  Based on the SU(2) lattice gauge theory formulation of the t-J model, we
discuss possible signature of the unit cell doubling associated with the
staggered flux (SF) state in the lightly doped spin liquid. Although the SF
state appears only dynamically in a uniform d-wave superconducting (SC) state,
a topological defect [SU(2) vortex] freezes the SF state inside the vortex
core. Consequently, the unit cell doubling shows up in the hopping
($\chi_{ij}$) and pairing ($\Delta_{ij}$) order parameters of physical
electrons. We find that whereas the center in the vortex core is a SF state, as
one moves away from the core center, a correlated staggered modulation of
$\chi_{ij}$ and $\Delta_{ij}$ becomes predominant. We predict that over the
region outside the core and inside the internal gauge field penetration depth
around a vortex center, the local density-of-states (LDOS) exhibits staggered
peak-dip (SPD) structure inside the V-shaped profile when measured on the
bonds. The SPD structure has its direct origin in the unit cell doubling
associated with the SF core and the robust topological texture, which has
little to do with the symmetry of the d-wave order parameter. Therefore the
structure may survive the tunneling matrix element effects and easily be
detected by STM experiment.
