Localization and Chern Numbers for Weakly Disordered BdG Operators

#### G. De Nittis, M. Drabkin, H. Schulz-Baldes

2015, v.21, №2, 463-482

ABSTRACT

After a short discussion of various random Bogoliubov\tire de Gennes (BdG) model operators and the associated physics, the Aizenman\tire 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 $p+\imath p$ wave and $d+\imath d$ wave superconductors.

Keywords: Anderson localization, weak disorder, random Bogoliubov\tire de Gennes operators