Theory of polarization textures in crystal supercells
Theory of polarization textures in crystal supercells
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DOI：
10.1103/physrevresearch.5.033216
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发表时间：
2023-05
影响因子：
4.2
通讯作者：
Daniel Bennett;W. Jankowski;G. Chaudhary;E. Kaxiras;Robert-Jan Slager
中科院分区：
文献类型：
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作者：
Daniel Bennett;W. Jankowski;G. Chaudhary;E. Kaxiras;Robert-Jan Slager
最近，拓扑非平凡的偏振纹理已被预测和观察到在纳米尺度系统。虽然这些偏振纹理在应用方面是有趣的和有前途的，但它们的拓扑结构一般还没有被完全理解。例如，拓扑极化结构和能带拓扑之间的关系还没有被探索，而极域结构通常被认为是拓扑平凡系统。特别地，晶体超晶胞中的局部极化没有很好地定义，并且通常使用不满足规范不变性的近似来计算。此外，超晶胞中的局部极化通常使用涉及较小单位晶胞的计算来近似，这意味着与超晶胞的电子结构的连接丢失。在这项工作中，我们提出了一个局部极化的定义，这是规范不变的，可以直接计算从一个超原胞没有近似。我们使用第一性原理计算相称的双层六方氮化硼，我们的局部极化的表达式给出正确的结果在单位晶胞水平，这是一个第一近似的局部极化的莫尔超晶格。我们还利用一个有效的模型说明了局域极化可以直接在真实的空间中计算。最后，我们讨论了偏振与能带拓扑的关系，指出偏振织构的正确定义是必不可少的。
Recently, topologically nontrivial polarization textures have been predicted and observed in nanoscale systems. While these polarization textures are interesting and promising in terms of applications, their topology in general is yet to be fully understood. For example, the relation between topological polarization structures and band topology has not been explored, and polar domain structures are typically considered in topologically trivial systems. In particular, the local polarization in a crystal supercell is not well-defined, and typically calculated using approximations which do not satisfy gauge invariance. Furthermore, local polarization in supercells is typically approximated using calculations involving smaller unit cells, meaning the connection to the electronic structure of the supercell is lost. In this work, we propose a definition of local polarization which is gauge invariant and can be calculated directly from a supercell without approximations. We show using first-principles calculations for commensurate bilayer hexagonal boron nitride that our expressions for local polarization give the correct result at the unit cell level, which is a first approximation to the local polarization in a moir\'e superlattice. We also illustrate using an effective model that the local polarization can be directly calculated in real space. Finally, we discuss the relation between polarization and band topology, for which it is essential to have a correct definition of polarization textures.