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arXiv · 1407.3427

The $Z_2$ Classification of Dimensional Reduced Hopf Insulators

Chang-Yan Wang·Yan He
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Abstract

The Hopf insulators are characterized by a topological invariant called Hopf index which classifies maps from three-sphere to two-sphere, instead of a Chern number or a Chern parity. In contrast to topological insulator, the Hopf insulator is not protected by any kind of symmetry. By dimensional reduction, we argue that there exists a new type of $\mathbb{Z}_2$ index for 2D Hamiltonian with vanishing Chern number. Specific model Hamiltonian with this nontrivial $\mathbb{Z}_2$ index is constructed. We also numerically calculate the topological protected edge modes of this dimensional reduced Hopf insulator and show that they are consistent with the $\mathbb{Z}_2$ classification.

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Chang-Yan Wang, Yan He. 2014-07-13. The $Z_2$ Classification of Dimensional Reduced Hopf Insulators. https://doi.org/10.1088/0953-8984/27/7/075603

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