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 π-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 (π, 0), (0, π), 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.

我们将空穴和电子掺杂的铜酸盐的赝能隙态建模为具有空穴和/或电子袋费米表面的金属。在缺乏长程反铁磁性的情况下，这样的费米表面违反了以相同密度包围与自由电子相同面积的路廷格要求。使用这种赝能隙态的 Ancilla 理论，我们通过在背景π通量自旋液体的涌现 SU(2) 规范对称性下，通过电荷e希格斯玻色子变换作为基本原理的凝聚来描述传统d波超导性的开始。在所有情况下，我们发现d波超导体在布里渊区对角线上的 4 个节点处具有无间隙 Bogoliubov 准粒子，具有显着的速度各向异性，就像 BCS 状态一样。这包括电子掺杂赝能隙金属的情况，其仅具有以波矢 ( π , 0) 、 (0,  π ) 为中心的电子袋，以及沿区域对角线的电子能隙。值得注意的是，在这种情况下，超导开始时，无间隙节点 Bogoliubov 准粒子也会出现在沿区域对角线的 4 个点的间隙内。