Metal-insulator transition in 2D random fermion systems of chiral symmetry classes

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 e
ects 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 Z2 theta terms on surfaces

of 3D topological insulators (in classes AIII and CII, respectively) overpower the vortex-induced localization.