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arXiv · 2208.08455

$\mathbb{Z}_{2}$ Spin Hopf Insulator: Helical Hinge States and Returning Thouless Pump

Penghao Zhu·A. Alexandradinata·Taylor L. Hughes
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Abstract

We introduce a time-reversal-symmetric analog of the Hopf insulator that we call a spin Hopf insulator. The spin Hopf insulator harbors nontrivial Kane-Mele $\Z_2$ invariants on its surfaces, and is the first example of a nonmagnetic delicate topological insulator with spin-orbit coupling. We show that the Kane-Mele $\Z_2$ topology on the surface is generically unstable, but can be stabilized by the addition of a composition of the particle hole and spatial inversion symmetry. Such a symmetry not only protects the surface $\Z_2$ invariant, but also protects gapless helical hinge states on the spin Hopf insulator. Furthermore, we show that in the presence of four-fold rotational symmetry, the spin Hopf insulator exhibits a returning Thouless pump, as well as surface states on sharp boundary terminations.

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Penghao Zhu, A. Alexandradinata, Taylor L. Hughes. 2022-08-17. $\mathbb{Z}_{2}$ Spin Hopf Insulator: Helical Hinge States and Returning Thouless Pump. https://doi.org/10.1103/physrevb.107.115159

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