  In the context of an effective model for doped antiferromagnets, whereby the
charge carriers are treated as hard-core bosons, we demonstrate that the ground
state energy close to half-filling 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 the charge q in the associated flux quantum
might be set equal to 2e. 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, signalling 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.
