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arXiv · 1403.7962

Weyl and Dirac semimetals with Z_2 topological charge

Takahiro Morimoto·Akira Furusaki
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Abstract

We study the stability of gap-closing (Weyl or Dirac) points in the three-dimensional Brillouin zone of semimetals using Clifford algebras and their representation theory. We show that a pair of Weyl points with $\mathbb{Z}_2$ topological charge are stable in a semimetal with time-reversal and reflection symmetries when the square of the product of the two symmetry transformations equals minus identity. We present toy models of $\mathbb{Z}_2$ Weyl semimetals which have surface modes forming helical Fermi arcs. We also show that Dirac points with $\mathbb{Z}_2$ topological charge are stable in a semimetal with time-reversal, inversion, and SU(2) spin rotation symmetries when the square of the product of time-reversal and inversion equals plus identity. Furthermore, we briefly discuss the topological stability of point nodes in superconductors using Clifford algebras.

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Takahiro Morimoto, Akira Furusaki. 2014-06-25. Weyl and Dirac semimetals with Z_2 topological charge. https://doi.org/10.1103/physrevb.89.235127

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