Non-perturbative approach to nearly antiferromagnetic Fermi liquids

We present a non-perturbative approach to the problem of quasiparticles coupled to spin-fluctuations. If the fully dressed spin-fluctuation propagator is used in the Feynman graph expansion of the single-particle Green's function, the problem of summing all spin-fluctuation exchange graphs (i.e without virtual fermion loops) can be cast as a functional integral over gaussian distributed random vector fields. A Monte Carlo sampling of this functional integral does not suffer from the 'fermion sign problem' and offers an attractive alternative to perturbative calculations. We compare the results of our computer simulations with perturbation theory and self-consistent one-loop calculations.Comment: 11 pages, 4 figure

The Influence of Magnetic Imperfections on the Low Temperature Properties of D-wave Superconductors

We consider the influence of planar ``magnetic" imperfections which destroy the local magnetic order, such as Zn impurities or $Cu^{2+}$ vacancies, on the low temperature properties of the cuprate superconductors. In the unitary limit, at low temperatures, for a $d_{x^2-y^2}$ pairing state such imperfections produce low energy quasiparticles with an anistropic spectrum in the vicinity of the nodes. We find that for the $La_{2-x}Sr_xCuO_4$ system, one is in the {\em quasi-one-dimensional} regime of quasiparticle scattering, discussed recently by Altshuler, Balatsky, and Rosengren, for impurity concentrations in excess of $\sim 0.16\%$ whereas YBCO$_7$ appears likely to be in the true 2D scattering regime for Zn concentrations less than $1.6\%$. We show the neutron scattering results of Mason et al. \cite{Aeppli} on $La_{1.86}Sr_{0.14}CuO_4$ provide strong evidence for ``dirty d-wave" superconductivity in their samples. We obtain simple expressions for the dynamic spin susceptibility and $^{63}Cu$ spin-lattice relaxation time, $^{63}T_1$, in the superconducting state.Comment: 10 pages; revtex; Los Alamos preprint LA-UR-94-53

Magnetically mediated superconductivity: Crossover from cubic to tetragonal lattice

We compare predictions of the mean-field theory of superconductivity for nearly antiferromagnetic and nearly ferromagnetic metals for cubic and tetragonal lattices. The calculations are based on the parametrization of an effective interaction arising from the exchange of magnetic fluctuations and assume that a single band is relevant for superconductivity. The results show that for comparable model parameters, the robustness of magnetic pairing increases gradually as one goes from a cubic structure to a more and more anisotropic tetragonal structure either on the border of antiferromagnetism or ferromagnetism.Comment: 16 pages 14 figure

Density Fluctuation Mediated Superconductivity

We conpare predictions of the mean-field theory of supercnductivity for metallic systems on the border of a density instability for cubic and tetragonal lattices. The calculations are based on a parametrisation of an effective interaction arising from the exchange of density fluctuations and assume that a single band is relevant for superconductivity. The results show that for comparable model parameters, desnity fluctuation mediated pairing is more robust in quasi-two dimensions than in three dimensions, and that the robustness of pairing increases gradually as one goes from a cubic to a more and more anisotropic tetragonal structure. We also find that the robustness of density fluctuation mediated pairing can depend sensitively on the incipient ordering wavevector. We discuss the similarities and differences between the mean-field theories of superconductivity for density and magnetically mediated pairing

Weak Pseudogap Behavior in the Underdoped Cuprate Superconductors

We report on an exact solution of the nearly antiferromagnetic Fermi liquid spin fermion model in the limit \pi T << \omega_{sf}, which demonstrates that the broad high energy features found in ARPES measurements of the spectral density of the underdoped cuprate superconductors are determined by strong antiferromagnetic (AF) correlations and precursor effects of an SDW state. We show that the onset temperature, T^{cr}, of weak pseudo-gap (pseudoscaling) behavior is determined by the strength, \xi, of the AF correlations, and obtain the generic changes in low frequency magnetic behavior seen in NMR experiments with \xi(T^{cr}) \approx 2, confirming the Barzykin and Pines crossover criterion.Comment: REVTEX, 4 pages, 3 EPS figure

On the vertex corrections in antiferromagnetic spin fluctuation theories

We argue that recent calculations by Amin and Stamp (PRL 77, 301 (1996); cond-mat/9601086) overestimate the strength of the vertex corrections in the spin-fermion model for cuprates. We clarify the physical origin of the apparent discrepancy between their results and earlier calculations. We also comment on the relative sign of the vertex correction.Comment: 3 pages, Revtex, 1 figure, ps-file also available at http://lifshitz.physics.wisc.edu/www/morr/morr_homepage.htm

Sensitivity of the Superconducting Transition Temperature to Changes in the Spin-Fluctuation Spectral Weight

In the simplest model of magnetic pairing, the transition temperature to the superconducting state depends on the dynamical susceptibility $\chi({\bf q},\omega)$. We discuss how $T_c$ is affected by different momentum and frequency parts of $\chi({\bf q},\omega)$ for nearly antiferromagnetic and nearly ferromagnetic metals in two dimensions. While in the case of phonon-mediated superconductivity any addition of spectral weight to $\alpha^2F(\omega)$ at $\omega >0$ leads to an increase in $T_c$, we find that adding magnetic spectral weight at any momentum ${\bf q}$ and low frequencies ($[0:3T_c]$ and $[0:(5-9)T_c]$ for nearly antiferromagnetic and ferromagnetic metals respectively) leads to a suppression of $T_c$. The most effective frequency and momentum range consists of large momenta ${\bf q} \sim (\pi,\pi)$ and frequencies around $10T_c$ for nearly antiferromagnetic metals and small momenta ${\bf q} \sim 0$ and frequencies of approximately $(13-22)T_c$ for nearly ferromagnetic metals.Comment: 18 pages, 39 figure

Diagrammatic perturbation theory and the pseudogap

We study a model of quasiparticles on a two-dimensional square lattice coupled to Gaussian distributed dynamical fields. The model describes quasiparticles coupled to spin or charge fluctuations and is solved by a Monte Carlo sampling of the molecular field distributions. The non-perturbative solution is compared to various approximations based on diagrammatic perturbation theory. When the molecular field correlations are sufficiently weak, the diagrammatic calculations capture the qualitative aspects of the quasiparticle spectrum. For a range of model parameters near the magnetic boundary, we find that the quasiparticle spectrum is qualitatively different from that of a Fermi liquid in that it shows a double peak structure, and that the diagrammatic approximations we consider fail to reproduce, even qualitatively, the results of the Monte Carlo calculations. This suggests that the pseudogap induced by a coupling to antiferromagnetic fluctuations and the spin-splitting of the quasiparticle peak induced by a coupling to ferromagnetic spin-fluctuations lie beyond diagrammatic perturbation theory

Electronic Structure of Sodium Cobalt Oxide: Comparing Mono- and Bilayer-hydrate

To shed new light on the mechanism of superconductivity in sodium cobalt oxide bilayer-hydrate (BLH), we perform a density functional calculation with full structure optimization for BLH and its related nonsuperconducting phase, monolayer hydrate (MLH). We find that these hydrates have similar band structures, but a notable difference can be seen in the $a_{1g}$ band around the Fermi level. While its dispersion in the $z$ direction is negligibly small for BLH, it is of the order of 0.1 eV for MLH. This result implies that the three dimensional feature of the $a_{1g}$ band may be the origin for the absence of superconductivity in MLH.Comment: 5 pages, 7 figures, to be published in Phys. Rev.