THEORY OF BICRYSTAL c-AXIS TWIST JOSEPHSON JUNCTIONS

Abstract

We calculate the critical current density [Formula: see text] for Josephson tunneling between identical high temperature superconductors twisted an angle (ϕ0) about the c-axis. Regardless of the shape of the two-dimensional Fermi surface and for very general tunneling matrix elements, an order parameter (OP) with general d-wave symmetry leads to [Formula: see text]. This general result is inconsistent with the data of Li et al. on Bi2Sr2CaCu2O8+δ (Bi2212), which showed [Formula: see text] to be independent of ϕ0. If the momentum parallel to the barrier is conserved in the tunneling process, [Formula: see text] should vary substantially with the twist angle (ϕ0) when the tight-binding Fermi surface appropriate for Bi2212 is taken into account, even if the OP is completely isotropic. We quantify the degree of momentum non-conservation necessary to render [Formula: see text] constant within experimental error for a variety of pair states by interpolating between the coherent and incoherent limits using five specific models to describe the momentum dependence of the tunneling matrix element squared. From the data of Li et al., we conclude that the c-axis tunneling in Bi2212 must be very nearly incoherent, and that the OP must have a non-vanishing Fermi surface average for T≤Tc.