Evolution from the Zhang-Rice singlet to pair formation in cuprate

In the resonating valence bond theory for high T_c superconductivity in cuprate, pairing emerges from doping holes into the parent Mott insulator with antiferromagnetic (AF) superexchange between Cu spins. The core physics is closely tied to the behavior of strongly-correlated holes in the AF background, which can be captured by the Hubbard model. We use scanning tunneling microscopy to visualize the electronic states of diluted holes dispersed into the Ca₂CuO₂Cl₂ Mott insulator of cuprate. An isolated monovalent dopant exhibits an in-gap electronic state and four-lobe clover-shaped spatial distribution representing a Zhang-Rice singlet. For multiple dopants close to each other, the overlap of wavefunctions generates the isolate unit of the electronic liquid crystal phase in SC cuprate, behaving like the stripe and ladder shapes. With increasing doping, a small U-shaped gap first emerges on relatively isolated stripe arrays, and evolves smoothly into a V-shaped gap characteristic of d-wave superconductivity in more extended patches. These results fully visualize the microscopic process of the single doped hole to the pair formation, ending with the superconductivity in the cuprate.