  Field-theoretical approach to Anderson localization in 2D disordered
fermionic systems of chiral symmetry classes (BDI, AIII, CII) is developed.
Important representatives of these symmetry classes are random hopping models
on bipartite lattices at the band center. As was found by Gade and Wegner two
decades ago within the sigma-model formalism, quantum interference effects in
these classes are absent to all orders of perturbation theory. We demonstrate
that the quantum localization effects emerge when the theory is treated
non-perturbatively. Specifically, they are controlled by topological
vortex-like excitations of the sigma models. We derive renormalization group
equations including these non-perturbative contributions. Analyzing them, we
find that the 2D disordered systems of chiral classes undergo a metal-insulator
transition driven by topologically induced Anderson localization. We also show
that the Wess-Zumino and Z_2 theta terms on surfaces of 3D topological
insulators (in classes AIII and CII, respectively) overpower the vortex-induced
localization.
