Electronic Raman response in anisotropic metals

Using a generalized response theory we derive the electronic Raman response function for metals with anisotropic relaxation rates. The calculations account for the long--range Coulomb interaction and treat the collision operator within a charge conserving relaxation time approximation. We extend earlier treatments to finite wavenumbers ($|{\bf q}|\ll k_{\rm F}$) and incorporate inelastic electron--electron scattering besides elastic impurity scattering. Moreover we generalize the Lindhard density response function to the Raman case. Numerical results for the quasiparticle scattering rate and the Raman response function for cuprate superconductors are presented.Comment: 5 pages, 4figures. accepted in PRB (Brief Report), in pres

Critical dynamics, duality, and the exact dynamic exponent in extreme type II superconductors

The critical dynamics of superconductors is studied using renormalization group and duality arguments. We show that in extreme type II superconductors the dynamic critical exponent is given exactly by $z=3/2$. This result does not rely on the widely used models of critical dynamics. Instead, it is shown that $z=3/2$ follows from the duality between the extreme type II superconductor and a model with a critically fluctuating gauge field. Our result is in agreement with Monte Carlo simulations.Comment: 7 pages, no figures; version accepted for publication in PR

Renormalization of the elementary excitations in hole- and electron-doped cuprates due to spin fluctuations

Extending our previous studies we present results for the doping-, momentum-, frequency-, and temperature- dependence of the kink-like change of the quasiparticle velocity resulting from the coupling to spin fluctuations. In the nodal direction a kink is found in both the normal and superconducting state while in the antinodal direction a kink occurs only below $T_c$ due to the opening of the superconducting gap. A pronounced kink is obtained only for hole-doped, but not for electron-doped cuprates and is characteristically different from what is expected due to electron-phonon interaction. We further demonstrate that the kink structure is intimately connected to the resonance peak seen in inelastic neutron scattering. Our results suggest similar effects in other unconventional superconductors like ${Sr}_2{RuO}_4$.Comment: revised version, 12 pages, 19 figures. accepted for publication in PR

Electronic theory for superconductivity in Sr2_2RuO4_4: triplet pairing due to spin-fluctuation exchange

Using a two-dimensional Hubbard Hamiltonian for the three electronic bands crossing the Fermi level in Sr$_2$RuO$_4$ we calculate the band structure and spin susceptibility $\chi({\bf q}, \omega)$ in quantitative agreement with nuclear magnetic resonance (NMR) and inelastic neutron scattering (INS) experiments. The susceptibility has two peaks at {\bf Q}$_i = (2\pi/3, 2\pi/3)$ due to the nesting Fermi surface properties and at {\bf q}$_i = (0.6\pi, 0)$ due to the tendency towards ferromagnetism. Applying spin-fluctuation exchange theory as in layered cuprates we determine from $\chi({\bf q}, \omega)$, electronic dispersions, and Fermi surface topology that superconductivity in Sr$_2$RuO$_4$ consists of triplet pairing. Combining the Fermi surface topology and the results for $\chi({\bf q}, \omega)$ we can exclude $s-$ and $d-$wave symmetry for the superconducting order parameter. Furthermore, within our analysis and approximations we find that $f$-wave symmetry is slightly favored over p-wave symmetry due to the nesting properties of the Fermi surface.Comment: 5 pages, 5 figures, misprints correcte

Collective Spin Fluctuation Mode and Raman Scattering in Superconducting Cuprates

Although the low frequency electronic Raman response in the superconducting state of the cuprates can be largely understood in terms of a d-wave energy gap, a long standing problem has been an explanation for the spectra observed in the $A_{1g}$ polarization orientations. We present calculations which suggest that the peak position of the observed $A_{1g}$ spectra is due to a collective spin fluctuation mode.Comment: 4 pages, 5 eps figure

Melt Production and Ejection From Lunar Intermediate-Sized Impact Craters: Where Is the Molten Material Deposited?

