Angular dependence of the penetration depth in unconventional superconductors

We examine the Meissner state nonlinear electrodynamic effects on the field and angular dependence of the low temperature penetration depth, $\lambda$, of superconductors in several kinds of unconventional pairing states, with nodes or deep minima (``quasinodes'') in the energy gap. Our calculations are prompted by the fact that, for typical unconventional superconducting material parameters, the predicted size of these effects for $\lambda$ exceeds the available experimental precision for this quantity by a much larger factor than for others. We obtain expressions for the nonlinear component of the penetration depth, $\Delta\lambda$, for different two- and three- dimensional nodal or quasinodal structures. Each case has a characteristic signature as to its dependence on the size and orientation of the applied magnetic field. This shows that $\Delta\lambda$ measurements can be used to elucidate the nodal or quasinodal structure of the energy gap. For nodal lines we find that $\Delta\lambda$ is linear in the applied field, while the dependence is quadratic for point nodes. For layered materials with $\rm{YBa_2Cu_3O_{7-\delta}}$ (YBCO) type anisotropy, our results for the angular dependence of $\Delta\lambda$ differ greatly from those for tetragonal materials and are in agreement with experiment. For the two- and three- dimensional quasinodal cases, $\Delta\lambda$ is no longer proportional to a power of the field and the field and angular dependences are not separable, with a suppression of the overall signal as the node is filled in.Comment: 16 pages plus nine figure

Gaussian Tunneling Model of c-Axis Twist Josephson Junctions

We calculate the critical current density $J^J_c$ for c-axis Josephson tunneling between identical high temperature superconductors twisted an angle $\phi_0$ about the c-axis. We model the tunneling matrix element squared as a Gaussian in the change of wavevector q parallel to the junction, $<|t({\bf q})|^2>\propto\exp(-{\bf q}^2a^2/2\pi^2\sigma^2)$. The $J^J_c(\phi_0)/J^J_c(0)$ obtained for the s- and extended-s-wave order parameters (OP's) are consistent with the Bi$_2$Sr$_2$CaCu$_2$O$_{8+\delta}$ data of Li {\it et al.}, but only for strongly incoherent tunneling, $\sigma^2\ge0.25$. A $d_{x^2-y^2}$-wave OP is always inconsistent with the data. In addition, we show that the apparent conventional sum rule violation observed by Basov et al. might be understandable in terms of incoherent c-axis tunneling, provided that the OP is not $d_{x^2-y^2}$-wave.Comment: 6 pages, 6 figure

Supportive communication with parents moderates the negative effects of electronic media use on life satisfaction during adolescence

Objectives To examine the impact of electronic media (EM) use on teenagers’ life satisfaction (LS) and to assess the potential moderating effect of supportive communication with parents (SCP). Methods Data were drawn from the cross-national Health Behaviour in School-aged Children (HBSC) study (2009/2010) in Canada, England, Germany, Hungary, Italy, Israel, The Netherlands, Poland and Scotland. Sample size: 53,973 students aged 11–15 years. Results More hours per day spent on the computer were associated with lower LS; more EM communication with friends with higher LS. This relationship became negative if EM use reached and exceeded a certain threshold. SCP moderated the effect of EM communication with friends, but not computer use for the total sample. SCP seems to be more important than computer use or EM communication with friends for LS and it seems to buffer negative effects of EM use. Conclusions Communication with parents seems to buffer the negative effects of EM use on LS during adolescence. Higher computer use was related to lower LS, but “optimal” frequency of EM communication with friends was country specific.Peer reviewe