Pi excitation of the t-J model

In this paper, we present analytical and numerical calculations of the pi resonance in the t-J model. We show in detail how the pi resonance in the particle-particle channel couples to and appears in the dynamical spin correlation function in a superconducting state. The contribution of the pi resonance to the spin excitation spectrum can be estimated from general model-independent sum rules, and it agrees with our detailed calculations. The results are in overall agreement with the exact diagonalization studies of the t-J model. Earlier calculations predicted the correct doping dependence of the neutron resonance peak in the YBCO superconductor, and in this paper detailed energy and momentum dependence of the spin correlation function is presented. The microscopic equations of motion obtained within current formalism agree with that of the SO(5) nonlinear sigma model, where the pi resonance is interpreted as a pseudo Goldstone mode of the spontaneous SO(5) symmetry breaking.Comment: 33 pages, LATEX, 14 eps fig

Neutron Scattering and the B_{1g} Phonon in the Cuprates

The momentum dependent lineshape of the out-of-phase oxygen vibration as measured in recent neutron scattering measurements is investigated. Starting from a microscopic coupling of the phonon vibration to a local crystal field, the phonon lineshift and broadening is calculated as a function of transfered momentum in the superconducting state of YBa$_{2}$Cu$_{3}$O$_{7}$. It is shown that the anisotropy of the density of states, superconducting energy gap, and the electron-phonon coupling are all crucial in order to explain these experiments.Comment: new figures and discussio

Resonant Spin Excitation in an Overdoped High Temperature Superconductor

An inelastic neutron scattering study of overdoped Bi_2Sr_2CaCu_2O_{8+\delta} $ (T_c = 83 K) has revealed a resonant spin excitation in the superconducting state. The mode energy is E_res=38 meV, significantly lower than in optimally doped Bi_2Sr_2CaCu_2O_{8+\delta} (T_c = 91 K, E_ res =43 meV). This observation, which indicates a constant ratio E_res /k_B T_c \sim 5.4, helps resolve a long-standing controversy about the origin of the resonant spin excitation in high-temperature superconductors.Comment: final version: PRL 86, 1610 (2001

Deformation of canonical morphisms and the moduli of surfaces of general type

In this article we study the deformation of finite maps and show how to use this deformation theory to construct varieties with given invariants in a projective space. Among other things, we prove a criterion that determines when a finite map can be deformed to a one--to--one map. We use this criterion to construct new simple canonical surfaces with different $c_1^2$ and $\chi$. Our general results enable us to describe some new components of the moduli of surfaces of general type. We also find infinitely many moduli spaces $\mathcal M_{(x',0,y)}$ having one component whose general point corresponds to a canonically embedded surface and another component whose general point corresponds to a surface whose canonical map is a degree 2 morphism.Comment: 32 pages. Final version with some simplifications and clarifications in the exposition. To appear in Invent. Math. (the final publication is available at springerlink.com

Incommensurate Magnetic Fluctuations in YBa2Cu3O6.6

We use inelastic neutron scattering to demonstrate that at low temperatures, the low frequency magnetic fluctuations in YBa_2Cu_3O_{6.6} ($T_c=62.7$ K) are incommensurate, being found at positions displaced by $\pm\delta$ ($0.057\pm 0.006$ r.l.u.) along the $[\pi,\pi]$ direction from the wave vector $(\pi,\pi)$ associated with the antiferromagnetic order of the parent insulator, YBa_2Cu_3O_{6}. The dynamical susceptibility $\chi''(q,\omega)$ at the incommensurate positions increases on cooling below $T_c$, accompanied by a suppression of magnetic fluctuations at the commensurate points.Comment: 11 pages, Latex, 4 figure

Excitations in antiferromagnetic cores of superconducting vortices

We study excitations of the predicted antiferromagnetically ordered vortex cores in the superconducting phase of the newly proposed SO(5) model of strongly correlated electrons. Using experimental data from the literature we show that the susceptibilities in the spin sector and the charge sector are nearly equal, and likewise for the stiffnesses. In the case of strict equality SO(5) symmetry is possible, and we find that if present the vortices give rise to an enhanced neutron scattering cross section near the so called pi resonance at 41 meV. In the case of broken SO(5) symmetry two effects are predicted. Bound excitations can exist in the vortex cores with ``high'' excitation energies slightly below 41 meV, and the massless Goldstone modes corresponding to the antiferromagnetic ordering of the core can acquire a mass and show up as core excitation with ``low'' excitation energies around 2 meV.Comment: 9 pages, RevTeX, including 3 postscript figures, submitted to Phys. Rev. B, July 10, 199

What the resonance peak cannot do

In certain cuprates, a spin 1 resonance mode is prominent in the magnetic structure measured by neutron scattering. It has been proposed that this mode is responsible for significant features seen in other spectroscopies, such as photoemission and optical absorption, which are sensitive to the charge dynamics, and even that this mode is the boson responsibile for ``mediating'' the superconducting pairing. We show that its small (measured) intensity and weak coupling to electron-hole pairs (as deduced from the measured lifetime) disqualifies the resonant mode from either proposed role.Comment: 4 pages, no figur

Collective Excitations in High-Temperature Superconductors

Collective, low-energy excitations in quasi-two-dimensional d-wave superconductors are analyzed. While the long-range Coulomb interaction shifts the charge-density-wave and phase modes up to the plasma energy, the spin-density-wave excitation that arises due to a strong local electron-electron repulsion can propagate as a damped collective mode within the superconducting energy gap. It is suggested that these excitations are relevant to high-Tc superconductors, close to the antiferromagnetic phase boundary, and may explain some of the exotic features of the experimentally observed spectral-density and neutron-scattering data.Comment: 5 jolly page

Effect of Nonmagnetic Impurities on the Magnetic Resonance Peak in YBa2Cu3O7

The magnetic excitation spectrum of a YBa_2 Cu_3 O_7 crystal containing 0.5% of nonmagnetic (Zn) impurities has been determined by inelastic neutron scattering. Whereas in the pure system a sharp resonance peak at E ~ 40 meV is observed exclusively below the superconducting transition temperature T_c, the magnetic response in the Zn-substituted system is broadened significantly and vanishes at a temperature much higher than T_c. The energy-integrated spectral weight observed near q = (pi,pi) increases with Zn substitution, and only about half of the spectral weight is removed at T_c

The magnetic neutron scattering resonance of high-T_c superconductors in external magnetic fields: an SO(5) study

The magnetic resonance at 41 meV observed in neutron scattering studies of Y Ba_2 Cu_3 O_7 holds a key position in the understanding of high-T_c superconductivity. Within the SO(5) model for superconductivity and antiferromagnetism, we have calculated the effect of an applied magnetic field on the neutron scattering cross-section of the magnetic resonance. In the presence of vortices, the neutron scattering cross-section shows clear signatures of not only the fluctuations in the superconducting order parameter \psi, but also the modulation of the phase of \psi due to vortices. In reciprocal space we find that i) the scattering amplitude is zero at (pi/a,pi/a), ii) the resonance peak is split into a ring with radius pi/d centered at (pi/a,pi/a), d being the vortex lattice constant, and consequently, iii) the splitting pi/d scales with the magnetic field as sqrt{B}.Comment: 4 pages including 3 eps-figures - minor changes and one reference added. Accepted for publication in Phys. Rev.