  The quest to understand the nature of superconductivity in cuprates has
spotlighted the pair density wave (PDW) -- a superconducting state
characterized by a spatially modulated order parameter. Despite significant
advances in understanding PDW properties, conclusively demonstrating its
presence in systems pertinent to cuprate superconductors remains elusive. In
this study, we present a systematic density-matrix renormalization group study
to investigate the Emery model (or the three-band Hubbard model) on two-leg
square cylinders with negative electron hopping term $t_{pp}$ between adjacent
oxygen sites. Kinetic frustration - introduced by changing the sign of
oxygen-oxygen hopping - leads to a much reduced Cu-Cu antiferromagnetic
exchange along with an enlarged charge transfer energy that changes the local
properties of the model. At light doping levels, our findings reveal a ground
state remarkably consistent with a PDW, exhibiting mutually commensurate
superconducting (SC), charge and spin density wave correlations. Intriguingly,
the dominant SC pairing is observed between neighboring oxygen sites, diverging
from the expected Cu sites in the positive $t_{pp}$ case. When the system
incorporates moderate near-neighbor interactions, particularly an attractive
$V_{pp}$ between adjacent oxygen sites, the SC correlations become
quasi-long-ranged, accompanied by a pronounced divergence in the PDW
susceptibility. When further increase the attractive $V_{pp}$, the system gives
ways to an unconventional $d$-wave superconductivity.
