Classification of crystalline insulators without symmetry indicators: Atomic and fragile topological phases in twofold rotation symmetric systems
Classification of crystalline insulators without symmetry indicators: Atomic and fragile topological phases in twofold rotation symmetric systems
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DOI：
10.1103/physrevb.100.115160
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发表时间：
2019-06
影响因子：
3.7
通讯作者：
S. Kooi;Guido van Miert;C. Ortix
中科院分区：
文献类型：
--
作者：
S. Kooi;Guido van Miert;C. Ortix
电子结构中的拓扑晶相一般可以利用价带的空间对称性特征进行分类，并将它们映射到适当的对称性指示剂上。这些映射最近已被应用于识别数千种拓扑电子材料。然而，可能存在超越这一范式的拓扑晶体非平凡阶段：它们不能使用空间对称标签来识别，因此缺乏任何分类。在这项工作中，我们实现了第一个这样的分类，展示了具有双重旋转对称性的二维晶体的范例。我们对具有强自旋-轨道耦合的时反不变系统中的有隙相进行了分类，确定了一组对应于嵌套量子化部分Berry相的拓扑不变量集。通过进一步分离可用指数局域对称Wannier函数表示的原子绝缘体集合，我们推断存在脆性类型的拓扑晶相，这种拓扑晶相将被用对称性指示符诊断为拓扑平凡的，并构造了许多展示这一相的微观模型。考虑到脆弱的拓扑相有望在扭曲的双层石墨烯等新型二维材料中发挥核心作用，我们的工作有望产生重要的影响。
Topological crystalline phases in electronic structures can be generally classified using the spatial symmetry characters of the valence bands and mapping them onto appropriate symmetry indicators. These mappings have been recently applied to identify thousands of topological electronic materials. There can exist, however, topological crystalline nontrivial phases that go beyond this paradigm: They cannot be identified using spatial symmetry labels and consequently lack any classification. In this work, we achieve the first of such classifications showcasing the paradigmatic example of two-dimensional crystals with twofold rotation symmetry. We classify the gapped phases in time-reversal invariant systems with strong spin-orbit coupling identifying a set of three ${\mathbb{Z}}_{2}$ topological invariants, which correspond to nested quantized partial Berry phases. By further isolating the set of atomic insulators representable in terms of exponentially localized symmetric Wannier functions, we infer the existence of topological crystalline phases of the fragile type that would be diagnosed as topologically trivial using symmetry indicators and construct a number of microscopic models exhibiting this phase. Our work is expected to have important consequences given the central role fragile topological phases are expected to play in novel two-dimensional materials such as twisted bilayer graphene.