  Based on the self-consistent $T$-matrix approximation, the quantum
interference (QI) effect is studied with the diagrammatic technique in
weakly-disordered two-dimensional crystals with nearly half-filled bands. In
addition to the usual 0-mode cooperon and diffuson, there exist $\pi$-mode
cooperon and diffuson in the unitary limit due to the particle-hole symmetry.
The diffusive $\pi$-modes are gapped by the deviation from the exactly-nested
Fermi surface. The conductivity diagrams with the gapped $\pi$-mode cooperon or
diffuson are found to give rise to unconventional features of the QI effect.
Besides the inelastic scattering, the thermal fluctuation is shown to be also
an important dephasing mechanism in the QI processes related with the diffusive
$\pi$-modes. In the proximity of the nesting case, a power-law
anti-localization effect appears due to the $\pi$-mode diffuson. For large
deviation from the nested Fermi surface, this anti-localization effect is
suppressed, and the conductivity remains to have the usual logarithmic
weak-localization correction contributed by the 0-mode cooperon. As a result,
the dc conductivity in the unitary limit becomes a non-monotonic function of
the temperature or the sample size, which is quite different from the
prediction of the usual weak-localization theory.
