Novel $\mathbb{Z}_2$-topological metals and semimetals

Y. X. Zhao; Z. D. Wang

doi:10.1103/physrevlett.116.016401

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arXiv · 1505.05826

Novel $\mathbb{Z}_2$-topological metals and semimetals

Y. X. Zhao·Z. D. Wang

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Abstract

We report two theoretical discoveries for $\mathbb{Z}_2$-topological metals and semimetals. It is shown first that any dimensional $\mathbb{Z}_2$ Fermi surface is topologically equivalent to a Fermi point. Then the famous conventional no-go theorem, which was merely proven before for $\mathbb{Z}$ Fermi points in a periodic system without any discrete symmetry, is generalized to that the total topological charge is zero for all cases. Most remarkably, we find and prove an unconventional strong no-go theorem: all $\mathbb{Z}_2$ Fermi points have the same topological charge $ν_{\mathbb{Z}_2} =1$ or $0$ for periodic systems. Moreover, we also establish all six topological types of $\mathbb{Z}_2$ models for realistic physical dimensions.

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Y. X. Zhao, Z. D. Wang. 2015-12-10. Novel $\mathbb{Z}_2$-topological metals and semimetals. https://doi.org/10.1103/physrevlett.116.016401

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