  Doped antiferromagnets, described by a t-t'-J model and a suitable 1/N
expansion, exhibit a metallic phase-modulated antiferromagnetic ground state
close to half-filling. Here we demonstrate that the energy of latter state is
an even periodic function of the external magnetic flux threading the square
lattice in an Aharonov-Bohm geometry. The period is equal to the flux quantum
$\Phi_{0}=2\pi\hbar c/q$ entering the Peierls phase factor of the hopping
matrix elements. Thus flux quantization and a concomitant finite value of
superfluid weight D_s occur along with metallic antiferromagnetism. We argue
that in the context of the present effective model, whereby carriers are
treated as hard-core bosons, the charge q in the associated flux quantum might
be set equal to 2e. Finally, the superconducting transition temperature T_c is
related to D_s linearly, in accordance to the generic Kosterlitz-Thouless type
of transition in a two-dimensional system, signaling the coherence of the phase
fluctuations of the condensate. The calculated dependence of T_c on hole
concentration is qualitatively similar to that observed in the high-temperature
superconducting cuprates.
