  Based on the so called $t$-$\phi$ model in two-dimensional (2D) lattices, we
investigate the stabilities of a class of extended staggered-flux (SF) phases
(which are the extensions of the $\sqrt{2}\times\sqrt{2}$ SF phase to
generalized spatial periods) against the Fermi-liquid phase. Surprisingly, when
away from the nesting electron filling, some extended-SF phases take over the
dominant SF phase (the $\sqrt{2}\times\sqrt{2}$ SF phase for the square
lattice, a $1\times\sqrt{3}$ SF phase for the triangular one), compete with the
Fermi-liquid phase in nontrivial patterns, and still occupy significant space
in the phase diagram through the advantage in the total electronic kinetic
energies. The results can be termed as the generalized Perierls
orbital-antiferromagnetic instabilities of the Fermi-liquid phase in 2D
lattice-electron models.
