Topological insulators and K-theory

Oct 27, 2015
57 pages
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Abstract: (arXiv)
We analyze the topological Z2\mathbb{Z}_2 invariant, which characterizes time reversal invariant topological insulators, in the framework of index theory and K-theory. The topological Z2\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 Z2\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 Z2\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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  • 57 pages, 8 figures