Superconductivity and Spin Fluctuations

The organizers of the Memorial Session for Herman Rietschel asked that I review some of the history of the interplay of superconductivity and spin fluctuations. Initially, Berk and Schrieffer showed how paramagnon spin fluctuations could suppress superconductivity in nearly-ferromagnetic materials. Following this, Rietschel and various co-workers wrote a number of papers in which they investigated the role of spin fluctuations in reducing the T_c of various electron-phonon superconductors. Paramagnon spin fluctuations are also believed to provide the p-wave pairing mechanism responsible for the superfluid phases of $^3He$. More recently, antiferromagnetic spin fluctuations have been proposed as the mechanism for d-wave pairing in the heavy-fermion superconductors and in some organic materials as well as possibly the high T_c cuprates. Here I will review some of this early history and discuss some of the things we have learned more recently from numerical simulations.Comment: 9 pages, 10 encapsulated figures, Presented at MOS99, International Conference on Physics and Chemistry of Molecular and Oxide Superconductors, Stockholm, Sweden, 28 July-2 Aug, 1999, corrected typo

Determining the structure of the superconducting gap in Cu_{2}O_{3} 2-leg ladder materials

Superconductivity has been recently observed in Sr_{0.4}Ca_{13.6}Cu_{24}O_{41.84} which contains quasi-one-dimensional Cu_{2}O_{3} 2-leg ladders. If, as suggested by some theories, the superconductivity arises from these 2-leg ladders, it will be important to determine the structure of the superconducting gap. In particular, does the gap in a 2-leg ladder change sign when one goes from the bonding to antibonding fermi surface points? Here we carry out phenomenological calculations of nuclear relaxation rates and inelastic neutron scattering intensity in order to provide estimates of the experimental resolution that will be required to determine the structure of the superconducting gap associated with an array of weakly coupled 2-leg ladders.Comment: 12 pages including 7 eps figures, uses revtex with eps

Spin Susceptibility Representation of the Pairing Interaction for the two-dimensional Hubbard Model

Using numerical dynamic cluster quantum Monte Carlo results, we study a simple approximation for the pairing interaction of a two-dimensional Hubbard model with an on-site Coulomb interaction $U$ equal to the bandwidth. We find that with an effective temperature dependent coupling \Ub(T) and the numerically calculated spin susceptibility $\chi(K-K')$, the d-wave pairing interaction is well approximated by \frac{3}{2} \Ub^2\chi(K-K').Comment: 5 pages, 7 figure

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

Neutron scattering as a probe of the Fe-pnicitide superconducting gap

Inelastic neutron scattering provides a probe for studying the spin and momentum structure of the superconducting gap. Here, using a two-orbital model for the Fe-pnicitide superconductors and an RPA-BCS approximation for the dynamic spin susceptibility, we explore the scattering response for various gaps that have been proposed.Comment: 5 pages, 4 figure