Unconventional superconductivity

Superconducting pairing outside the simple conventional isotropic spin-singlet scenario, with the precise classification depending on the context and evidence. Gap symmetry, pairing mechanism, spin structure and time-reversal behavior are separate questions; a nonstandard gap does not establish every other proposed broken symmetry.

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.

Near clean two-dimensional d-wave nodes, linearized quasiparticle energies form anisotropic cones. Their low-energy density of states is proportional to $|E|$, so electronic heat capacity scales as $T^2$ rather than the activated low-temperature form of a full gap. The clean in-plane penetration-depth increment is linear in T. Disorder, dimensional effects, vortex fields and gap changes can alter these laws, so the assumptions should accompany any proposed diagnostic.

Vortex superflow Doppler-shifts low-energy quasiparticles in a nodal superconductor. For a circular cell of radius $R\propto B^{-1/2}$ and flow magnitude proportional to $1/r$, its spatially averaged magnitude is proportional to $1/R$. A linearly vanishing nodal density of states then acquires a zero-energy contribution proportional to $\sqrt{B}$, producing a low-temperature linear heat-capacity coefficient with that scaling. This is a clean semiclassical mixed-state estimate; the vector flow average can be zero, and disorder, screening, core states and other field effects change its range of validity.

For four equivalent nodes, two spin quasiparticles and local dispersion $E^2={\alpha }^2{q}_1^2+{\beta }^2{q}_2^2$, one node encloses momentum area $\pi E^2/(\alpha \beta )$. Counting states with measure $d^{2}q/(2\pi {)}^2$ gives the displayed positive-excitation density. The associated clean low-temperature heat capacity is $C/\mathcal{A}=18\zeta (3)k_B^3{T}^2/(\pi \alpha \beta )$. Electron-addition spectral density alone has a different count because its coherence weights do not count all particle and hole thermal excitations.

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.