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2010

Disordered Topological Insulators via $C^*$-Algebras

Loring, T. A., Hastings, M. B.

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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.

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Hastings M. B. and Loring T. A., J. Math. Phys
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Hastings M. B. and Loring T. A., arXiv:1012.1019

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Kitaev A., personal communication

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