Theory of coherent c-axis Josephson tunneling between layered superconductors

We calculate exactly the Josephson current for c-axis coherent tunneling be tween two layered superconductors, each with internal coherent tight-bindin g intra- and interlayer quasiparticle dispersions. Our results also apply w hen one or both of the superconductors is a bulk material, and include the usually neglected effects of surface states. For weak tunneling, our result s reduce to our previous results derived using the tunneling Hamiltonian. O ur results are also correct for strong tunneling. However, the c-axis tunne ling expressions of Tanaka and Kashiwaya are shown to be incorrect in any l imit. In addition, we consider the c-axis coherent critical current between two identical layered superconductors twisted an angle phi(0) about the c axis with respect to each other. Regardless of the order-parameter symmetry , our coherent tunneling results using a tight-binding intralayer quasipart icle dispersion are inconsistent with the recent c-axis twist bicrystal Bi2 Sr2CaCu2O8+delta twist junction experiments of Li et al.