D-wave superconductivity

Pairing with d-wave orbital structure, such as a crystal gap proportional to $k_x^2-k_y^2$. Its sign changes under a quarter-turn rotation, but a compensating overall phase change can leave gauge-invariant observables fourfold symmetric. Gap nodes and phase signs therefore do not by themselves establish nematicity or time-reversal breaking. A phase-sensitive test of d-wave pairing probes relative signs through interference.

A superconductor whose pairing order parameter has the angular or crystal-symmetry structure of d-wave superconductivity. The sign of the gap depends on momentum direction and nodes can permit low-energy fermionic Bogoliubov quasiparticles.

For nearest-neighbor spin-singlet pairing on a square lattice, opposite signs of the pairing amplitude on the two bond directions give the displayed momentum-dependent superconducting gap function. It changes sign under a quarter-turn and has nodes on the zone diagonals. This sign structure is distinct from a nonnegative gap whose magnitude is merely anisotropic. A real pure $d_{x^2-y^2}$ pattern does not by itself require broken time reversal.