Scanning SQUID microscope tests of the symmetry of the high-T_c gap

Direct observations of the half-integer flux quantum effect in rings, disks, and blanket films of the high-Tc cuprate superconductors YBa2Cu3O7-δ (YBCO), GdBa2Cu3O7-δ (GdBCO), Tl2Ba2CuO6+δ (T12201), and Bi2Sr2CaCu2O8+δ (BSCCO) with three tricrystal substrate geometries show that their gaps have sign changes consistent with d-wave symmetry. The blanket geometry gives the Josephson penetration depth directly, and provides a means for symmetry tests without patterning. T12201 is a tetragonal, single-layer, cuprate without chains. When combined with photoemission results, our BSCCO results imply that the gap follows dx2-y2 symmetry closely. Asymmetric 45 degree bicrystal grain boundary samples show spontaneous magnetization, as expected for d-wave superconductors with interface roughness.