Disordered Topological Insulators via $C^*$-Algebras

Details Disordered Topological Insulators via $C^*$-Algebras Disordered Topological Insulators via $C^*$-Algebras

2010-05-26

arxiv.org/abs/1005.4883v2

Europhysics Letters 92, 67004 (2010)

Physics

Condensed Matter

Mesoscale and Nanoscale Physics

Added detail regarding the mapping of almost commuting unitary matrices to almost commuting Hermitian matrices that form an ap

Scientific paper

The theory of almost commuting matrices can be used to quantify topological obstructions to the existence of localized Wannier functions with time-reversal symmetry in systems with time-reversal symmetry and strong spin-orbit coupling. We present a numerical procedure that calculates a Z_2 invariant using these techniques, and apply it to a model of HgTe. This numerical procedure allows us to access sizes significantly larger than procedures based on studying twisted boundary conditions. Our numerical results indicate the existence of a metallic phase in the presence of scattering between up and down spin components, while there is a sharp transition when the system decouples into two copies of the quantum Hall effect. In addition to the Z_2 invariant calculation in the case when up and down components are coupled, we also present a simple method of evaluating the integer invariant in the quantum Hall case where they are decoupled.

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