A d-wave superconductor's order parameter changes sign under 90 degree
rotation. As a result, the Josephson current across a tunnel junction
consisting of d-wave superconductors depends on not only the phase
difference but also the grain boundary orientation. In this talk, I
will lead an elementary discussion on two works utilizing the unusual
Josephson effect in d-wave superconductors: (a) the tri-crystal
experiment, which provided the most convincing evidence for d-wave
superconductivity in cuprates so far , and (b) the recent
theoretical proposal for engineering topological superconductivity in
twisted cuprate bilayers .
 C. C. Tsuei and J. R. Kirtley, "Pairing symmetry in cuprate
superconductors", Rev. Mod. Phys. vol. 72, 969 (2010); J. R. Kirtley,
"Probing the order parameter symmetry in the cuprate high temperature
superconductors by SQUID microscopy", C. R. Physique vol. 12, 436
 Oguzhan Can et al, "High-temperature topological superconductivity
in twisted double-layer copper oxides", Nat. Phys. vol. 17, 519 (2021).