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The superconducting gap function is a momentum-dependent pairing amplitude $\Delta (\mathbf{k})$, including a phase as well as a magnitude. A fully gapped isotropic state and a state with symmetry-required nodes can have different low-temperature responses. Heat capacity, thermal transport, London penetration depth and tunnelling spectra probe the low-energy quasiparticle spectrum. Activated behavior suggests a nonzero minimum gap; power laws can indicate nodes. For example, clean line nodes give a penetration-depth correction linear in temperature, whereas disorder can change the apparent power.

Such magnitude-sensitive probes require care: impurities, several bands, anisotropic full gaps and surface states can imitate or modify simple expectations. A node does not by itself establish a particular sign pattern, and the absence of a coherence peak is not a complete symmetry determination. The strongest identification combines momentum-sensitive spectra with phase-sensitive superconducting gap experiments.

For an illustrative $d_{x^2-y^2}$ state, $\Delta (\phi )\propto \cos 2\phi$ changes sign under a $90^{\circ }$ rotation. A Josephson junction to a conventional s-wave reference can turn that sign into an intrinsic phase shift. In a corner DC SQUID with junctions on orthogonal crystal faces, one branch can acquire an extra $\pi$ relative to the other. For equal junctions and negligible loop inductance,Changing ${\delta }_{\mathrm{int}}$ from zero to $\pi$ shifts the interference pattern by half a flux period. The 1993 YBCO–Pb experiment compared phase-coherent junction geometries and found evidence for that sign reversal, while explicitly discussing SQUID asymmetry and trapped vortices. Those controls matter: an arbitrary shifted trace is not by itself a proof of pairing symmetry.^[ref]

A tricrystal half-flux experiment arranges grain-boundary junctions so that a sign-changing order parameter produces an odd total $\pi$ shift around a ring. Fluxoid consistency then favors a half-integer flux state, with the detailed spontaneous flux depending on loop inductance and junction strengths. Choosing comparison geometries without that frustration and controlling trapped external flux separates the pairing-phase effect from ordinary flux trapping.^[ref]

The conclusion is strongest when the same candidate symmetry explains nodes, crystal-axis dependence and these phase-sensitive interference results. The phase-sensitive observation distinguishes a sign-changing gap from a merely anisotropic positive gap; no single temperature power law supplies that distinction.

A complex momentum-dependent pairing amplitude. Its crystal-symmetry transformation, nodes and relative signs distinguish candidate superconducting states. Magnitude-sensitive spectra alone generally do not establish all relative signs; phase-sensitive superconducting gap experiments test them through interference.