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arXiv · 1510.08001

Topological insulators and K-theory

Ralph M. Kaufmann·Dan Li·Birgit Wehefritz-Kaufmann
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Abstract

We analyze the topological $\mathbb{Z}_2$ invariant, which characterizes time reversal invariant topological insulators, in the framework of index theory and K-theory. The topological $\mathbb{Z}_2$ invariant counts the parity of generalized Majorana zero modes, which can be interpreted as an analytical index. As we show, it fits perfectly into a mod 2 index theorem, and the topological index provides an efficient way to compute the topological $\mathbb{Z}_2$ invariant. Finally, we give a new version of the bulk-boundary correspondence which yields an alternative explanation of the index theorem and the topological $\mathbb{Z}_2$ invariant. Here the boundary is not the geometric boundary of a probe, but an effective boundary in the momentum space.

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Ralph M. Kaufmann, Dan Li, Birgit Wehefritz-Kaufmann. 2018-10-29. Topological insulators and K-theory. https://arxiv.org/abs/1510.08001

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