Theory of bicrystal c-axis twist Josephson junctions

We calculate the critical current density J(C)(J) (phi (0)) for Josephson t unneling between identical high temperature superconductors twisted an angl e phi (0) about the c-axis. Regardless of the shape of the two-dimensional Fermi surface and for very general tunneling matrix elements, an order para meter (OP) with general d-wave symmetry leads to J(C)(J) (pi /4) = 0. This general result is inconsistent with the data of Li et al. on Bi2Sr2CaCu2O8delta (Bi2212), which showed J(C)(J) to be independent of phi (0). If the m omentum parallel to the barrier is conserved in the tunneling process, J(C) (J) should vary substantially with the twist angle phi (0) when the tight-b inding Fermi surface appropriate for Bi2212 is taken into account, even if the OP is completely isotropic. We quantify the degree of momentum non-cons ervation necessary to render J(C)(J)(phi (0)) constant within experimental error for a variety of pair states by interpolating between the coherent an d incoherent limits using five specific models to describe the momentum dep endence 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 incoh erent, and that the OP must have a non-vanishing Fermi surface average for T less than or equal to T-C.