Z2 Dirac points with topologically protected multihelicoid surface states
Z2 Dirac points with topologically protected multihelicoid surface states
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DOI：
10.1103/physrevresearch.4.033170
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发表时间：
2022-01
影响因子：
4.2
通讯作者：
Tiantian Zhang;D. Hara;S. Murakami
中科院分区：
文献类型：
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作者：
Tiantian Zhang;D. Hara;S. Murakami
在一些具有时间反转(T)和滑动(G)对称性的狄拉克系统中，出现了多螺旋面态（MHSSs），如在电子和光子系统中所讨论的那样。然而，人们对MHSSs的拓扑性质和出现的条件还不了解。这里我们证明了MHSSs是由$Z_2$单极子电荷Q的体面对应产生的，它不能被定义为与Dirac点相关的局部量，不像表征Weyl点的Z单极子电荷。先前已知的Q公式是非量规不变的，因此不能表征mhss。通过将Q重新定义为k空间中的全局拓扑不变量来修正Q定义的这个缺点。令人惊讶的是，新定义的表征GT不变无间隙系统的Q等于g保护的$Z_2$拓扑不变量v，它仅在t破缺间隙系统中是非平凡的。这种Q的全局定义，只要保持GT对称性，即使Dirac点分裂为Weyl点或节点环，也能通过降低对称性自动保证MHSSs的出现。当两个垂直的g保持不变时，Q可以简化为基于对称性的指标，当引起t破微扰时，在几种情况下可以诊断出强制填充的拓扑晶体绝缘子。候选材料Li2B4O7以及保留MHSSs的空间群列表也被提出。
In some Dirac systems with time-reversal (T) and glide (G) symmetries, multihelicoid surface states (MHSSs) appear, as discussed in various systems such as electronic and photonic ones. However, the topological nature and the conditions for the appearance of the MHSSs have not been understood. Here we show that MHSSs result from bulk-surface correspondence for the $Z_2$ monopole charge Q, which cannot be defined as a local quantity associated with the Dirac point, unlike the Z monopole charge characterizing Weyl points. The previously known formula of Q turns out to be non-gauge-invariant and thus cannot characterize the MHSSs. This shortcoming of the definition of Q is amended by redefining Q as a global topological invariant in k-space. Surprisingly, the newly defined Q, characterizing GT invariant gapless systems, is equal to the G-protected $Z_2$ topological invariant v, which is nontrivial only in T-breaking gapped systems. This global definition of Q automatically guarantees the appearance of MHSSs even when the Dirac point splits into Weyl points or a nodal ring by lowering the symmetry, as long as the GT symmetry is preserved. Q can be simplified to symmetry-based indicators when two vertical Gs are preserved, and filling-enforced topological crystalline insulators are diagnosed in several cases when a T-breaking perturbation is induced. Material candidate Li2B4O7 together with a list of space groups preserving MHSSs are also proposed.