# Bott--Kitaev periodic table and index theory

@article{Li2017BottKitaevPT, title={Bott--Kitaev periodic table and index theory}, author={Dan Li}, journal={arXiv: Mathematical Physics}, year={2017} }

We consider topological insulators and superconductors with discrete symmetries and clarify the relevant index theory behind the periodic table proposed by Kitaev.
An effective Hamiltonian determines the analytical index, which can be computed by a topological index. We focus on the spatial dimensions one, two and three, and only consider the bulk theory.
In two dimensions, the $\mathbb{Z}$-valued invariants are given by the first Chern number. Meanwhile, $\mathbb{Z}_2$-valued invariants can…

## 5 Citations

### Index theory & NCG of Topological insulators

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### Topological insulators and the Kane–Mele invariant: Obstruction and localization theory

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We present homotopy theoretic and geometric interpretations of the Kane–Mele invariant for gapped fermionic quantum systems in three dimensions with time-reversal symmetry. We show that the invariant…

### Index theory & NCG of Topological insulators

- Physics
- 2018

In this chapter, we report the recent progress in the understanding of the rich mathematical structures of topological insulators in the framework of index theory and noncommutative geometry.…

### Index theory and noncommutative geometry of topological insulator

- Mathematics
- 2018

In this chapter, we report the recent progress in the understanding of the rich mathematical structures of topological insulators in the framework of index theory and noncommutative geometry.

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