  In this Letter, we propose a mechanism of an emergent quasi-localized phase
in chiral symmetry classes, where wave function along a spatial direction with
weak topology is delocalized but exponentially localized along the other
directions. The Anderson transition in 2D chiral symmetry classes is induced by
the proliferation of vortex-antivortex pairs of a U(1) phase degree of freedom,
while the weak topology endows the pair with the Berry phase. We argue that the
Berry phase induces spatial polarizations of the pairs along the topological
direction through the quantum interference effect, and the proliferation of the
polarized vortex pairs results in the quasi-localized phase.
