Understanding the electron pairing in hole-doped cuprate superconductors has been a challenge, in particular because the “normal” state from which it evolves is unprecedented. Now, after three and a half decades of research, involving a wide range of experimental characterizations, it is possible to delineate a clear and consistent cuprate story. It starts with doping holes into a charge-transfer insulator, resulting in in-gap states. These states exhibit a pseudogap resulting from the competition between antiferromagnetic superexchange J between nearest-neighbor Cu atoms (a real-space interaction) and the kinetic energy of the doped holes, which, in the absence of interactions, would lead to extended Bloch-wave states whose occupancy is characterized in reciprocal space. To develop some degree of coherence on cooling, the spin and charge correlations must self-organize in a cooperative fashion. A specific example of resulting emergent order is that of spin and charge stripes, as observed in La${}_{2-x}$Ba${}_x$CuO${}_4$. While stripe order frustrates bulk superconductivity, it nevertheless develops pairing and superconducting order of an unusual character. The antiphase order of the spin stripes decouples them from the charge stripes, which can be viewed as hole-doped, two-leg, spin-$\frac{1}{2}$ ladders. Established theory tells us that the pairing scale is comparable to the singlet-triplet excitation energy, $\sim J/2$, on the ladders. To achieve superconducting order, the pair correlations in neighboring ladders must develop phase order. In the presence of spin stripe order, antiphase Josephson coupling can lead to pair-density-wave superconductivity. Alternatively, in-phase superconductivity requires that the spin stripes have an energy gap, which empirically limits the coherent superconducting gap. Hence, superconducting order in the cuprates involves a compromise between the pairing scale, which is maximized at $x\sim \frac{1}{8}$, and phase coherence, which is optimized at $x\sim 0.2$. To understand further experimental details, it is necessary to take account of the local variation in hole density resulting from dopant disorder and poor screening of long-range Coulomb interactions. At large hole doping, kinetic energy wins out over J, the regions of intertwined spin and charge correlations become sparse, and the superconductivity disappears. While there are a few experimental mysteries that remain to be resolved, I believe that this story captures the essence of the cuprates.

了解空穴掺杂的铜酸盐超导体中的电子配对一直是一个挑战，特别是因为它演变的“正常”状态是前所未有的。现在，经过三年半的研究，涉及广泛的实验表征，有可能描绘出一个清晰一致的铜酸盐故事。它从将空穴掺杂到电荷转移绝缘体中开始，导致间隙状态。这些状态表现出由反铁磁超交换J之间的竞争引起的赝隙最近邻 Cu 原子（实空间相互作用）和掺杂空穴的动能之间的关系，在没有相互作用的情况下，这将导致扩展的布洛赫波态，其占有率以倒易空间为特征。为了在冷却时形成一定程度的相干性，自旋和电荷相关性必须以协作方式自组织。产生的涌现顺序的一个具体例子是自旋和电荷条纹，如在 La${}_{2-X}$巴${}_X$氧化铜${}_4$. 虽然条纹有序阻碍了体超导，但它仍然发展出具有不同寻常特征的配对和超导有序。自旋条纹的反相顺序将它们与电荷条纹解耦，电荷条纹可以看作是空穴掺杂的、双腿的、自旋的$\frac{1}{2}$梯子。已建立的理论告诉我们配对尺度与单重态-三重态激发能相当，$～J/2$，在梯子上。为了实现超导有序，相邻阶梯中的对相关性必须形成相序。在存在自旋条纹顺序的情况下，反相约瑟夫森耦合会导致对密度波超导。或者，同相超导要求自旋条纹具有能隙，这在经验上限制了相干超导能隙。因此，铜酸盐中的超导顺序涉及配对尺度之间的折衷，在$X～\frac{1}{8}$, 和相位相干, 优化在 $X～0.2$. 为了了解进一步的实验细节，有必要考虑由掺杂剂无序和长程库仑相互作用筛选不良导致的空穴密度的局部变化。在大空穴掺杂时，动能胜过J，自旋和电荷相关性相互交织的区域变得稀疏，超导性消失。虽然还有一些实验谜团有待解决，但我相信这个故事抓住了铜酸盐的本质。