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

TL;DR

This paper develops a non-perturbative field-theoretical approach to demonstrate a metal-insulator transition in 2D disordered fermionic systems with chiral symmetry, highlighting the role of topological excitations.

Contribution

It introduces a non-perturbative analysis of Anderson localization in 2D chiral classes, revealing topological vortex effects as the mechanism for the transition.

Findings

Quantum interference effects are absent in perturbation theory.

Topological vortex excitations induce localization and drive the transition.

Surface terms in topological insulators suppress localization effects.

Abstract

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.