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 [1], and (b) the recent

theoretical proposal for engineering topological superconductivity in

twisted cuprate bilayers [2].

[1] 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

(2011).

[2] Oguzhan Can et al, "High-temperature topological superconductivity

in twisted double-layer copper oxides", Nat. Phys. vol. 17, 519 (2021).