Josephson (001) tilt grain boundary junctions of high-temperature superconductors

We calculate the Josephson critical current I, across in-plane (001) tilt grain boundary junctions of high-temperature superconductors. We assume the Fermi surface has either an electron-doped form, or one of three hole-doped forms, and either random or specular tunneling across the junctions. We find that in-plane 'phase-sensitive' experiments are consistent with our results for the electron-doped superconductors. For the hole-doped superconductors, however, the results depend strongly upon the details of both the Fermi surface topology and the nature of the tunneling, and are therefore considerably less robust than has generally been believed. Hence, the tricrystal, tetracrystal, and interferometry experiments on hole-doped high-temperatures superconductors are unreliable, and should be redesigned.