Nodal quasiparticle density of states in a two-dimensional d-wave superconductor ($g_{\mathrm{qp}}(E)/\mathcal{A}=4E/(\pi \alpha \beta )$)

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.