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

Toward a Soft X-Ray Fourier-Transform Spectrometer

The use of Fourier transform spectroscopy (FTS) in the soft x-ray region is advocated as a possible route to spectral resolution superior to that attainable with a grating system. A technical plan is described for applying FTS to the study of the absorption spectrum of helium in the region of double ionization around 60--80 eV. The proposed scheme includes a Mach-Zehnder interferometer deformed into a rhombus shape to provide grazing incidence reflections. The path difference between the interfering beams is to be tuned by translation of a table carrying four mirrors over a range {+-}1 cm which, in the absence of errors generating relative tilts of the wave fronts, would provide a resolving power equal to the number of waves of path difference: half a million at 65 eV, for example. The signal-to-noise ratio of the spectrum is analyzed and for operation on an Advanced Light Source bending magnet beam line should be about 330