 Solution

The clearest examples are the cuprate superconductors. Their unusual properties should be compared with the clean, weak-coupling, fully gapped s-wave electron–phonon limit of BCS theory; that limit is not a definition of all possible BCS-like paired states.

Cuprates are layered copper oxides with strongly anisotropic transport. Their undoped parents are antiferromagnetic Mott insulators or, more specifically for many compounds, charge-transfer insulators, despite partially filled bands in a simple band picture. Doping produces a superconducting dome rather than simply improving an ordinary weakly interacting metal. This points to strong electronic correlations. Near optimal doping, an extended temperature range often shows approximately linear electrical resistivity, termed strange-metal behaviour, instead of the low-temperature $T^2$ law of a conventional Fermi liquid. Neither law applies at every temperature and doping.

The dominant Cooper pair symmetry is spin-singlet $d_{x^2-y^2}$, with a representative gapIt changes sign under a quarter turn and has nodes on the zone diagonals. Phase-sensitive experiments detect that sign change; it is not established by a large transition temperature alone. ^[ref] Clean nodal quasiparticles give power-law low-temperature responses, for example electronic heat capacity $C\propto T^2$ and penetration-depth change $\lambda (T)-\lambda (0)\propto T$, in contrast with activated responses of a fully gapped s-wave state. Disorder, dimensional crossover and competing phases can alter these powers.

The cuprate pseudogap is a partial, momentum-dependent loss of low-energy electronic spectral weight extending above the superconducting transition in underdoped materials. It need not be identical to the superconducting gap, and observing it alone does not identify its microscopic origin or prove preformed pairs. ^[ref]

Short coherence lengths, anisotropy and low phase stiffness in underdoped systems make thermal phase and vortex fluctuations important. Many cuprates are strong type-II superconductors, with large London penetration depths relative to their superconducting coherence lengths. Gap-to-transition-temperature ratios and isotope effects vary with doping and need not obey the simplest weak-coupling benchmarks $2\Delta (0)/(k_{\mathrm{B}}{T}_c)=3.53$ and $T_c\propto M_{\mathrm{ion}}^{-1/2}$. A weak or variable isotope effect by itself does not identify the pairing mechanism.

These features motivate strongly correlated pairing descriptions, often involving spin fluctuations, but do not uniquely establish a microscopic pairing glue. Other high-temperature families need not share every cuprate property: iron-based superconductors are multiband and may be nodeless. The robust distinction is the observed combination of correlated normal states, unusual gap symmetry and important collective fluctuations, rather than high $T_c$ alone.