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arXiv · 1511.05314

Controlled topological phases and bulk-edge correspondence

Yosuke Kubota
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Abstract

In this paper, we introduce a variation of the notion of topological phase reflecting metric structure of the position space. This framework contains not only periodic and non-periodic systems with symmetries in Kitaev's periodic table but also topological crystalline insulators. We also define the bulk and edge indices as invariants taking values in the twisted equivariant $\mathrm{K}$-groups of Roe algebras as generalizations of existing invariants such as the Hall conductance or the Kane--Mele $\mathbb{Z}_2$-invariant. As a consequence, we obtain a new mathematical proof of the bulk-edge correspondence by using the coarse Mayer-Vietoris exact sequence.

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Yosuke Kubota. 2016-02-09. Controlled topological phases and bulk-edge correspondence. https://doi.org/10.1007/s00220-016-2699-3

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