  Understanding the doped Mott insulator is a central challenge in condensed
matter physics. This study identifies an intrinsic Berry-phase-like sign
structure for the square-lattice $t$-$t'$-$J$ model with the nearest-neighbor
($t$) and next-nearest-neighbor hopping ($t'$), which could help explain the
origin of the quasi-long-range superconducting and stripe phases observed
through density matrix renormalization group (DMRG) calculation. We first
demonstrate that the hole binding underlies both the superconducting and stripe
orders, and then show that the hole pairing generically disappears once the
phase-string or mutual statistics component of the sign structure is switched
off in DMRG calculation. In the latter case, the superexchange interaction no
longer plays a crucial role in shaping the charge dynamics, where a
Fermi-liquid-like phase with small hole Fermi pockets is found. It is in sharp
contrast to the large Fermi surfaces in either the stripe phase found at
$t'/t<0$ or the superconducting phase at $t'/t>0$ in the original $t$-$t'$-$J$
model on the 6-leg ladder.
