Symmetry dependence of phonon lineshapes in superconductors with anisotropic gaps

The temperature dependence below $T_{c}$ of the lineshape of optical phonons of different symmetry as seen in Raman scattering is investigated for superconductors with anisotropic energy gaps. It is shown that the symmetry of the electron-phonon vertex produces non-trivial couplings to an anisotropic energy gap which leads to unique changes in the phonon lineshape for phonons of different symmetry. The phonon lineshape is calculated in detail for $B_{1g}$ and $A_{1g}$ phonons in a superconductor with $d_{x^{2}-y^{2}}$ pairing symmetry. The role of satellite peaks generated by the electron-phonon coupling are also addressed. The theory accounts for the substantial phonon narrowing of the $B_{1g}$ phonon, while narrowing of the $A_{1g}$ phonon which is indistinguishable from the normal state is shown, in agreement with recent measurements on BSCCO.Comment: 15 pages (3 Figures available upon request), Revtex, 1

Quasiparticle interference and the interplay between superconductivity and density wave order in the cuprates

Scanning tunneling spectroscopy (STS) is a useful probe for studying the cuprates in the superconducting and pseudogap states. Here we present a theoretical study of the Z-map, defined as the ratio of the local density of states at positive and negative bias energies, which frequently is used to analyze STS data. We show how the evolution of the quasiparticle interference peaks in the Fourier transform Z-map can be understood by considering different types of impurity scatterers, as well as particle-hole asymmetry in the underlying bandstructure. We also explore the effects of density wave orders, and show that the Fourier transform Z-map may be used to both detect and distinguish between them.Comment: final version published in Phys. Rev.

Fast Times at Ridgemont High? The Effect of Compulsory Schooling Laws on Teenage Births

Research suggests that teenage childbearing adversely affects both the outcomes of the mothers as well as those of their children. We know that low-educated women are more likely to have a teenage birth, but does this imply that policies that increase educational attainment reduce early fertility? This paper investigates whether increasing mandatory educational attainment through compulsory schooling legislation encourages women to delay childbearing. We use variation induced by changes in compulsory schooling laws in both the United States and Norway to estimate the effect in two very different institutional environments. We find evidence that increased compulsory schooling does in fact reduce the incidence of teenage childbearing in both the United States and Norway, and these results are quite robust to various specification checks. Somewhat surprisingly, we also find that the magnitude of these effects is quite similar in the two countries. These results suggest that legislation aimed at improving educational outcomes may have spillover effects onto the fertility decisions of teenagers.

Critical Current Peaks at 3BΦ3B_{\Phi} in Superconductors with Columnar Defects: Recrystalizing the Interstitial Glass

The role of commensurability and the interplay of correlated disorder and interactions on vortex dynamics in the presence of columnar pins is studied via molecular dynamics simulations. Simulations of dynamics reveal substantial caging effects and a non-monotonic dependence of the critical current with enhancements near integer values of the matching field $B_{\phi}$ and $3B_{\phi}$ in agreement with experiments on the cuprates. We find qualitative differences in the phase diagram for small and large values of the matching field.Comment: 5 pages, 4 figures (3 color

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

Comment on "Superconducting gap anisotropy vs. doping level in high-T_c cuprates" by C. Kendziora et al, PRL 77, 727 (1996)

In a recent paper Kendziora et al concluded that the superconducting gap in overdoped Bi-2212 is isotropic. From data obtained from electronic Raman scattering measurements, their conclusion was based on the observation that pair breaking peaks occured at approximately the same frequency in different scattering geometries and that the normalized scattering intensity at low energies was strongly depleted. We discuss a different interpretation of the raw data and present new data which is consistent with a strongly anisotropic gap with nodes. The spectra can be successfully described by a model for Raman scattering in a d_{x^{2}-y^{2}} superconductor with spin fluctuations and impurity scattering included.Comment: 1 page revtex plus 1 postscript figur

Quantum Dynamics of the Hubbard-Holstein Model in Equilibrium and Non-Equilibrium: Application to Pump-Probe Phenomena

The spectral response and physical features of the 2D Hubbard-Holstein model are calculated both in equilibrium at zero and low chemical dopings, and after an ultra short powerful light pulse, in undoped systems. At equilibrium and at strong charge-lattice couplings, the optical conductivity reveals a 3-peak structure in agreement with experimental observations. After an ultra short pulse and at nonzero electron-phonon interaction, phonon and spin subsystems oscillate with the phonon period $T_{ph} \approx 80$ fs. The decay time of the phonon oscillations is about 150-200 fs, similar to the relaxation time of the charge system. We propose a criterion for observing these oscillations in high $T_c$ compounds: the time span of the pump light pulse $\tau_{pump}$ has to be shorter than the phonon oscillation period $T_{ph}$.Comment: 4 pages, 4 figure