Emergence of nodal Bogoliubov quasiparticles across the transition from the pseudogap metal to the d-wave superconductor

We model the pseudogap state of the hole- and electron-doped cuprates as a metal with hole and/or electron pocket Fermi surfaces. In the absence of long-range antiferromagnetism, such Fermi surfaces violate the Luttinger requirement of enclosing the same area as free electrons at the same density. Using the Ancilla theory of such a pseudogap state, we describe the onset of conventional $d$-wave superconductivity by the condensation of a charge e Higgs boson transforming as a fundamental under the emergent SU(2) gauge symmetry of a background $\pi$-flux spin liquid. In all cases, we find that the $d$-wave superconductor has gapless Bogoliubov quasiparticles at 4 nodal points on the Brillouin zone diagonals with significant velocity anisotropy, just as in the BCS state. This includes the case of the electron-doped pseudogap metal with only electron pockets centered at wavevectors $(\pi, 0)$, $(0, \pi)$, and an electronic gap along the zone diagonals. Remarkably, in this case too, gapless nodal Bogoliubov quasiparticles emerge within the gap at 4 points along the zone diagonals upon the onset of superconductivity.