Magnetic scaling in cuprate superconductors

We determine the magnetic phase diagram for the YBa$_2$Cu$_3$O$_{6+x}$ and La$_{2-x}$Sr$_x$CuO$_4$ systems from various NMR experiments. We discuss the possible interpretation of NMR and neutron scattering experiments in these systems in terms of both the non-linear $\sigma$-model of nearly localized spins and a nearly antiferromagnetic Fermi liquid description of magnetically coupled quasiparticles. We show for both the 2:1:4 and 1:2:3 systems that bulk properties, such as the spin susceptibiltiy, and probes at the antiferromagnetic wavevector $(\pi, \pi)$, such as $^{63}T_1$, the $^{63}Cu$ spin relaxation time, both display a crossover at a temperature $T_{cr}$, which increases linearly with decreasing hole concentration, from a non-universal regime to a $z=1$ scaling regime characterized by spin pseudogap behavior. We pursue the consequences of the ansatz that $T_{cr}$ corresponds to a fixed value of the antiferromagnetic correlation length, $\xi$, and show how this enables one to extract the magnitude and temperature dependence of $\xi$ from measurements of $T_1$ alone. We show that like $T_{cr}$, the temperature $T_*$ which marks a crossover at low temperatures from the $z=1$ scaling regime to a quantum disordered regime, exhibits the same dependence on doping for the 2:1:4 and 1:2:3 systems, and so arrive at a unified description of magnetic behavior in the cuprates, in which the determining factor is the planar hole concentration. We apply our quantitative results for YBa$_2$Cu$_3$O$_7$ to the recent neutron scattering experiments of Fong {\em et al}, and show that the spin excitation near $40 meV$ measured by them corresponds to a spin gap excitation, which is overdamped in the normal state, but becomes visible in the superconducting state.Comment: 18 pages, RevTex, 18 figures are available upon request; submitted to Phys. Rev.

Effect of Anisotropic Reactivity on the Rate of Diffusion-Controlled Reactions: Comparative Analysis of the Models of Patches and Hemispheres

AbstractA comparative analysis of two models of anisotropic reactivity in bimolecular diffusion-controlled reaction kinetics is presented. One is the conventional model of reactive patches (MRP), where the surface of a molecule is assumed to be reactive over a certain region (circular patch) with the rest of the surface being inert. Another one is the model of reactive hemispheres (MRH), assuming that a molecule is reactive within a certain distance from a point on its surface. The accuracy of the known and newly derived simple analytical expressions for the reaction rate is tested by comparison with the simulation results obtained by the original Brownian dynamics method. These formulas prove to be quite accurate in the practically important limit of strong anisotropy corresponding to small size of the reactive patches or hemispheres. Numerical calculations confirm earlier predictions that the MRP rates are much smaller than the MRH rates for the same radii of the reactive regions, especially in the case where both reacting molecules are anisotropic

Unconventional properties of superconducting cuprates

We present an explanation of the unusual peak/dip/hump features observed in photoemission experiments on Bi2212 at $T \ll T_c$. We argue that these features arise from the interaction of the fermionic quasi-particles with overdamped spin fluctuations. We show that the strong spin-fermion interaction combined with the feedback effect on the spin damping due to superconductivity yields a Fermi-liquid form of the fermionic spectral function for $\omega < 2 \Delta$ where $\Delta$ is the maximum value of the superconducting gap, and a non-Fermi-liquid form for $\omega > 2 {\Delta}$. In the Fermi-liquid regime, the spectral function $A({\bf k}_F,\omega)$ displays a quasiparticle peak at $\omega = {\Delta}$; in the non-Fermi-liquid regime it possesses a broad maximum (hump) at $\omega \gg {\Delta}$. In between the two regimes, the spectral function has a dip at $\omega \sim 2 {\Delta}$. We argue that our theory also explains the tunneling data for the superconducting density of states.Comment: 4 pages, RevTeX, 4 eps figures embedded in the tex

Quantum Protectorates in the Cuprate Superconductors

Following the identification of the pairing state, the major challenge in understanding the cuprate superconductors has been determining the evolution with doping and temperature of their anomalous normal state behavior. Key to this understanding is the experimentally determined magnetic phase diagram for the cuprates, which provides information on the protected magnetic properties of the normal state, generic behavior that is reliably the same one system to the next, regardless of details. I discuss the constraints this places on candidate quantum protectorates, and the status of microscopic model calculations for a protectorate consistent with these constraints, the nearly antiferromagnetic Fermi liquid.Comment: Invited paper to be published in Physica C as part of the proceedings of M2S-HTSC-VI, Houston, Feb.200

Quantitative expression of the spin gap via bosonization for a dimerized spin-1/2 chain

Using results on the mass gap in the sine-Gordon model combined with the exact amplitudes in the bosonized representation of the Heisenberg spin-1/2 chain and one-loop renormalization group, we derive a quantitative expression for the gap in a dimerized spin-1/2 chain. This expression is shown to be in good agreement with recent numerical estimates when a marginally irrelevant perturbation is taken into account.Comment: 5 pages, 2 EPS figures, uses svjour.cl