Nodal quasiparticle power laws

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.

The nodal quasiparticle power laws of a clean d-wave superconductor assume that the excitation energy exceeds any disorder-induced low-energy scale. Scattering from impurities changes the quasiparticle spectrum and can introduce a finite low-energy density of states. A measured power law can consequently cross over as temperature falls, even if the underlying pairing symmetry stays the same.

For example, strong impurity scattering can replace a clean linear-in-temperature London penetration depth increment by a quadratic law at sufficiently low temperature. A power-law exponent alone therefore does not determine the pairing symmetry without a stated scattering regime. Comparing several observables, sample purities and temperature intervals helps distinguish a robust gap feature from a disorder crossover. ^[ref]