The defining characteristic of hole-doped cuprates is d-wave high temperature superconductivity. However, intense theoretical interest is now focused on whether a pair density wave state (PDW) could coexist with cuprate superconductivity [D. F. Agterberg et al., Annu. Rev. Condens. Matter Phys. 11, 231 (2020)]. Here, we use a strong-coupling mean-field theory of cuprates, to model the atomic-scale electronic structure of an eight-unit-cell periodic, d-symmetry form factor, pair density wave (PDW) state coexisting with d-wave superconductivity (DSC). From this PDW + DSC model, the atomically resolved density of Bogoliubov quasiparticle states Nr,E is predicted at the terminal BiO surface of Bi₂Sr₂CaCu₂O₈ and compared with high-precision electronic visualization experiments using spectroscopic imaging scanning tunneling microscopy (STM). The PDW + DSC model predictions include the intraunit-cell structure and periodic modulations of Nr,E, the modulations of the coherence peak energy Δpr, and the characteristics of Bogoliubov quasiparticle interference in scattering-wavevector space q-space. Consistency between all these predictions and the corresponding experiments indicates that lightly hole-doped Bi₂Sr₂CaCu₂O₈ does contain a PDW + DSC state. Moreover, in the model the PDW + DSC state becomes unstable to a pure DSC state at a critical hole density p*, with empirically equivalent phenomena occurring in the experiments. All these results are consistent with a picture in which the cuprate translational symmetry-breaking state is a PDW, the observed charge modulations are its consequence, the antinodal pseudogap is that of the PDW state, and the cuprate critical point at p* ≈ 19% occurs due to disappearance of this PDW.

空穴掺杂的铜酸盐的定义特征是d波高温超导。但是，现在人们对理论上的浓厚兴趣集中在线对密度波态（PDW）是否可以与铜酸盐超导性共存[DF Agterberg等人，Annu。Biol。Chem。，1993，53，1959] 。凝视牧师 物质物理学 11，231（2020）]。在这里，我们使用铜酸盐的强耦合平均场理论，对与d波共存的8单元胞周期d对称形状因子，对密度波（PDW）状态的原子尺度电子结构进行建模超导（DSC）。从这个PDW + DSC模型中，Bogoliubov准粒子态的原子分辨密度ñ[R，Ë在Bi ₂ Sr ₂ CaCu ₂ O ₈的末端BiO表面预测了γ射线，并与使用光谱成像扫描隧道显微镜（STM）的高精度电子可视化实验进行了比较。PDW + DSC模型的预测包括单元格内结构和周期性调制ñ[R，Ë，相干峰值能量的调制 Δp[R， 波矢量空间中的波哥廖布夫准粒子干涉及其特性 q--空间。所有这些预测与相应实验之间的一致性表明，轻度掺杂Bi ₂ Sr ₂ CaCu ₂ O ₈的确包含PDW + DSC状态。此外，在该模型中，PDW + DSC状态在临界孔密度p *下变得不稳定，成为纯DSC状态，实验中出现了经验上相同的现象。所有这些结果与图片一致，在该图片中，铜酸盐的平移对称性破坏状态为PDW，观察到的电荷调制为其结果，抗结伪间隙为PDW状态，且铜酸盐的临界点为p * ≈19 ％由于此PDW的消失而发生。