Metal-insulator transition in two-dimensional random fermion systems of chiral symmetry classes

E. J. König, P. M. Ostrovsky, I. V. Protopopov, and A. D. Mirlin
Phys. Rev. B 85, 195130 – Published 15 May 2012

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 nonperturbatively. Specifically, they are controlled by topological vortexlike excitations of the sigma models. We derive renormalization-group equations including these nonperturbative 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 θ terms on surfaces of 3D topological insulators (in classes AIII and CII, respectively) overpower the vortex-induced localization.

  • Figure
  • Received 30 January 2012

DOI:https://doi.org/10.1103/PhysRevB.85.195130

©2012 American Physical Society

Authors & Affiliations

E. J. König1,2, P. M. Ostrovsky3,4, I. V. Protopopov3,4, and A. D. Mirlin1,2,3,5

  • 1Institute für Theorie der kondensierten Materie, Karlsruhe Institute of Technology, 76128 Karlsruhe, Germany
  • 2DFG Center for Functional Nanostructures, Karlsruhe Institute of Technology, 76128 Karlsruhe, Germany
  • 3Institut für Nanotechnologie, Karlsruhe Institute of Technology, 76021 Karlsruhe, Germany
  • 4L. D. Landau Institute for Theoretical Physics RAS, 119334 Moscow, Russia
  • 5Petersburg Nuclear Physics Institute, 188300 St. Petersburg, Russia

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Issue

Vol. 85, Iss. 19 — 15 May 2012

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