论文标题
美元
$\mathbb{Z}_{2}$ Spin Hopf Insulator: Helical Hinge States and Returning Thouless Pump
论文作者
论文摘要
我们介绍了一种称为旋转HopF绝缘子的HopF绝缘子的时间反向对称的类似物。 Spin Hopf绝缘子在其表面上拥有非平凡的Kane-Mele $ \ Z_2 $不变性，并且是带有旋转轨道耦合的非磁性精致拓扑绝缘子的第一个例子。我们表明，表面上的Kane-Mele $ \ Z_2 $拓扑通常是不稳定的，但是可以通过添加粒子孔和空间反演对称性的组成来稳定。这样的对称性不仅可以保护表面$ \ z_2 $不变，而且还保护自旋Hopf绝缘子上的无间隙螺旋铰链状态。此外，我们表明，在存在四倍的旋转对称性的情况下，自旋Hopf绝缘子表现出返回的泵，以及在急剧边界终止上的表面状态。
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.
