Macroscopic Symmetry Group Describes Josephson Tunneling in Twinned Crystals

A macroscopic symmetry group describing the superconducting state of an orthorhombically twinned crystal of YBCO is introduced. This macroscopic symmetry group is different for different symmetries of twin boundaries. Josephson tunneling experiments performed on twinned crystals of YBCO determine this macroscopic symmetry group and hence determine the twin boundary symmetry (but do not experimentally determine whether the microscopic order parameter is primarily d- or s-wave). A consequence of the odd-symmetry twin boundaries in YBCO is the stability of vortices containing one half an elementary flux quantum at the intersection of a twin boundary and certain grain boundaries.