Differently aged impact melt in lunar samples is key to unveiling the early bombardment history of the Moon. Due to the mixing of melt products ejected from distant craters, the interpretations of the origin of lunar samples are difficult. We use numerical modeling for a better quantitative understanding of the production of impact-induced melt and in particular its distribution in ejecta blankets for lunar craters with sizes ranging from 1.5 to 50 km. We approximate the lunar stratigraphy with a porosity gradient, which represents the gradual transition from upper regolith via megaregolith to the solid crustal material. For this lunar setting, we quantify the melt production relative to crater volume and derive parameters describing its increasing trend with increasing transient crater size. We found that about 30%–40% of the produced melt is ejected from the crater. The melt concentration in the ejecta blanket increases almost linearly with distance from the crater center, while the thickness of the ejecta blanket decreases following a power law. Our study demonstrates that if in lunar samples the concentration of a melt with a certain age is interpreted to be of a nonlocal origin, these melts could be the impact products of a large crater (>10 km) located hundreds of kilometers away

A multi-level examination of school programs, policies and resources associated with physical activity among elementary school youth in the PLAY-ON study

<p>Abstract</p> <p>Background</p> <p>Given the decline in physical activity (PA) levels among youth populations it is vital to understand the factors that are associated with PA in order to inform the development of new prevention programs. Many studies have examined individual characteristics associated with PA among youth yet few have studied the relationship between the school environment and PA despite knowing that there is variability in student PA levels across schools.</p> <p>Methods</p> <p>Using multi-level logistic regression analyses we explored the school- and student-level characteristics associated with PA using data from 2,379 grade 5 to 8 students attending 30 elementary schools in Ontario, Canada as part of the PLAY-Ontario study.</p> <p>Results</p> <p>Findings indicate that there was significant between-school random variation for being moderately and highly active; school-level differences accounted for 4.8% of the variability in the odds of being moderately active and 7.3% of the variability in the odds of being highly active. Students were more likely to be moderately active if they attended a school that used PA as a reward and not as discipline, and students were more likely to be highly active if they attended a school with established community partnerships. Important student characteristics included screen time sedentary behaviour, participating in team sports, and having active friends.</p> <p>Conclusion</p> <p>Future research should evaluate if the optimal population level impact for school-based PA promotion programming might be achieved most economically if intervention selectively targeted the schools that are putting students at the greatest risk for inactivity.</p

Electronic and phononic Raman scattering in detwinned YBa2_2Cu3_3O6.95_{6.95} and Y0.85_{0.85}Ca0.15_{0.15}Ba2_2Cu3_3O6.95_{6.95}: s-wave admixture to the dx2−y2d_{x^2-y^2}-wave order parameter

Inelastic light (Raman) scattering has been used to study electronic excitations and phonon anomalies in detwinned, slightly overdoped YBa$_2$Cu$_3$O$_{6.95}$ and moderately overdoped Y$_{0.85}$Ca$_{0.15}$Ba$_2$Cu$_3$O$_{6.95}$ single crystals. In both samples modifications of the electronic pair-breaking peaks when interchanging the a- and b-axis were observed. The lineshapes of several phonon modes involving plane and apical oxygen vibrations exhibit pronounced anisotropies with respect to the incident and scattered light field configurations. Based on a theoretical model that takes both electronic and phononic contributions to the Raman spectra into account, we attribute the anisotropy of the superconductivity-induced changes in the phonon lineshapes to a small s-wave admixture to the $d_{x^2-y^2}$ pair wave-function. Our theory allows us to disentangle the electronic Raman signal from the phononic part and to identify corresponding interference terms. We argue that the Raman spectra are consistent with an s-wave admixture with an upper limit of 20 percent.Comment: accepted in Phys. Rev. B, 11 page

Effect of a Normal-State Pseudogap on Optical Conductivity in Underdoped Cuprate Superconductors

We calculate the c-axis infrared conductivity $\sigma_c(\omega)$ in underdoped cuprate superconductors for spinfluctuation exchange scattering within the CuO$_2$-planes including a phenomenological d-wave pseudogap of amplitude $E_g$. For temperatures decreasing below a temperature $T^* \sim E_g/2$, a gap for $\omega < 2E_g$ develops in $\sigma_c(\omega)$ in the incoherent (diffuse) transmission limit. The resistivity shows 'semiconducting' behavior, i.e. it increases for low temperatures above the constant behavior for $E_g=0$. We find that the pseudogap structure in the in-plane optical conductivity is about twice as big as in the interplane conductivity $\sigma_c(\omega)$, in qualitative agreement with experiment. This is a consequence of the fact that the spinfluctuation exchange interaction is suppressed at low frequencies as a result of the opening of the pseudogap. While the c-axis conductivity in the underdoped regime is described best by incoherent transmission, in the overdoped regime coherent conductance gives a better description.Comment: to be published in Phys. Rev. B (November 1, 1999