spin-orbit coupling. The latter results mainly from different values of the $g$-factor for the transverse and longitudinal components of the spin susceptibility (i.e. the matrix elements differ). Most importantly, this anisotropy and the presence of incommensurate antiferromagnetic and ferromagnetic fluctuations have strong consequences for the symmetry of the superconducting order parameter. In particular, reviewing spin fluctuation-induced Cooper-pairing scenario in application to Sr$_2$RuO$_4$ we show how p-wave Cooper-pairing with line nodes between neighboring RuO$_2$-planes may occur. We also discuss the open issues in Sr$_2$RuO$_4$ like the influence of magnetic and non-magnetic impurities on the superconducting and normal state of Sr$_2$RuO$_4$. It is clear that the physics of triplet superconductivity in Sr$_2$RuO$_4$ is still far from being understood completely and remains to be analyzed more in more detail. It is of interest to apply the theory also to superconductivity in heavy-fermion systems exhibiting spin fluctuations.Comment: short review article. Annalen der Physik, vol. 13 (2004), to be publishe

Exchange Enhancement of the Electron-Phonon Pair Interaction

The critical temperature of high-$T_c$ superconductors is determined, at least in part, by the electron-phonon coupling. We include the effect of an exchange interaction between the electrons and calculate the renormalization of the bare phonon frequencies and the electron-phonon verticies in a random phase approximation and obtain a strongly enhanced attractive phonon-induced electron-electron interaction. Using Fast Fourier Transform techniques, the weak-coupling selfconsistency equation for the order parameter is solved in the 2D first Brillouin zone for the Emery tight-binding band with different band fillings. The enhancement of $T_c$ arises primarily from the softening of the phonon frequencies rather than the vertex renormalization.Comment: (2 pages, postscript file, hardcopies available from the authors

Momentum dependence of the electron-phonon coupling and self-energy effects in YBa_2Cu_3O_7 within the local density approximation

Using the local density approximation (LDA) and a realistic phonon spectrum we determine the momentum and frequency dependence of $\alpha^2F({\bf k},\omega)$ in YBa$_2$Cu$_3$O$_7$ for the bonding, antibonding, and chain band. The resulting self-energy $\Sigma$ is rather small near the Fermi surface. For instance, for the antibonding band the maximum of $Re \Sigma$ as a function of frequency is about 7 meV at the nodal point in the normal state and the ratio of bare and renormalized Fermi velocities 1.18. These values are a factor 3-5 too small compared to the experiment showing that only a small part of $\Sigma$ can be attributed to phonons. Furthermore, the frequency dependence of the renormalization factor $Z({\bf k},\omega)$ is smooth and has no anomalies at the observed kink frequencies which means that phonons cannot produce well-pronounced kinks in stoichiometric YBa$_2$Cu$_3$O$_7$, at least, within the LDA.Comment: Figure 1 slightly revised, text shortened, accepted as a PR