  Cooper pairing instability in a Fermi liquid is well understood by the BCS
theory, but pairing mechanism for doped Mott insulators still remains elusive.
Previously it has been shown by density matrix renormalization group (DMRG)
method that a single doped hole is always self-localized due to the quantum
destructive interference of the phase string signs hidden in the t-J ladders.
Here we report a DMRG investigation of hole binding in the same model, where a
novel pairing-glue scheme beyond the BCS realm is discovered. Specifically, we
show that, in addition to spin pairing due to superexchange interaction, the
strong frustration of the phase string signs on the kinetic energy gets
effectively removed by pairing the charges, which results in strong binding of
two holes. By contrast, if the phase string signs are switched off
artificially, the pairing strength diminishes significantly even if the
superexchange coupling remains the same. In the latter, unpaired holes behave
like coherent quasiparticles with pairing drastically weakened, whose sole
origin may be attributed to the resonating-valence-bond (RVB) pairing of spins.
Such non-BCS pairing mechanism is therefore beyond the RVB picture and may shed
important light on the high-T_c cuprate superconductors.
