Measuring the Relative Phase of the Energy Gap in a High-Temperature Superconductor with EELS

A method of measuring the relative phase of the energy gap in a high-temperature superconductor is suggested for electron energy loss spectroscopy. Energy-resolved measurements of off-specular scattering should show a feature similar to the specular feature associated with the gap. Unlike the specular feature, which reflects an average of the gap over the (normal) Fermi surface, the energy loss of the off-specular feature depends on the superconducting energy gap at only two locations on the Fermi surface. The onset of the feature reflects the relative phase between these two points. This result is independent of surface characteristics. Such characteristics affect the {\it magnitude} of the off-specular feature, not its location or onset. The size of the feature is estimated for a simple surface model. Implications of specific measurements on $\rm Bi_2Sr_2CaCu_2O_8$ are discussed

Kohn Anomalies in Superconductors

I present the detailed behavior of phonon dispersion curves near momenta which span the electronic Fermi sea in a superconductor. I demonstrate that an anomaly, similar to the metallic Kohn anomaly, exists in a superconductor's dispersion curves when the frequency of the phonon spanning the Fermi sea exceeds twice the superconducting energy gap. This anomaly occurs at approximately the same momentum but is {\it stronger} than the normal-state Kohn anomaly. It also survives at finite temperature, unlike the metallic anomaly. Determination of Fermi surface diameters from the location of these anomalies, therefore, may be more successful in the superconducting phase than in the normal state. However, the superconductor's anomaly fades rapidly with increased phonon frequency and becomes unobservable when the phonon frequency greatly exceeds the gap. This constraint makes these anomalies useful only in high-temperature superconductors such as $\rm La_{1.85}Sr_{.15}CuO_4$.Comment: 18 pages (revtex) + 11 figures (upon request), NSF-ITP-93-7

Kondo Insulator: p-wave Bose Condensate of Excitons

In the Anderson lattice model for a mixed-valent system, the $d-f$ hybridization can possess a $p$-wave symmetry. The strongly-correlated insulating phase in the mean-field approximation is shown to be a $p$-wave Bose condensate of excitons with a spontaneous lattice deformation. We study the equilibrium and linear response properties across the insulator-metal transition. Our theory supports the empirical correlation between the lattice deformation and the magnetic susceptibility and predicts measurable ultrasonic and high-frequency phonon behavior in mixed-valent semiconductors.Comment: 5 pages, 3 encapsulated PostScript figure

Method for Measuring the Momentum-Dependent Relative Phase of the Superconducting Gap of High-Temperature Superconductors

The phase variation of the superconducting gap over the (normal) Fermi surface of the high-temperature superconductors remains a significant unresolved question. Is the phase of the gap constant, does it change sign, or is it perhaps complex? A detailed answer to this question would provide important constraints on various pairing mechanisms. Here we propose a new method for measuring the relative gap PHASE on the Fermi surface which is direct, is angle-resolved, and probes the bulk. The required experiments involve measuring phonon linewidths in the normal and superconducting state, with resolution available in current facilities. We primarily address the La_1.85Sr_.15CuO_4 material, but also propose a more detailed study of a specific phonon in Bi_2Sr_2CaCu_2O_8.Comment: 13 pages (revtex) + 5 figures (postscript-included), NSF-ITP-93-2