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

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.

20 pages, 1 figure

References in corpus (11)

• The electronic properties of graphene
• Topological insulators and superconductors
• Quantum Spin Hall Insulator State in HgTe Quantum Wells
• Anderson Transitions
• Electron transport in disordered graphene
• Quantum criticality and minimal conductivity in graphene with long-range disorder
• Conductivity of disordered graphene at half filling
• Symmetries of multifractal spectra and field theories of Anderson localization
• Metal-insulator transition from combined disorder and interaction effects in Hubbard-like electronic lattice models with random hopping
• Long range disorder and Anderson transition in systems with chiral symmetry
• Logarithmic scaling of Lyapunov exponents in disordered chiral two-dimensional lattices

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