  The parent compound of cuprates is a charge-transfer-type Mott insulator with
strong hybridization between the Cu $3d_{\mathrm x^2-y^2}$ and O $2p$ orbitals.
A key question concerning the pairing mechanism is the behavior of doped holes
in the antiferromagnetic (AF) Mott insulator background, which is a
prototypical quantum many-body problem. It was proposed that doped hole on the
O site tends to form a singlet, known as Zhang-Rice singlet (ZRS), with the
unpaired Cu spin. But experimentally little is known about the properties of a
single hole and the interplay between them that leads to superconductivity.
Here we use scanning tunneling microscopy to visualize the electronic states in
hole-doped $\mathrm{Ca_2CuO_2Cl_2}$, aiming to establish the atomic-scale local
basis for pair formation. A single doped hole is shown to have an in-gap state
and a clover-shaped spatial distribution that can be attributed to a localized
ZRS. When the dopants are close enough, they develop delocalized molecular
orbitals with characteristic stripe- and ladder-shaped patterns, accompanied by
the opening of a small gap around the Fermi level ($E_{\mathrm F}$). With
increasing doping, the molecular orbitals proliferate in space and gradually
form densely packed plaquettes, but the stripe and ladder patterns remain
nearly the same. The low-energy electronic states of the molecular orbitals are
intimately related to the local pairing properties, thus play a vitally
important role in the emergence of superconductivity. We propose that the
Cooper pair is formed by two holes occupying the stripe-like molecular orbital,
while the attractive interaction is mediated by the AF spin background.
