Localization and Chern numbers for weakly disordered BdG operators

Abstract

After a short discussion of various random Bogoliubov-de Gennes (BdG) model operators and the associated physics, the Aizenman-Molchanov method is applied to prove Anderson localization in the weak disorder regime for the spectrum in the central gap. This allows to construct random BdG operators which have localized states in an interval centered at zero energy. Furthermore, techniques for the calculation of Chern numbers are reviewed and applied to two non-trivial BdG operators, the p+ip wave and d+id wave superconductors.

Minor corrections, to appear in Markov Process Related Fields

References in corpus (4)

• Classification of topological insulators and superconductors in three spatial dimensions
• Quantum Thermal Hall Effect in a Time-Reversal-Symmetry-Broken Topological Superconductor in Two Dimensions : Approach From Bulk Calculations
• Localisation for non-monotone Schroedinger operators
• Localization for random block operators

Cited by in corpus (6)

• Bulk and Boundary Invariants for Complex Topological Insulators: From K-Theory to Physics
• Spectral flows associated to flux tubes
• Chern numbers as half-signature of the spectral localizer
• Quantization of interface currents
• The non-commutative topology of two-dimensional dirty superconductors
• Many-Body Localization: Concepts and Simple Models