Gaussian Tunneling Model of c-Axis Twist Josephson Junctions

Abstract

We calculate the critical current density $J_c^J$ for c-axis Josephson tunneling between identical high temperature superconductors twisted an angle ${\varphi }_0$ about the c-axis. We model the tunneling matrix element squared as a Gaussian in the change of wavevector q parallel to the junction, $<|t(\mathbf{q}){|}^2>\propto \exp (-{\mathbf{q}}^2{a}^2/2{\pi }^2{\sigma }^2)$. The $J_c^J({\varphi }_0)/J_c^J(0)$ 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, ${\sigma }^2\ge 0.25$. 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.

6 pages, 6 figures

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• Precise determination of the superconducting gap along the diagonal direction of Bi2Sr2CaCu2O8+y: Evidence for extended s-wave gap symmetry
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• Probing the order parameter symmetry of two-dimensional superconductors by twisted Josephson interferometry
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• Comment on "c-axis Josephson tunneling in $D_{x^2-y^2}$-wave superconductors''
• Bi_2 Sr_2 CaCu_2 O_{8+delta} Bicrystal c-Axis Twist Josephson Junctions: A New Phase-Sensitive Test of Order Parameter Symmetry
• Preserving the Josephson Coupling of Twisted Cuprate Junctions via Tailored Silicon Nitride Circuits Boards
• Incoherent tunneling and topological superconductivity in twisted cuprate bilayers