Topological effect on the Anderson transition in chiral symmetry classes

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.